Physics Midterm Review E Ms. Sherwood

Teacher Answer Key January 13, 2017

4 1. Which object has the greatest inertia?

1. a 0.010-kg bullet traveling at 90. m/s 3. a 490-kg elephant walking with a speed of 1.0 m/s

2. a 30.-kg child traveling at 10. m/s on her bike 4. a 1500-kg car at rest in a parking lot4 Inertia is determined solely by an object's mass. The 1500-kilogram car has the greatest inertia.1 2. An 8.0-newton wooden block slides across a horizontal wooden floor at constant velocity. What is the magnitude of the force of kinetic friction between the block and the floor?1. 2.4 N 3. 8.0 N2. 3.4 N 4. 27 N1 In order to calculate the force of kinetic friction between the wooden block and the wood floor, we must know the coefficient of kinetic friction and the normal force on the block. According to Reference Table C, the coefficient of kinetic friction between wood and wood is 0.30. Since the wood is on a horizontal surface, its weight (8.0 newtons) is equal to the normal force on the block. Use Equation ME9 on Reference Table K: (see image)4 3. A ball is thrown with an initial speed of 10. meters per second. At what angle above the horizontal should the ball be thrown to reach the greatest height?1. 0o 3. 45o

2. 30.o 4. 90.o

4 The vertical component of the ball's velocity determines the time that the ball will remain in the air and, therefore, the height to which it will rise. The vertical component is greatest when the angle with the horizontal is 90o.

Wrong Choice Explained:(3) If thrown at 45o, the ball will travel the greatest horizontal distance.3 4. Which situation represents a person in equilibrium?1. a child gaining speed while sliding down a slide 3. a man standing still on a bathroom scale

2. a woman accelerating upward in an elevator 4. a teenager driving around a corner in his car3 An object in equilibrium has no net force acting on it. Therefore, according to Newton¿s second law, the object must either be at rest or be traveling at constant speed in a straight line. Of the choices given, only choice(3), a man standing still on a bathroom scale, meets these criteria.3 5. A rock is thrown straight up into the air. At the highest point of the rock's path, the magnitude of the net force acting on the rock is1. less than the magnitude of the rock's weight, 3. the same as the magnitude of the rock's weight

but greater than zero2. greater than the magnitude of the rock's weight 4. zero3 At its highest point, the rock is at rest. The net force acting on it is the gravitational force, which is the same as the object¿s weight.1 6. The accompanying diagram shows a compressed spring between two carts initially at rest on a horizontal, frictionless surface. Cart A has a mass of 2 kilograms and cart B has a mass of 1 kilogram. A string holds the carts together.

The string is cut and the carts move apart. Compared to the magnitude of the force the spring exerts on cart A, the magnitude of the force the spring exerts on cart B is

1. the same 3. twice as great2. half as great 4. four times as great1 The spring is the means by which cart A interacts with cart B. Therefore, according to Newton's third law, the force exerted by the spring on cart A must be equal in magnitude (and opposite in direction) to the force exerted by the spring on cart B.2 7. An 8.0-newton block is accelerating down a frictionless ramp inclined at 15o to the horizontal, as shown in the accompanying diagram.

What is the magnitude of the net force causing the block's acceleration?

1. 0 N 3. 7.7 N2. 2.1 N 4. 8.0 N2 The force acting on the block parallel to the ramp (F||) is the component of the block's weight parallel to the incline of the ramp. This component is equal to the product of the block's weight (mg) and the sine of the angle of the ramp (sin ø). Use the following equation:(see image)2 8. At a certain location, a gravitational force with a magnitude of 350 newtons acts on a 70.-kilogram astronaut. What is the magnitude of the gravitational field strength at this location?

2 Use Equation ME11 on Reference Table K:(see image)2 9. The approximate length of an unsharpened No. 2 pencil is

1. 2.0 X 10-2 m 3. 2.0 X 100 m2. 2.0 X 10-1 m 4. 2.0 X 101 m2 An unsharpened pencil is about 10 inches long. Since 1 inch is approximately equal to 2 centimeters, the length of the pencil is approximately 20 centimeters or 2 x 10-1 meter.

Wrong Choices Explained:(1) 2 x 10-2 meter is approximately equal to 1 inch.(3) 2 meters is approximately equal to 80 inches.(4) 20 meters is approximately equal to 60 feet.1 10. The accompanying diagram shows an 8.0-kilogram cart moving to the right at 4.0 meters per second about to make a head-on collision with a 4.0-kilogram cart moving to the left at 6.0 meters per second.

After the collision, the 4.0-kilogram cart moves to the right at 3.0 meters per second. What is the velocity of the 8.0-kilogram cart after the collision?

1. 0.50 m/s left 3. 5.5 m/s left2. 0.50 m/s right 4. 5.5 m/s right1 This question involves the conservation of (linear) momentum. Use Equations ME12 and ME13 on Reference Table K:

(see image)This means the 8.0-kilogram cart is moving to the left at 0.50 meter per second.4 11. Four forces act concurrently on a block on a horizontal surface as shown in the accompanying diagram.

As a result of these forces, the block

1. moves at constant speed to the right 3. accelerates to the right2. moves at constant speed to the left 4. accelerates to the left4 We need only consider the forces in the x-direction since the vertical forces add to 0 newton. The two horizontal forces produce a net force of 20. newtons to the left. Therefore, the block will accelerate to the left.

1 12. Base your answer on the accompanying information.

In a drill during basketball practice, a player runs the length of the 30.-meter court and back. The player does this three times in 60. seconds.

The magnitude of the player's total displacement after running the drill is

1. 0.0 m 3. 60. m2. 30. m 4. 180 m1 Displacement is the net change of position of an object. Since the player returns to the starting point, the player's displacement is 0.0 meter.

Wrong Choice Explained:(4) You calculated the total distance rather than the displacement.3 13. Base your answer on the accompanying information.

In a drill during basketball practice, a player runs the length of the 30.-meter court and back. The player does this three times in 60. seconds.

The average speed of the player during the drill is

1. 0.0 m/s 3. 3.0 m/s2. 0.50 m/s 4. 30. m/s3 The player runs a total distance of 180 meters in 60. seconds. Use Equation ME1 on Reference Table K:(see image)3 14. A baseball is thrown at an angle of 40.0o above the horizontal. The horizontal component of the baseball's initial velocity is 12.0 meters per second. What is the magnitude of the ball's initial velocity?1. 7.71 m/s 3. 15.7 m/s

2. 9.20 m/s 4. 18.7 m/s3 Velocity is a vector quantity and can be separated into horizontal and vertical components. Use Equation ME7 on Reference Table K:(see image)1 15. Which object has the greatest inertia?1. a 15-kg mass traveling at 5.0 m/s 3. a 10.-kg mass traveling at 5.0 m/s2. a 10.-kg mass traveling at 10. m/s 4. a 5.0-kg mass traveling at 15 m/s1 Inertia is the property of matter that resists changes in motion. The measure of an object's inertia is its mass, not its speed. Choice (1) has the largest mass (15 kilograms) and, therefore, the greatest inertia.2 16. A space probe is launched into space from Earth's surface. Which graph represents the relationship between the magnitude of the gravitational force exerted on Earth by the space probe and the distance between the space probe and the center of Earth?

2 See Equation ME10 on Reference Table K. Gravitational force follows an inverse square law. As the distance between two masses increases, the gravitational force between them decreases. In addition, neither the force nor the distance can be reduced to zero. Of the choices given, only the graph in choice (2) meets both of these criteria.4 17. A car, initially traveling east with a speed of 5.0 meters per second, is accelerated uniformly at 2.0 meters per second2 east for 10. seconds along a straight line. During this 10.-second interval the car travels a total distance of1. 50. m 3. 1.0 X 102 m2. 60. m 4. 1.5 X 102 m4 Use Equation ME4 on Reference Table K:(see image)4 18. Which situation describes an object that has no unbalanced force acting on it?1. an apple in free fall 3. a hockey puck moving at constant velocity

across ice

2. a satellite orbiting Earth 4. a laboratory cart moving down a frictionless 30.o incline

3 An object that has no unbalanced force acting on it will have no acceleration. Of the choices given, only choice (3), the moving hockey puck, has no acceleration.

Wrong Choices Explained:(1) This object has an acceleration equal to g. The unbalanced force on it is equal to the object's weight.(2) This object has a centripetal acceleration. Therefore, an unbalanced centripetal force acts on it. The centripetal force is equal to the gravitational force on the object.(4) This object has an acceleration equal to g/2(g • sin 30o). The unbalanced force is equal to one-half the object's weight.3 19. A child riding a bicycle at 15 meters per second accelerates at −3.0 meters per second2 for 4.0 seconds. What is the child's speed at the end of this 4.0-second interval?1. 12 m/s 3. 3.0 m/s2. 27 m/s 4. 7.0 m/s3 Use Equation ME3 on Reference Table K:(see image)4 20. An unbalanced force of 40. newtons keeps a 5.0-kilogram object traveling in a circle of radius 2.0 meters. What is the speed of the object?1. 8.0 m/s 3. 16 m/s2. 2.0 m/s 4. 4.0 m/s4 The unbalanced force in this question is the centripetal force on the object. Use Equations ME17 and ME18 on Reference Table K:(see image)2 21. A 5.00-kilogram block slides along a horizontal, frictionless surface at 10.0 meters per second for 4.00 seconds. The magnitude of the block's momentum is

2 The momentum of an object is the product of the object's mass and its velocity. Use Equation ME12 on Reference Table K:(see image)1 22. A 0.50-kilogram puck sliding on a horizontal shuffleboard court is slowed to rest by a frictional force of 1.2 newtons. What is the coefficient of kinetic friction between the puck and the surface of the shuffleboard court?1. 0.24 3. 0.602. 0.42 4. 4.11 The coefficient of kinetic friction determines the amount of frictional force that exists on an object

when it slides over a surface. Since the surface is horizontal, the normal force on the object (FN) is equal to its weight. Use Reference Table A and Equations ME8 and ME9 on Reference Table K:(see image)1 23. A number of 1.0-newton horizontal forces are exerted on a block on a frictionless, horizontal surface. Which top-view diagram shows the forces producing the greatest magnitude of acceleration of the block?

1 The block with the largest net force will have the greatest acceleration. In choices (2) and (4), the net force is zero. Therefore, the acceleration will be zero. In choice (3), the vertical forces cancel each other since they are in the opposite direction. The net force in this case is 1.0 newton to the right. In choice (1), the two 1.0-newton forces do not cancel. They add to produce a net force of 1.4 newtons that is directed at 45o to the horizontal force. Therefore, the block in choice (1) will have the greatest acceleration.(see image)4 24. A rock is dropped from a bridge. What happens to the magnitude of the acceleration and the speed of the rock as it falls? [Neglect friction.]1. Both acceleration and speed increase. 3. Acceleration increases and speed decreases.

2. Both acceleration and speed remain the same. 4. Acceleration remains the same and speed increases.

4 As the rock drops, its speed increases. However, the acceleration due to gravity remains the same.3 25. A soccer ball kicked on a level field has an initial vertical velocity component of 15.0 meters per second. Assuming the ball lands at the same height from which it was kicked, what is the total time the ball is in the air? [Neglect friction.]1. 0.654 s 3. 3.06 s2. 1.53 s 4. 6.12 s3 At the highest point in the soccer ball's flight, the vertical component of the ball's velocity is 0 meter per second. Use Reference Table A and Equation ME3 on Reference Table K to find the time

for the ball to reach the highest point:(see image)Since the time of the downward trip equals the time of the upward trip, the total time that the ball is in flight equals 2 × 1.53 s or 3.06 s.1 26. An object accelerates uniformly from 3.0 meters per second east to 8.0 meters per second east in 2.0 seconds. What is the magnitude of the acceleration of the object?1. 2.5 m/s2 3. 5.5 m/s2

2. 5.0 m/s2 4. 11 m/s2

1 Use Equation ME2 on Reference Table K:(see image)1 27. A student is standing in an elevator that is accelerating downward. The force that the student exerts on the floor of the elevator must be1. less than the weight of the student when at rest 3. less than the force of the floor on the student2. greater than the weight of the student when at rest

4. greater than the force of the floor on the student

1 When the elevator is at rest, the force that the student exerts on the elevator floor equals the student's weight. As the elevator accelerates downward, the floor of the elevator "falls away" from the student. Therefore, the force exerted by the student on the floor is less than the student's weight.1 28. The magnitude of the centripetal force acting on an object traveling in a horizontal, circular path will decrease if the1. radius of the path is increased 3. direction of motion of the object is reversed2. mass of the object is increased 4. speed of the object is increased1 Combine Equations ME17 and ME18 on Reference Table K to obtain:Solution: Fc = mv2 ÷ rThe centripetal force on the object will decrease if its mass is decreased, its velocity is decreased, or its radius is increased.4 29. The centripetal force acting on the space shuttle as it orbits Earth is equal to the shuttle's1. inertia 3. velocity2. momentum 4. weight4 As a space shuttle orbits Earth, the gravitational force on the shuttle (i.e., its weight) provides the centripetal force needed to maintain its orbit.2 30. Four identical projectiles are launched with the same initial speed, v, but at various angles above the level ground. Which diagram represents the initial velocity of the projectile that will have the largest total horizontal displacement? [Neglect air resistance.]

2 A projectile that is launched at an angle will attain a maximum horizontal displacement if its launch angle is 45o.4 31. Two forces act concurrently on an object on a horizontal, frictionless surface, as shown in the accompanying diagram.

What additional force, when applied to the object, will establish equilibrium?

1. 16 N toward the right 3. 4 N toward the right2. 16 N toward the left 4. 4 N toward the left4 When an object is in equilibrium, the vector sum of the forces on the object must be 0 N. In order to establish equilibrium, an additional force of 4 N toward the left must be applied to the object.2 32. As shown in the accompanying diagram, an open box and its contents have a combined mass of 5.0 kilograms. A horizontal force of 15 newtons is required to push the box at a constant speed of 1.5 meters per second across a level surface.

The inertia of the box and its contents increases if there is an increase in the

1. speed of the box 3. magnitude of the horizontal force applied to the box

2. mass of the contents of the box 4. coefficient of kinetic friction between the box and the level surface

2 Inertia is the property of matter that resists changes in an object's motion. The inertia of an object

depends solely on the mass of the object.1 33. The accompanying graph shows the relationship between the speed and elapsed time for an object falling freely from rest near the surface of a planet.

What is the total distance the object falls during the first 3.0 seconds?

1. 12 m 3. 44 m2. 24 m 4. 72 m1 In order to find the total distance traveled by the object, calculate the area of the right triangle under the graph. The triangle has a height of 8.0 meters per second and a base of 3.0 seconds. Use Equation GT2 on Reference Table K:(see image)

Wrong Choice Explained:(2) You probably forgot to multiply the product by ½.3 34. A 75-kilogram hockey player is skating across the ice at a speed of 6.0 meters per second. What is the magnitude of the average force required to stop the player in 0.65 second?1. 120 N 3. 690 N2. 290 N 4. 920 N3 Use Equations ME14 and ME12 on Reference Table K:(see image)NOTE: The negative sign means that the force acts in a direction opposite to the player's motion. The magnitude of this force is 690 N.3 35. A child pulls a wagon at a constant velocity along a level sidewalk. The child does this by applying a 22-newton force to the wagon handle, which is inclined at 35o to the accompanying sidewalk as shown.

What is the magnitude of the force of friction on the wagon?

1. 11 N 3. 18 N2. 13 N 4. 22 N3 The horizontal component of the child's force is equal and opposite to the force of friction on the sled. Use Equation ME7 on Reference Table K:(see image)3 36. The accompanying diagram represents a mass, m, being swung clockwise at constant speed in a horizontal circle.

At the instant shown, the centripetal force acting on mass m is directed toward point

1. A 3. C2. B 4. D3 The centripetal force on any object traveling in a circular path is directed toward the center of the circle. In this case, the force is directed toward point C.

Wrong Choice Explained:(4) Point D represents the direction of the velocity of the mass when it is at the position shown in the diagram.2 37. A 3.1-kilogram gun initially at rest is free to move. When a 0.015-kilogram bullet leaves the gun with a speed of 500. meters per second, what is the speed of the gun?1. 0.0 m/s 3. 7.5 m/s2. 2.4 m/s 4. 500. m/s2 The initial momentum of the gun-bullet system (0 kilogram•meter/second) must equal the final momentum of the gun-bullet system. Use Equations ME12 and ME13 on Reference Table K: (see image)

The speed of the gun is the magnitude of its velocity, or 2.4 m/s.4 38. Four projectiles, A, B, C, and D, were launched from, and returned to, level ground. The accompanying data table shows the initial horizontal speed, initial vertical speed, and time of flight for each projectile.

Which projectile traveled the greatest horizontal distance? [Neglect friction.]

1. A 3. C2. B 4. D4 The horizontal distance traveled by a projectile depends on the magnitude of its initial horizontal speed and the time that it is in flight. Since the horizontal speed does not change during the flight, the horizontal distance can be calculated from the following equation:

dx = vixt

Of the choices given, choice (4), vix = 80.8 m/s; t = 4.00 s, yields the greatest horizontal distance of 320. meters.

Wrong Choices Explained:(1), (2) The calculated horizontal distance for each choice is 240. meters. (3) The calculated horizontal distance is 250. meters.4 39. A student throws a baseball vertically upward and then catches it. If vertically upward is considered to be the positive direction, which graph best represents the relationship between velocity and time for the baseball? [Neglect friction.]

4 As the baseball rises, its positive velocity decreases until it comes to rest. The baseball then begins

to descend with an increasing negative velocity. Throughout the trip, the ball has a constant negative gravitational acceleration. Therefore, a graph of velocity versus time would yield a continuous straight-line graph that has a negative slope, as shown in choice (4).3 40. A 5.0-kilogram sphere, starting from rest, falls freely 22 meters in 3.0 seconds near the surface of a planet. Compared to the acceleration due to gravity near Earth's surface, the acceleration due to gravity near the surface of the planet is approximately1. the same 3. one-half as great2. twice as great 4. four times as great3 Use Equation ME4 on Reference Table K to calculate the gravitational acceleration near the planet's surface, setting the initial speed of the sphere equal to 0 meter per second. (see image)

The gravitational acceleration near the surface of the planet is approximately one-half the gravitational acceleration near Earth's surface, which is 9.81 m/s2 as shown on Reference Table A.1 41. Scalar is to vector as1. speed is to velocity 3. displacement is to velocity2. displacement is to distance 4. speed is to distance1 This question asks you to choose a pair of quantities, the first being a scalar and the second being a vector. Speed is a scalar quantity, and velocity is a vector quantity.

Wrong Choices Explained:(2) Displacement is a vector, and distance is a scalar.(3) Displacement and velocity are both vectors.(4) Speed and distance are both scalars.2 42. If a car accelerates uniformly from rest to 15 meters per second over a distance of 100. meters, the magnitude of the car's acceleration is1. 0.15 m/s2 3. 2.3 m/s2

2. 1.1 m/s2 4. 6.7 m/s2

2 The acceleration of the car is found by using Equation ME5 on Reference Table K:(see image)4 43. Which body is in equilibrium?1. a satellite moving around Earth in a circular orbit

3. an apple falling freely toward the surface of Earth

2. a cart rolling down a frictionless incline 4. a block sliding at constant velocity across a tabletop

4 When a body is in equilibrium, the vector sum of all the forces acting on it must equal 0. As a result, the body's acceleration must also equal 0. So a body in equilibrium must be either at rest or moving at constant velocity.4 44. A 0.149-kilogram baseball, initially moving at 15 meters per second, is brought to rest in 0.040

second by a baseball glove on a catcher's hand. The magnitude of the average force exerted on the ball by the glove is1. 2.2 N 3. 17 N2. 2.9 N 4. 56 N4 The impulse delivered by the glove changes the momentum of the baseball. Use Equations ME12 and ME14 on Reference Table K: (see image)

The negative sign associated with the force indicates that it is acting opposite to the direction of the baseball's momentum.1 45. As shown in the accompanying diagram, a student standing on the roof of a 50.0-meter-high building kicks a stone at a horizontal speed of 4.00 meters per second. How much time is required for the stone to reach the level ground below? [Neglect friction.]1. 3.19 s 3. 10.2 s2. 5.10 s 4. 12.5 s1 The time needed for the stone to reach the ground depends on only the vertical component of the stone's motion. Its initial vertical velocity is 0.0 meter/second. It accelerates toward the ground at 9.81 meters/second2 (g), as shown on Reference Table A. Use Equation ME4 on Reference Table K: (see image)2 46. On the surface of Earth, a spacecraft has a mass of 2.00 X 104 kilograms. What is the mass of the spacecraft at a distance of one Earth radius above Earth's surface?1. 5.00 X 103 kg 3. 4.90 X 104 kg2. 2.00 X 104 kg 4. 1.96 X 105 kg2 This is a bit of a trick question. The mass of the spacecraft remains constant, whether on Earth or in space. It is the gravitational force on the spacecraft that decreases as the craft moves farther from the Earth.1 47. A student pulls a 60.-newton sled with a force having a magnitude of 20. newtons. What is the magnitude of the force that the sled exerts on the student?1. 20. N 3. 60. N2. 40. N 4. 80. N1 Newton's third law states that if object A exerts a force on object B, then object B will exert an equal and opposite force on object A. Since the student pulls on the sled with a force of 20.0 newtons, the sled pulls back on the student with a force of 20.0 newtons. The weight of the sled (60.0 newtons) is irrelevant to this problem.4 48. The accompanying data table lists the mass and speed of four different objects.

Which object has the greatest inertia?

1. A 3. C2. B 4. D4 The inertia of the cart is measured by its mass, not by its speed. Object D has the greatest mass and, therefore, the greatest inertia.4 49. The accompanying diagram shows a horizontal 12-newton force being applied to two blocks, A and B, initially at rest on a horizontal, frictionless surface. Block A has a mass of 1.0 kilogram and block B has a mass of 2.0 kilograms.

The magnitude of the acceleration of block B is

1. 6.0 m/s2 3. 3.0 m/s2

2. 2.0 m/s2 4. 4.0 m/s2

4 The 12-newton force is being used to accelerate both blocks, which have a total mass of 3.0 kilograms. Use Equation ME8 on Reference Table K: (see image)3 50. A ball is thrown vertically upward with an initial velocity of 29.4 meters per second. What is the maximum height reached by the ball? [Neglect friction.]1. 14.7 m 3. 44.1 m2. 29.4 m 4. 88.1 m3 Use Reference Table A and Equation ME5 on Reference Table K. At its highest point, the velocity of the object is 0 meter/second. Since the direction of the gravitational acceleration is opposite to the direction of the object's motion, it must be entered as a negative number: (see image)4 51. Which two quantities can be expressed using the same units?1. energy and force 3. momentum and energy2. impulse and force 4. impulse and momentum4 Refer to Equation ME14 on Reference Table K. Since impulse equals the change in momentum, both quantities must be measured in equivalent units. In other words, a kilogram meter/second must be equal to a newton • second. (Recall that a newton equals a kilogram • meter/second2, and the product of a newton and a second equals a kilogram • meter/second.)

Wrong Choices Explained:(1), (2), (3) Energy is measured in joules (kilogram • meter2/second2), while force is measured in newtons (kilogram • meter/second2).1 52. A volleyball hit into the air has an initial speed of 10. meters per second. Which vector best represents the angle above the horizontal that the ball should be hit to remain in the air for the greatest amount of time?

1 The phrase "remain[s] in the air for the greatest amount of time" means that the volleyball must have risen to the greatest height--a quantity that depends on the initial speed of the ball in the vertical direction. This speed can be calculated from Equation ME6 on Reference Table K:

Since the sine of an angle has its maximum value at 90o, the volleyball will remain in the air the longest when it is projected at this angle.1 53. Which is not a vector quantity?1. electric charge 3. velocity2. magnetic field strength 4. displacement1 A vector quantity must have both magnitude and direction. Of the choices given, only choice (1), electric charge, does not have both properties. It has magnitude only.1 54. An astronaut standing on a platform on the Moon drops a hammer. If the hammer falls 6.0 meters vertically in 2.7 seconds, what is its acceleration?1. 1.6 m/s2 3. 4.4 m/s2 2. 2.2 m/s2 4. 9.8 m/s2

1 The initial speed of the hammer is 0 m/s. The time it falls is 2.7 s. The distance traveled by the hammer is 6.0 m. Use Equation ME4 on Reference Table K:2 55. A 2.00-kilogram object weighs 19.6 newtons on Earth. If the acceleration due to gravity on Mars is 3.71 meters per second2, what is the object's mass on Mars?1. 2.64 kg 3. 19.6 N2. 2.00 kg 4. 7.42 N2 The mass of an object is constant. Mass does not depend on the gravitational acceleration.4 56. A car moves with a constant speed in a clockwise direction around a circular path of radius r, as represented in the accompanying diagram.

When the car is in the position shown, its acceleration is directed toward the

1. north 3. south2. west 4. east4 When an object travels in a circular path at constant speed, the acceleration always points toward the center of the circle. In this case, the direction of the acceleration is east.2 57. As the angle between two concurrent forces decreases, the magnitude of the force required to produce equilibrium1. decreases 3. remains the same2. increases2 When the angle between two concurrent forces is 180o, the forces act in opposite directions and the resultant has its minimum value. When the angle between the forces is 0o, the forces point in exactly the same direction and the resultant has its maximum value. As the angle between the two forces decreases, the forces point more nearly in the same direction and the magnitude of their resultant increases.2 58. A child walks 5.0 meters north, then 4.0 meters east, and finally 2.0 meters south. What is the magnitude of the resultant displacement of the child after the entire walk?1. 1.0 m 3. 3.0 m2. 5.0 m 4. 11.0 m2 Refer to the accompanying diagram:

When the student walks 5.0 meters north and then 2.0 meters south, the student has a net

displacement of 3.0 meters north. When this displacement is added to 4.0 meters east, the magnitude of the resultant displacement is 5.0 meters.2 59. The accompanying diagram represents a spring hanging vertically that stretches 0.075 meter when a 5.0-newton block is attached. The spring-block system is at rest in the position shown.

The value of the spring constant is

1. 38 N/m 3. 130 N/m2. 67 N/m 4. 650 N/m2 Use Equation ME15 on Reference Table K:1 60. A distance of 1.0 meter separates the centers of two small charged spheres. The spheres exert gravitational force Fg and electrostatic force Fe on each other. If the distance between the spheres' centers is increased to 3.0 meters, the gravitational force and electrostatic force, respectively, may be represented as

1 The equations for gravitational and electrostatic forces obey inverse square laws. (See Equations ME10 and EL1 on Reference Table K.) A change in the distance (r) between the centers of the two spheres causes each of the forces to change by a factor of 1/r 2 . Therefore, increasing the distance from 1.0 meter to 3.0 meters will decrease each force to 1/9 of its original value.

Wrong Choices Explained:(2) You used the factor 1/r rather than 1/r 2 .(4) You used the factor r 2 rather than 1/r 2 .4 61. What is the weight of a 2.00-kilogram object on the surface of Earth?1. 4.91 N 3. 9.81 N2. 2.00 N 4. 19.6 N4 The weight of an object is the gravitational force acting on it. Use Reference Table A and Equation ME11 on Reference Table K, solving for Fg: (see image)

4 62. When Earth and Moon are separated by a distance of 3.84 x 108 meters, the magnitude of the gravitational force of attraction between them is 2.0 x 1020 newtons. What would be the magnitude of this gravitational force of attraction if Earth and the Moon were separated by a distance of 1.92 x 108 meters?1. 5.0 x 1019 N 3. 4.0 x 1020 N2. 2.0 x 1020 N 4. 8.0 x 1020 N4 The gravitational force of attraction obeys an inverse square law. (See Equation ME10 and EL1 on Reference Table K.) A change in the distance (r) between Earth and the Moon causes the gravitational force to change by a factor of 1/r 2. Since the distance between the Earth and the Moon has been halved, the gravitational force between these bodies will increase by a factor of 1/r 2, which is 1/(1/2)2 or 4. The new gravitational force will be 8.0 x 1020 newtons.1 63. Base your answer on the accompanying graph, which represents the motion of a car during a 6.0-second time interval.

What is the acceleration of the car at t = 5.0 seconds?

1. 0.0 m/s2 3. 2.5 m/s2

2. 2.0 m/s2 4. 10. m/s2

1 Refer to the graph for this question. At t = 5.0 seconds, the car is moving at a constant velocity of 10.0 meters per second. Its acceleration is 0.0 meter per second per second (m/s2).3 64. Base your answer on the accompanying graph, which represents the motion of a car during a 6.0-second time interval.

What is the total distance traveled by the car during this 6.0-second interval?

1. 10. m 3. 40. m2. 20. m 4. 60. m3 The distance covered during the 6.0-second interval is equal to the total area under the graph. Between t = 0.0 second and t = 4.0 seconds, the area is that of a right triangle. Use Equation GT2 on Reference Table K: (see image A)

Between t = 4.0 seconds and 6.0 seconds, the area is that of a rectangle. Use Equation GT1 on Reference Table K: (see image B)

Add the area of the right triangle and the area of the rectangle to find the total area under the graph:

Solution: 20. m + 20. m = 40. m

The total area under the graph is 40. m.2 65. A person weighing 785 newtons on the surface of Earth would weigh 298 newtons on the surface of Mars. What is the magnitude of the gravitational field strength on the surface of Mars?1. 2.63 N/kg 3. 6.09 N/kg2. 3.72 N/kg 4. 9.81 N/kg2 Use Reference Table A. On the surface of Earth, the gravitational field strength is 9.81 N/kg (the same numerical value as the acceleration due to gravity). Since the person's mass on Mars and Earth are the same, we can use Equation ME11 on Reference Table K to set up a proportion using the Mars and Earth data: (see image)4 66. A motorcycle being driven on a dirt path hits a rock. Its 60.-kilogram cyclist is projected over the handlebars at 20. meters per second into a haystack. If the cyclist is brought to rest in 0.50 second, the magnitude of the average force exerted on the cyclist by the haystack is1. 6.0 x 101 N 3. 1.2 x 103 N2. 5.9 x 102 N 4. 2.4 x 103 N4 The magnitude of the impulse delivered to the cyclist is equal to the magnitude of the change in the cyclist's momentum. Use Equations ME12 and ME14 on Reference Table K: (see image)2

67. A baseball player runs 27.4 meters from the batter's box to first base, overruns first base by 3.0 meters, and then returns to first base. Compared to the total distance traveled by the player, the magnitude of the player's total displacement from the batter's box is 1. 3.0 m shorter 3. 3.0 m longer2. 6.0 m shorter 4. 6.0 m longer2 The total distance traveled by the player is 33.4 meters (27.4 m + 3.0 m + 3.0 m). The displacement of the player is the net change of the player's position. Since the player starts at home plate and ends at first base, the player's displacement is 27.4 meters. Therefore, the displacement is 6.0 meters shorter than the distance.3 68. A motorboat, which has a speed of 5.0 meters per second in still water, is headed east as it crosses a river flowing south at 3.3 meters per second. What is the magnitude of the boat's resultant velocity with respect to the starting point?1. 3.3 m/s 3. 6.0 m/s2. 5.0 m/s 4. 8.3 m/s3 The vector diagram for this situation is shown: (see image)

The resultant velocity of the boat is the hypotenuse of the vector triangle. Use the Pythagorean theorem, which is Equation GT4A on Reference Table K: (see image)3 69. A car traveling on a straight road at 15.0 meters per second accelerates uniformly to a speed of 21.0 meters per second in 12.0 seconds. The total distance traveled by the car in this 12.0-second time interval is1. 36.0 m 3. 216 m2. 180. m 4. 252 m3 The acceleration of the car is found by using Equation ME2 on Reference Table K: (see image)

Calculate the distance traveled by using Equation ME4 on Reference Table K: (see image)4 70. A golf ball is propelled with an initial velocity of 60. meters per second at 37o above the horizontal. The horizontal component of the golf ball's initial velocity is1. 30. m/s 3. 40. m/s2. 36 m/s 4. 48 m/s4 Use Equation ME7 on Reference Table K:1 71. The accompanying diagram represents a force vector, A, and a resultant vector, R.

Which force vector B could be added to force vector A to produce resultant vector R ?

1 Note that the resultant vector R is significantly larger than the vector A. The addition of vectors takes place in a head-to-tail fashion as shown in the accompanying diagram:

Wrong Choices Explained:(2) Refer to the diagram (2): Note that the resultant vector is shorter and points in the wrong direction.(3) Refer to the diagram (3): Note that the resultant vector points in approximately the right direction, but it is shorter than the resultant shown in the question.(4) Refer to the diagram (4): Note that the resultant has the correct length, but it points in the wrong direction.4 72. Which object has the greatest inertia?1. a 1.0-kilogram object moving at 15 meters per second

3. a 10.-kilogram object moving at 2.0 meters per second

2. a 5.0-kilogram object at rest 4. a 15-kilogram object at rest4 Inertia is a property of matter that is measured solely by its mass: the greater the mass, the greater the inertia.3 73. A 3-newton force and a 4-newton force are acting concurrently on a point. Which force could not produce equilibrium with these two forces?1. 1 N 3. 9 N2. 7 N 4. 4 N3 The addition of two concurrent forces can produce a minimum resultant equal to the difference of the magnitudes of the two forces and a maximum resultant equal to the sum of the magnitudes of the two forces. In this question, the minimum resultant equals 1 N (4 N -- 3 N) and the maximum resultant equals 7 N (3 N + 4 N). Producing a resultant less than 1 newton or more than 7 newtons is not possible.1 74. Base your answer on the information below and the accompanying diagram.

The diagram shows the top view of a 65-kilogram student at point A on an amusement park ride.

The ride spins the student in a horizontal circle of radius 2.5 meters, at a constant speed of 8.6 meters per second. The floor is lowered and the student remains against the wall without falling to the floor.

Which vector best represents the direction of the centripetal acceleration of the student at point A?

1 Centripetal acceleration is always directed toward the center of the circle. Of the choices given, only choice (1) points from the student at A toward the center of the circle.2 75. Base your answer on the information below and the accompanying diagram.

The diagram shows the top view of a 65-kilogram student at point A on an amusement park ride. The ride spins the student in a horizontal circle of radius 2.5 meters, at a constant speed of 8.6 meters per second. The floor is lowered and the student remains against the wall without falling to the floor.

The magnitude of the centripetal force acting on the student at point A is approximately

1. 1.2 x 104 N 3. 2.2 x 102 N2. 1.9 x 103 N 4. 3.0 x 101 N2 Use the information given and Equations ME17M and ME18 on Reference Table K:3 76. A 60-kilogram student jumps down from a laboratory counter. At the instant he lands on the floor his speed is 3 meters per second. If the student stops in 0.2 second, what is the average force of the floor on the student?1. 1 × 10-2 N 3. 9 × 102 N2. 1 × 102 N 4. 4 N3 The initial speed of the student at the instant he lands on the floor is 3 m/s. His final speed is 0 m/s. Use Equations ME12 and ME14 on Reference Table K:

The negative sign means that the force is acting in a direction opposite to the motion of the student.4 77. Which diagram best represents the gravitational field lines surrounding Earth?

4 The direction of the gravitational field is a collection of arrows that point in the direction of motion of a small test mass, that is, toward the center of Earth. Of the choices given, only choice (4) shows arrows that all point toward the center of Earth.1 78. A 2.0-kilogram object is falling freely near Earth's surface. What is the magnitude of the gravitational force that Earth exerts on the object?1. 20. N 3. 0.20 N2. 2.0 N 4. 0.0 N1 Use Reference Table A and Equation ME11 on Reference Table K:

4 79. A force of 6.0 newtons changes the momentum of a moving object by 3.0 kilogram • meters per second. How long did the force act on the mass?1. 1.0 s 3. 0.25 s2. 2.0 s 4. 0.50 s4 Refer to Equation ME14 on Reference Table K:1 80. The accompanying graph represents the relationship between the force applied to a spring and spring elongation for four different springs.

Which spring has the greatest spring constant?

1. A 3. C2. B 4. D1 Refer to Equation ME15 on Reference Table K:

Since the spring constant (k) is the ratio of the applied force to the elongation of the spring, the constant is calculated from the slope of a graph of force versus elongation. Since line A has the greatest slope, it has the greatest spring constant.1 81. A 3.0-kilogram steel block is at rest on a frictionless horizontal surface. A 1.0 kilogram lump of clay is propelled horizontally at 6.0 meters per second toward the block as shown in the accompanying diagram.

Upon collision, the clay and steel block stick together and move to the right with a speed of

1. 1.5 m/s 3. 3.0 m/s

2. 2.0 m/s 4. 6.0 m/s1 Use Equations ME12 and ME13 on Reference Table K:3 82. On a highway, a car is driven 80. kilometers during the first 1.00 hour of travel, 50. kilometers during the next 0.50 hour, and 40. kilometers in the final 0.50 hour. What is the car's average speed for the entire trip?1. 45 km/h 3. 85 km/h2. 60. km/h 4. 170 km/h3 The car drives a total of 170 kilometers in 2.0 hours. Use Equation ME1 on Reference Table K: (see image)4 83. The accompanying vector diagram represents the horizontal component, FH, and the vertical component, FV, of a 24-newton force acting at 35o above the horizontal. What are the magnitudes of the horizontal and vertical components?

1. FH = 3.5 N and FV = 4.9 N 3. FH = 14 N and FV = 20. N2. FH = 4.9 N and FV = 3.5 N 4. FH = 20. N and FV = 14 N4 Use Equations ME6 and ME7 on Reference Table K to resolve the force into its horizontal (x) and vertical (y) components: (see image)4 84. The accompanying diagram represents two masses before and after they collide. Before the collision, mass mA is moving to the right with speed v, and mass mB is at rest. Upon collision, the two masses stick together.

Which expression represents the speed, v 1, of the masses after the collision? [Assume no outside forces are acting on mA or mB.]

4 The law of conservation of momentum states that the total momentum of two objects before a collision must be equal to the total momentum after the collision. Since the objects stick together, both objects must have the same final speed. Apply Equations ME12 and ME13 on Reference Table K:

1 85. Which quantity is a vector?1. impulse 3. speed2. power 4. time1 Vector quantities have both magnitude and direction. Of the choices given, only choice (1), impulse, has magnitude and direction.

Wrong Choices Explained:(2), (3), (4) Power, speed, and time are described only by their magnitudes; they are scalar quantities.4 86. A high-speed train in Japan travels a distance of 300. kilometers in 3.60 x 103 seconds. What is the average speed of this train?1. 1.20 x 10-2 m/s 3. 12.0 m/s2. 8.33 x 10-2 m/s 4. 83.3 m/s4 The average speed of an object is equal to the total distance it travels divided by the elapsed time. Use Equation ME1 on Reference Table K: (see image)3 87. A 25-newton weight falls freely from rest from the roof of a building. What is the total distance the weight falls in the first 1.0 second?1. 19.6 m 3. 4.9 m2. 9.8 m 4. 2.5 m3 The initial speed of the weight is 0.0 meter per second, its time of fall is 1.0 second, and the gravitational acceleration (from Reference Table A) is 9.8 meters per second squared (m/s2). Use Equation ME4 on Reference Table K: (see image)2

88. A golf ball is given an initial speed of 20. meters per second and returns to level ground. Which launch angle above level ground results in the ball traveling the greatest horizontal distance? [Neglect friction.]1. 60.o 3. 30.o

2. 45o 4. 15o

2 Neglecting friction, a launch angle of 45o above the level ground results in the greatest horizontal distance for the golf ball.2 89. Base your answer on the information below.

A go-cart travels around a flat, horizontal, circular track with a radius of 25 meters. The mass of the go-cart with the rider is 200. kilograms. The magnitude of the maximum centripetal force exerted by the track on the go-cart is 1200. newtons.

What is the maximum speed the 200.-kilogram go-cart can travel without sliding off the track?1. 8.0 m/s 3. 150 m/s2. 12 m/s 4. 170 m/s2 The maximum speed is found from the mass, the radius, and the centripetal force on the go-cart. Use Equations ME17 and ME18 on Reference Table K, and solve for v : (see image)3 90. Base your answer on the information below.

A go-cart travels around a flat, horizontal, circular track with a radius of 25 meters. The mass of the go-cart with the rider is 200. kilograms. The magnitude of the maximum centripetal force exerted by the track on the go-cart is 1200. newtons.

Which change would increase the maximum speed at which the go-cart could travel without sliding off this track?1. Decrease the coefficient of friction between the go-cart and the track. 3. Increase the radius of the track.

2. Decrease the radius of the track. 4. Increase the mass of the go-cart.3 Using the equation for v given in the previous question, we can see that three changes will allow the maximum speed to be increased:

Increase the radius of the track. Increase the centripetal force on the go-cart. Decrease the mass of the go-cart.

4 91. A 0.50-kilogram cart is rolling at a speed of 0.40 meter per second. If the speed of the cart is doubled, the inertia of the cart is1. halved 3. quadrupled2. doubled 4. unchanged

4 The inertia of the cart is measured by its mass, not by its speed. If the mass is unchanged, the inertia will be unchanged.2 92. Two forces, F1 and F2, are applied to a block on a frictionless, horizontal surface as shown below. If the magnitude of the block's acceleration is 2.0 meters per second2, what is the mass of the block?

1. 1 kg 3. 6 kg2. 5 kg 4. 7 kg2 The magnitude of the net force on the block is 10 newtons (12N — 2N). Newton's second law of motion relates the net force, mass, and acceleration. Use Equation ME8 on Reference Table K, and solve for m: (see image)3 93. Which body is in equilibrium?

1. a satellite orbiting Earth in a circular orbit 3. a car moving with a constant speed along a straight, level road

2. a ball falling freely toward the surface of Earth 4. a projectile at the highest point in its trajectory3 A body is in equilibrium if the net force on the body is 0 newton. This means that the body cannot be accelerating. Either the body is at rest, or it is moving at constant speed in a straight line.3 94. Note that this question has only three choices.A carpenter hits a nail with a hammer. Compared to the magnitude of the force the hammer exerts on the nail, the magnitude of the force the nail exerts on the hammer during contact is1. less 3. the same2. greater3 Newton's third law of motion states that if object A exerts a force on object B, then object B exerts an equal and opposite force on object A.3 95. As a meteor moves from a distance of 16 Earth radii to a distance of 2 Earth radii from the center of Earth, the magnitude of the gravitational force between the meteor and Earth becomes1. 1/8 as great 3. 64 times as great2. 8 times as great 4. 4 times as great3 Use Equation ME10 on Reference Table K to compare the magnitudes of the gravitational forces between Earth and the meteor:

2 96. A 0.45-kilogram football traveling at a speed of 22 meters per second is caught by an 84-kilogram stationary receiver. If the football comes to rest in the receiver's arms, the magnitude of the impulse imparted to the receiver by the ball is

2 The magnitude of the impulse imparted to the receiver is equal to the magnitude of the change in the momentum of the football. Use Equations ME12 and ME14 on Reference Table K:

3 97. The mass of a paper clip is approximately1. 1 x 106 kg 3. 1 x 10-3 kg2. 1 x 103 kg 4. 1 x 10-6 kg3 1 x 10-3 kilogram (1 gram, or an approximate weight of 0.002 pound) is a reasonable mass of a single paper clip.

Wrong Choices Explained:(1) 1 x 106 kilogram would have an approximate weight of 2,000,000 pounds.(2) 1 x 103 kilogram would have an approximate weight of 2,000 pounds.(4) 1 x 10-6 kilogram would have an approximate weight of 0.000002 pound.4 98. The accompanying graph represents the displacement of an object moving in a straight line as a function of time.

What was the total distance traveled by the object during the 10.0-second time interval?

1. 0 m 3. 16 m2. 8 m 4. 24 m4 Refer to the graph for this question.

From 0.0—4.0 seconds, the object travels a distance of 8.0 meters. From 4.0—6.0 seconds, the object is at rest (distance equals 0.0 meter). From 6.0—8.0 seconds, the object travels a distance of 8.0 meters. From 8.0—10.0 seconds, the object travels a distance of 8.0 meters (in the reverse direction).

The total distance traveled is (8 + 0 + 8 + 8) 24 meters.

3 99. Which diagram best represents the gravitational forces, Fg, between a satellite, S, and Earth?

3 Gravity is an attractive force. Of the choices given, only the diagram in choice (3) shows the mutual attraction between the satellite and Earth.2 100. A block weighing 10.0 newtons is on a ramp inclined at 30.0o to the horizontal. A 3.0-newton force of friction, Ff, acts on the block as it is pulled up the ramp at constant velocity with force F, which is parallel to the ramp, as shown in the accompanying diagram.

What is the magnitude of force F ?

1. 7.0 N 3. 10. N2. 8.0 N 4. 13 N2 Since the block is traveling up the incline at constant velocity, the force F, directed up the plane, must be equal in magnitude to the sum of the frictional force, Ff , and the component of the gravitational force that acts down the incline, which has a magnitude of Fg sinθ:

1 101. A 25-newton horizontal force northward and a 35-newton horizontal force southward act concurrently on a 15-kilogram object on a frictionless surface. What is the magnitude of the object's acceleration?1. 0.67 m/s2 3. 2.3 m/s2

2. 1.7 m/s2 4. 4.0 m/s2

1 The magnitude of the net force acting on the object is 10. N (southward). Use Equation ME8 on Reference Table K:

3 102. The accompanying diagram represents two concurrent forces.

Which vector represents the force that will produce equilibrium with these two forces?

3 When three forces are in equilibrium, the sum of the forces must equal zero. The first step in solving this problem is to find the resultant force, as shown in the diagram shown. The force needed to place the two concurrent forces in equilibrium must be equal in magnitude to the resultant force but opposite in direction.

1 103. The speed of a car is decreased uniformly from 30. meters per second to 10. meters per second in 4.0 seconds. The magnitude of the car's acceleration is1. 5.0 m/s2 3. 20. m/s2

2. 10. m/s2 4. 40. m/s2

4 104. A ball starting from rest accelerates uniformly at 5.0 meters per second2 as it rolls 40. meters down an incline. How much time is required for the ball to roll the 40. meters?1. 2.8 s 3. 16 s2. 8.0 s 4. 4.0 s

2 105. Objects A and B are dropped from rest near Earth's surface. Object A has mass m and object B has mass 2m. After 2 seconds of free fall, object A has a speed v and has fallen a distance d. What are the speed and distance of fall of object B after 2 seconds of free fall?1. speed = v/2; distance = d/2 3. speed = v/2; distance = 2d2. speed = v; distance = d 4. speed = 2v; distance = 2d

4 106. A ball is thrown horizontally from the top of a building with an initial velocity of 15 meters per second.At the same instant, a second ball is dropped from the top of the building. The two balls have the same1. path as they fall 3. initial horizontal velocity2. final velocity as they reach the ground 4. initial vertical velocity

2 107. In the accompanying diagram, the upward drag force acting on a parachute is equal in magnitude but opposite in direction to the weight of the parachutist and equipment.As a result of the forces shown, the parachutist may be moving

1. downward with decreasing speed 3. upward with decreasing speed2. downward at constant speed 4. upward with constant acceleration

3 108. The accompanying diagram shows a 2.0-kilogram block being moved across a frictionless horizontal surface by a 6.0-newton horizontal force.What is the magnitude of the acceleration of the block?

1. 0.33 m/s2 3. 3.0 m/s2

2. 6.0 m/s2 4. 12 m/s2

2 109. The magnitude of the acceleration due to gravity on the surface of planet A is twice as great as on the surface of planet B. What is the ratio of the weight of mass X on the surface of planet A to its weight on the surface of planet B?1. 1:2 3. 1:4

2. 2:1 4. 4:1

1 110. Base your answer on the information given and accompanying diagram.A roller coaster cart starts from rest and accelerates, due to gravity, down a track. The cart starts at a height that enables it to complete a loop in the track. [Neglect friction.]The magnitude of the centripetal force keeping the cart in circular motion would be greatest at point

1. A 3. C2. B 4. D

1 111. Base your answer on the information given and accompanying diagram.A roller coaster cart starts from rest and accelerates, due to gravity, down a track. The cart starts at a height that enables it to complete a loop in the track. [Neglect friction.]Which diagram best represents the path followed by an object that falls off the cart when the cart is at point D?

3 112. The accompanying diagram shows two carts initially at rest on a horizontal frictionless surface being pushed apart when a compressed spring attached to one of the carts is released.If the 1.0-kilogram cart moves to the left with a speed of 6.0 meters per second, then the 2.0-kilogram cart moves to the right with a speed of

1. 6.0 m/s 3. 3.0 m/s2. 2.0 m/s 4. 12 m/s

1

113. A mother pushes her 120-newton child, who is sitting on a swing. If the mother exerts a 10.-newton force on the child for 0.50 second, what is the magnitude of the impulse imparted to the child by the mother?

3 114. A ball having mass m is struck by a bat having mass 9 m. Compared to the magnitude of the force exerted by the bat on the ball, the magnitude of the force exerted by the ball on the bat is1. less 3. the same2. greater

1 115. Gravitational force F exists between point objects A and B separated by distance R. If the mass of A is doubled and distance R is tripled, what is the new gravitational force between A and B?

1 116. The thickness of one page of this test booklet is closest to1. 10-4 m 3. 100 m2. 10-2 m 4. 102 m

4 117. The accompanying diagram represents two forces acting concurrently on an object at point P.Which diagram best represents the resultant of these two forces?

1 118. Two students are pushing a car. What should be the angle of each student's arms with respect to the flat ground to maximize the horizontal component of the force?1. 0o 3. 45o

2. 30o 4. 90o

4 119. A student performed a laboratory investigation to determine the spring constant of a spring. The force applied to the spring was varied and the resulting elongation of the spring measured. The student graphed the data collected, as shown in the accompanying graph.

According to the student's graph, what is the spring constant for this spring?

4 120. A net force of 25 newtons is applied horizontally to a 10.-kilogram block resting on a table. What is the magnitude of the acceleration of the block?1. 0.0 m/s2 3. 0.40 m/s2

2. 0.26 m/s2 4. 2.5 m/s2

4 121. An object is in equilibrium. Which force vector diagram could represent the force(s) acting on the object?

4 In diagram 4 the horizontal components of the generally upward vector forces could negate each other and the vertical components could negate the downward force vector.

Wrong Choices Explained:(1) This diagram indicates a net force in the downward direction.(2) In this diagram, the magnitude of the upward force vector is smaller than the downward vector, which would result in a net force downward.(3) In this diagram, the 2 horizontal vectors look equal in magnitude so, being that they are opposite in direction, would result in a net force of zero in the horizontal direction. However, there is no force to counteract the downward vector; therefore, there would be a net force in the downward direction.2 122. The speed of a car is increased uniformly from 20. meters per second to 30. meters per second in 4.0 seconds. The magnitude of the car¿s average acceleration in this 4.0-second interval is1. 0.40 m/s2 3. 10. m/s2

2. 2.5 m/s2 4. 13 m/s2

3 123. A roller coaster, traveling with an initial speed of 15 meters per second, decelerates uniformly at -7.0 meters per second2 to a full stop. Approximately how far does the roller coaster travel during its deceleration?1. 1.0 m 3. 16 m2. 2.0 m 4. 32 m

4 124. The diagram shown represents a 0.40-kilogram stone attached to a string. The stone is moving at a constant speed of 4.0 meters per second in a horizontal circle having a radius of 0.80 meter.

The magnitude of the centripetal acceleration of the stone is

1. 0.0 m/s2 3. 5.0 m/s2

2. 2.0 m/s2 4. 20. m/s2

3 125. In the diagram shown, a box is at rest on an inclined plane.

Which vector best represents the direction of the normal force acting on the box?

1. A 3. C2. B 4. D

3 126. Note: This question has only three choices.If the magnitude of the gravitational force of Earth on the Moon is F, the magnitude of the gravitational force of the Moon on Earth is1. smaller than F 3. equal to F2. larger than F

1 127. Which term represents a scalar quantity?

1. distance 3. force2. displacement 4. weight

1 128. A 1.0-kilogram rubber ball traveling east at 4.0 meters per second hits a wall and bounces back toward the west at 2.0 meters per second. Compared to the kinetic energy of the ball before it hits the wall, the kinetic energy of the ball after it bounces off the wall is1. one-fourth as great 3. the same2. one-half as great 4. four times as great

4 129. Which is an acceptable unit for impulse?

3 130. The centers of two 15.0-kilogram spheres are separated by 3.00 meters. The magnitude of the gravitational force between the two spheres is approximately1. 1.11 x 10-10 N 3. 1.67 x 10-9 N2. 3.34 x 10-10 N 4. 5.00 x 10-9 N

3 131. During a collision, an 84-kilogram driver of a car moving at 24 meters per second is brought to rest by an inflating air bag in 1.2 seconds. The magnitude of the force exerted on the driver by the air bag is approximately1. 7.0 x 101 N 3. 1.7 x 103 N2. 8.2 x 102 N 4. 2.0 x 103 N

1 132. An apple weighing 1 newton on the surface of Earth has a mass of approximately1. 1 x 10-1 kg 3. 1 x 101 kg2. 1 x 100 kg 4. 1 x 102 kg

3 133. In which situation is the net force on the object equal to zero?1. a satellite moving at constant speed around Earth in a circular orbit

3. a bicycle moving at constant speed on a straight, level road

2. an automobile braking to a stop 4. a pitched baseball being hit by a bat

2 134. The accompanying diagram shows a 4.0-kilogram cart moving to the right and a 6.0-kilogram cart moving to the left on a horizontal frictionless surface.

When the two carts collide they lock together. The magnitude of the total momentum of the two-cart system after the collision is

1. 1 3. 32. 2 4. 4

2 135. The accompanying diagram shows a 10.0-kilogram mass held at rest on a frictionless 30.0o incline by force F.

What is the approximate magnitude of force F?

1. 9.81 N 3. 85.0 N2. 49.1 N 4. 98.1 N

3 136. An archer uses a bow to fire two similar arrows with the same string force. One arrow is fired at an angle of 60.o with the horizontal, and the other is fired at an angle of 45o with the horizontal. Compared to the arrow fired at 60.o, the arrow fired at 45o has a1. longer flight time and longer horizontal range 3. shorter flight time and longer horizontal range2. longer flight time and shorter horizontal range 4. shorter flight time and shorter horizontal range

3 137. The accompanying graph shows the velocity of a race car moving along a straight line as a function of time.

What is the magnitude of the displacement of the car from t = 2.0 seconds to t = 4.0 seconds?

1. 20. m 3. 60. m2. 40. m 4. 80. m

2 138. Which vector diagram represents the greatest magnitude of displacement for an object?

1 139. Which is a vector quantity?1. gravitational field strength of Earth 3. charge of an electron2. mass of a jogger 4. kinetic energy of a freely falling body

1 140. A 160.-kilogram space vehicle is traveling along a straight line at a constant speed of 800. meters per second. The magnitude of the net force on the space vehicle is1. 0 N 3. 8.00 x 102 N2. 1.60 x 102 N 4. 1.28 x 105 N1 Because the vehicle is traveling in a straight line at constant speed, according to Newton's First Law, the net force on the vehicle would be equal to 0 N.3 141. A student throws a 5.0-newton ball straight up. What is the net force on the ball at its maximum height?1. 0.0 N 3. 5.0 N, down2. 5.0 N, up 4. 9.8 N, down3 The only force acting on the ball is the force due to gravity, in this case the weight of the ball, which is 5.0 N.2 142. A vertical spring has a spring constant of 100. newtons per meter. When an object is attached to the bottom of the spring, the spring changes from its unstretched length of 0.50 meter to a length of 0.65 meter. The magnitude of the weight of the attached object is1. 1.1 N 3. 50. N2. 15 N 4. 65 N21 143. An airplane traveling north at 220. meters per second encounters a 50.0-meters-per-second crosswind from west to east, as represented in the accompanying diagram.

What is the resultant speed of the plane?

1. 170. m/s 3. 226 m/s2. 214 m/s 4. 270. m/s1 To solve this problem we use the technique of vector addition. We recognize that if we place the vectors head to tail, the resultant vector would be the hypotenuse of a right triangle and we can use the Pythagorean theorem to solve algebraically for the resultant vector:(see image)3 144. A 1.5-kilogram cart initially moves at 2.0 meters per second. It is brought to rest by a constant net force in 0.30 second. What is the magnitude of the net force?1. 0.40 N 3. 10. N2. 0.90 N 4. 15 N32 145. As a 5.0 x 102-newton basketball player jumps from the floor up toward the basket, the magnitude of the force of her feet on the floor is 1.0 x 103 newtons. As she jumps, the magnitude of the force of the floor on her feet is1. 5.0 x 102 N 3. 1.5 x 103 N2. 1.0 x 103 N 4. 5.0 x 105 N2 According to Newton's Third Law, if object A exerts a force on object B, then object B exerts an equal and opposite force back on object A. In this case, the basketball player's feet exert a 1.0 x 103 N force on the floor; therefore, the floor exerts a 1.0 x 103 N force on her feet.3 146. A 0.0600-kilogram ball traveling at 60.0 meters per second hits a concrete wall. What speed must a 0.0100-kilogram bullet have in order to hit the wall with the same magnitude of momentum as the ball?1. 3.60 m/s 3. 360. m/s2. 6.00 m/s 4. 600. m/s33 147. The Hubble telescope's orbit is 5.6 x 105 meters above Earth's surface. The telescope has a mass of 1.1 x 104 kilograms. Earth exerts a gravitational force of 9.1 x 104 newtons on the telescope. The magnitude of Earth's gravitational field strength at this location is1. 1.5 x 10-20 N/kg 3. 8.3 N/kg2. 0.12 N/kg 4. 9.8 N/kg31 148. When two point charges are a distance d apart, the magnitude of the electrostatic force between them is F. If the distance between the point charges is increased to 3d, the magnitude of the electrostatic force between the two charges will be1. 1/9 F 3. 2 F2. 1/3 F 4. 4 F

1 (refer to image)2 149. Which diagram best represents the position of a ball, at equal time intervals, as it falls freely from rest near Earth's surface?

2 As a ball falls freely from rest, it is acted upon by a gravitational force downward, which results in its speed increasing from rest at a rate of 9.81 meters per second. Therefore, with each increasing second, the ball will fall a greater distance during each time second interval.

Wrong Choices Explained:(1) This diagram represents movement at constant velocity as the distance for each time interval is identical.(3) This diagram represents movement with decreasing velocity as the distance traveled for each time interval decreases.(4) This diagram represents movement with decreasing then increasing velocity as the distance traveled for each time interval decreases then increases.4 150. A different force is applied to each of four different blocks on a frictionless, horizontal surface. In which diagram does the block have the greatest inertia 2.0 seconds after starting from rest?

4 Mass is the quantitative measure of inertia. The block in diagram 4 has the greatest mass of all the 4 blocks, 20. kg, and thus has the greatest inertia.4 151. Without air resistance, a kicked ball would reach a maximum height of 6.7 meters and land 38 meters away. With air resistance, the ball would travel

1. 6.7 m vertically and more than 38 m horizontally

3. more than 6.7 m vertically and less than 38 m horizontally

2. 38 m horizontally and less than 6.7 m vertically

4. less than 38 m horizontally and less than 6.7 m vertically

4 Air resistance would have the effect of slowing the motion or velocity of the ball. As a result the horizontal and vertical components of the velocity would be decreased. The ball would not reach as great a height. It would therefore have a shorter amount of time in the air or hang time and thus not travel as far horizontally.4 152. A car is moving with a constant speed of 20. meters per second. What total distance does the car travel in 2.0 minutes?1. 10. m 3. 1200 m2. 40. m 4. 2400 m41 153. A car, initially traveling at 15 meters per second north, accelerates to 25 meters per second north in 4.0 seconds. The magnitude of the average acceleration is1. 2.5 m/s2 3. 10. m/s2

2. 6.3 m/s2 4. 20. m/s2

1 (refer to image)1 154. A 15-kilogram cart is at rest on a horizontal surface. A 5-kilogram box is placed in the cart. Compared to the mass and inertia of the cart, the cart-box system has1. more mass and more inertia 3. the same mass and more inertia2. more mass and the same inertia 4. less mass and more inertia1 Inertia is the property of an object that resists a change in motion. The measure of an object's inertia is its mass. Therefore, the more mass an object has, the more inertia it has.3 155. The height of a 30-story building is approximately1. 100 m 3. 102 m2. 101 m 4. 103 m3 Each story of a building is approximately 3 meters. How would you know that? Take a look at the room you're in right now. Imagine how many meter sticks would be needed to go from floor to ceiling—about 3 of them. A 30-story building would then be about 90 meters high. This is approximately 100 meters, which is 102 meters or roughly the size of a football field. Of the choices, this seems the most reasonable.

Wrong Choices Explained:(1) 100 m is 1 meter, which is clearly too small.(2) 101 m is 10 meters. This is a better answer than choice (1) but is still too small. This would be a the height of a 3-story building.

(4) 103 m is 1,000 m or 1 kilometer, which is about 2/3 of a mile. This measurement is much too large.1 156. An air bag is used to safely decrease the momentum of a driver in a car accident. The air bag reduces the magnitude of the force acting on the driver by 1. increasing the length of time the force acts on the driver 3. increasing the rate of acceleration of the driver

2. decreasing the distance over which the force acts on the driver 4. decreasing the mass of the driver

1 Use Equation ME14 on Reference Table K. The product of the force acting on an object and the time that force acts equals the object's change in momentum. The change in momentum of a driver in a car accident will be the same whether he or she hits an air bag or the steering wheel. In either case, the driver goes from moving very fast to being stopped. If the driver hits the steering wheel, he or she stops very quickly since the wheel is hard. So a large force must be applied. If the driver hits an air bag, he or she stops more slowly since the air bag compresses. Thus a smaller force is applied, doing less damage to the driver. Look at the equation to see this mathematically:(see image)3 157. A 1.0 x 103-kilogram car travels at a constant speed of 20. meters per second around a horizontal circular track. The diameter of the track is 1.0 x 102 meters. The magnitude of the car's centripetal acceleration is1. 0.20 m/s2 3. 8.0 m/s2

2. 2.0 m/s2 4. 4.0 m/s2

3 Use Equation ME18 on Reference Table K. The mass of the car is irrelevant. Be sure to divide the diameter by 2 to get the radius:(see image)

Wrong Choices Explained:(1) You probably forgot to square the velocity and also to divide the diameter by 2.(4) You probably forgot to divide the diameter by 2.4 158. Which graph best represents an object in equilibrium moving in a straight line?

4 An object in equilibrium is either at rest or moving with a constant velocity (constant speed in a straight line). Since this object is moving in a straight line, it must have a constant speed. Equation ME20 on Reference Table K shows that if the speed is constant, so is the kinetic energy.

Wrong Choices Explained:(1) This graph shows an object that is accelerating, not moving at a constant speed.(2) This graph shows an object whose velocity (speed) is decreasing.(3) This graph shows an object whose velocity (speed) is increasing. As shown in Equation ME12 on Reference Table K, momentum is the product of mass and velocity.3 159. A body, B, is moving at constant speed in a horizontal circular path around point P. Which diagram shows the direction of the velocity (v) and the direction of the centripetal force (Fc) acting on the body?

3 When an object travels at constant speed in a horizontal circle, the force causing it to move in a circle (centripetal force) is always pointed toward the center of the circle. The word "centripetal" means center-seeking. If it were not for this force, according to Newton's first law, the object would continue traveling in a straight line in the direction it was already moving, that is, tangent to the

circle.4 160. Which combination of initial horizontal velocity, (vH) and initial vertical velocity, (vv) results in the greatest horizontal range for a projectile over level ground? [Neglect friction.]

4 The greatest horizontal range for a projectile, in the absence of air resistance, is when the angle of launch is at 45° above the horizontal. See Equations ME6 and ME7 on Reference Table K. This means that both the horizontal and vertical components of the initial velocity are equal.1 161. Which quantities are scalar?1. speed and work 3. distance and acceleration2. velocity and force 4. momentum and power1 Both speed and work are scalar quantities.

Wrong Choices Explained:(2) Both velocity and force are vector quantities.(3) Distance is a scalar quantity while acceleration is a vector quantity.(4) Momentum is a vector quantity while power is a scalar quantity.2 162. A 3.00-kilogram mass is thrown vertically upward with an initial speed of 9.80 meters per second. What is the maximum height this object will reach? [Neglect friction.]1. 1.00 m 3. 9.80 m2. 4.90 m 4. 19.6 m2 When dealing with a word problem requiring a mathematical solution, it is most helpful to translate the words into which quantities/variables are explicitly given and which constants or other variables can be deduced from the situation or words. We also write down the variable that needs to be solved for or found. Then it is much easier to determine which formula is required and then use it to solve the problem.(see image)4 163. Which graph represents the relationship between the magnitude of the gravitational force, Fg, between two masses and the distance, r, between the centers of the masses?

4 Refer to Equation ME10 on Reference Table K. The gravitational force between two masses varies inversely as the square of the distance between the masses. As the distance decreases, the force increases rapidly. As the distance increases, the force decreases rapidly. Neither the force nor the distance can ever equal zero. Only the graph shown in choice (4) meets all of these criteria.1 164. Which quantity is scalar?1. mass 3. momentum2. force 4. acceleration1 A scalar quantity has magnitude (a measured value) but not direction. The mass of an object has magnitude only (for example, 50. kilograms) but not direction. Therefore, mass is a scalar quantity.

Wrong Choices Explained:(2), (3), (4) Force, momentum, and acceleration all have direction associated with them. For example, a force can be 20. newtons north. Since these quantities have both magnitude and direction, they are vector quantities.1 165. What is the final speed of an object that starts from rest and accelerates uniformly at 4.0 meters per second2 over a distance of 8.0 meters?1. 8.0 m/s 3. 32 m/s2. 16 m/s 4. 64 m/s1 Use Equation ME5 on Reference Table K:

(see image)2 166. The components of a 15-meters-per-second velocity at an angle of 60.o above the horizontal are1. 7.5 m/s vertical and 13 m/s horizontal 3. 6.0 m/s vertical and 9.0 m/s horizontal2. 13 m/s vertical and 7.5 m/s horizontal 4. 9.0 m/s vertical and 6.0 m/s horizontal2 Use Equations ME6 and ME7 on Reference Table K:

(see image)

2 167. A 4.0-kilogram object is accelerated at 3.0 meters per second2 north by an unbalanced force. The same unbalanced force acting on a 2.0-kilogram object will accelerate this object toward the north at1. 12 m/s2 3. 3.0 m/s2

2. 6.0 m/s2 4. 1.5 m/s2

2 The net force needed to accelerate the 4.0-kilogram object at 3.0 meters per second2 is determined by using Newton's second law (Equation ME8 on Reference Table K):(see image)Now apply Newton's second law to the 2.0-kilogram mass:(see image)3 168. What is the time required for an object starting from rest to fall freely 500. meters near Earth's surface?1. 51.0 s 3. 10.1 s2. 25.5 s 4. 7.14 s3 Since it is released from rest, the initial speed, vi , is 0.0 meters per second. The acceleration due to gravity is 9.81 meters per second squared (see Reference Table A). Use Equation ME4 on Reference Table K:(see image)1 169. A baseball bat exerts a force of magnitude F on a ball. If the mass of the bat is three times the mass of the ball, the magnitude of the force of the ball on the bat is1. F 3. 3F2. 2F 4. F/31 Newton's third law states that if object A exerts a force on object B, then object B exerts an equal and opposite force on object A. An alternate way of stating this is that for every action, there is an equal and opposite reaction. Hence these forces are called an "action-reaction pair." So the magnitude of the force that the ball exerts on the bat is equal to the force that the bat exerts on the ball.

Wrong Choices Explained:(2), (3), (4) The relative masses of the objects do not affect the forces described.3 170. A 2.0-kilogram mass is located 3.0 meters above the surface of Earth. What is the magnitude of Earth's gravitational field strength at this location? 1. 4.9 N/kg 3. 9.8 N/kg2. 2.0 N/kg 4. 20. N/kg3 Earth's gravitational field strength is symbolized by the letter g. See the definition of symbols on Reference Table K. The letter g is also the symbol for the acceleration due to gravity, which near the surface of Earth is 9.81 m/s2 (see Reference Table A). Since the question states that the mass is 3.0 meters above the surface of Earth, this location is considered to be near the surface. To 2 significant digits, the gravitational field strength can be rounded to 9.8. Note that N/kg are equivalent units to

m/s2.

Wrong Choices Explained:(1), (4) In the absence of air resistance, all objects accelerate at the same rate when they fall. So the gravitational field strength does not depend on the mass of the falling object.4 171. A truck, initially traveling at a speed of 22 meters per second, increases speed at a constant rate of 2.4 meters per second2 for 3.2 seconds. What is the total distance traveled by the truck during this 3.2-second time interval?1. 12 m 3. 70. m2. 58 m 4. 83 m4 Use Equation ME4 on Reference Table K:

(see image)2 172. A 750-newton person stands in an elevator that is accelerating downward. The upward force of the elevator floor on the person must be 1. equal to 0 N 3. equal to 750 N2. less than 750 N 4. greater than 750 N2 According to Newton's second law, when the forces acting on an object are unbalanced, the object will accelerate in the direction of the greater force. To accelerate downward, the downward force must be greater than the upward force. In this case, the downward force is the gravitational force (the person's weight) of 750 newtons. So the upward force (the normal force coming from the floor of the elevator) must be less than 750 newtons.2 173. A 3.0-kilogram object is acted upon by an impulse having a magnitude of 15 newton·seconds. What is the magnitude of the object's change in momentum due to this impulse?

2 An impulse is a force acting for a certain amount of time. An impulse acting on an object causes the object to change its momentum. Use Equation ME14 on Reference Table K. The impulse is numerically equal to the object's change in momentum (J = Δp). If the impulse is 15 newton•seconds, then the change in momentum is 15 kg•m/s. Note that kg•m/s are equivalent units to newton•seconds.

Wrong Choices Explained:(1), (4) Since impulse and change in momentum are equal, the mass of the object is irrelevant.3 174. Approximately how much time does it take light to travel from the Sun to Earth?1. 2.00 x 10-3 s 3. 5.00 x 102 s2. 1.28 x 100 s 4. 4.50 x 1019 s3 Use the information on Reference Table A. The speed of light in a vacuum is 3 x 108 m/s and the

Earth-Sun distance is 1.5 x 1011 m. Use Equation ME1 on Reference Table K:

3 175. A rock falls from rest a vertical distance of 0.72 meter to the surface of a planet in 0.63 second. The magnitude of the acceleration due to gravity on the planet is1. 1.1 m/s2 3. 3.6 m/s2

2. 2.3 m/s2 4. 9.8 m/s2

3 The initial speed of the rock is 0 m/s. Use Equation ME4 on Reference Table K:4 176. Cart A has a mass of 2 kilograms and a speed of 3 meters per second. Cart B has a mass of 3 kilograms and a speed of 2 meters per second. Compared to the inertia and magnitude of momentum of cart A, cart B has1. the same inertia and a smaller magnitude of momentum

3. greater inertia and a smaller magnitude of momentum

2. the same inertia and the same magnitude of momentum

4. greater inertia and the same magnitude of momentum

4 The inertia of an object is measured by its mass. Cart B has more inertia than cart A. The magnitude of an object's momentum is measured by calculating the product of its mass and speed (p = mv). The magnitude of the momentum of both carts is 6 kg · m/s.1 177. Two stones, A and B, are thrown horizontally from the top of a cliff. Stone A has an initial speed of 15 meters per second and stone B has an initial speed of 30. meters per second. Compared to the time it takes stone A to reach the ground, the time it takes stone B to reach the ground is1. the same 3. half as great2. twice as great 4. four times as great1 The time needed to reach the ground is determined by the initial vertical speeds of the two stones. In each case, the initial vertical speed is 0 m/s. Therefore, both stones will reach the ground at the same time. (However, stone B will travel a longer horizontal distance than stone A.)3 178. The speed of an object undergoing constant acceleration increases from 8.0 meters per second to 16.0 meters per second in 10. seconds. How far does the object travel during the 10. seconds?1. 3.6 x 102 m 3. 1.2 x 102 m2. 1.6 x 102 m 4. 8.0 x 101 m3 The long way to solve this problem is to use Equations ME2 and ME4 on Reference Table K. The "quick and dirty" way to solve it is to recognize that under constant acceleration, the average speed is one-half the sum of the initial and final speeds:

3 179. A 1200-kilogram space vehicle travels at 4.8 meters per second along the level surface of Mars. If the magnitude of the gravitational field strength on the surface of Mars is 3.7 newtons per kilogram, the magnitude of the normal force acting on the vehicle is1. 320 N 3. 4400 N

2. 930 N 4. 5800 N3 Since the vehicle is not accelerating in the vertical direction, the magnitude of the normal force on the vehicle must be equal to the magnitude of the gravitational force. Use Equation ME11 on Reference Table K:

2 180. Which diagram represents a box in equilibrium?

2 In order to be in equilibrium, the net force on the box must equal 0 N. This means that the sum of the horizontal forces and the sum of the vertical forces must each equal 0 N. Of the choices given, only the diagram in choice (2) has a net force of 0 N.

Wrong Choices Explained:(1) The box has a net downward force of 5 N.(3) The box has a net downward force of 3 N.(4) The box has a net upward force of 2 N and a net force of 2 N to the right.2 181. The accompanying diagram shows an object moving counterclockwise around a horizontal, circular track. Which diagram represents the direction of both the object's velocity and the centripetal force acting on the object when it is in the position shown?

2 When an object travels in a circular path, its instantaneous velocity is tangent to the circle. In this case, the velocity is directed upward. The centripetal acceleration of an object always points toward the center of the circle. In this case, the acceleration is directed toward the left.2 182. An airplane flies with a velocity of 750. kilometers per hour, 30.0o south of east. What is the magnitude of the eastward component of the plane's velocity?1. 866 km/h 3. 433 km/h2. 650. km/h 4. 375 km/h2 Refer to the accompanying diagram:

The eastward component of the plane's velocity is the x-component of the velocity. Use Equation ME7 on Reference Table K:

3 183. An 80-kilogram skier slides on waxed skis along a horizontal surface of snow at constant velocity while pushing with his poles. What is the horizontal component of the force pushing him forward?1. 0.05 N 3. 40 N2. 0.4 N 4. 4 N3 Since the skier is not accelerating in either the horizontal or the vertical direction, the sum of the forces in each direction must total 0 N. Therefore, the magnitude of the normal force must be equal to the magnitude of the gravitational force. Additionally, the magnitude of the frictional force must be equal to the magnitude of the horizontal component of the force pushing the skier forward. First

use Equation ME11 on Reference Table K to calculate the magnitude of both the gravitational and normal forces on the skier:

Next, use the information on Reference Table C and Equation ME9 on Reference Table K to calculate the magnitude of the frictional force on the skier:

3 184. A 1750-kilogram car travels at a constant speed of 15.0 meters per second around a horizontal, circular track with a radius of 45.0 meters. The magnitude of the centripetal force acting on the car is1. 5.00 N 3. 8750 N2. 583 N 4. 3.94 x 105 N3 Use Equations ME18 and ME17 on Reference Table K:

3 185. Which situation will produce the greatest change of momentum for a 1.0-kilogram cart?1. accelerating it from rest to 3.0 m/s 3. applying a net force of 5.0 N for 2.0 s2. accelerating it from 2.0 m/s to 4.0 m/s 4. applying a net force of 10.0 N for 0.5 s3 The change in momentum is given by Equations ME12 and ME14 on Reference Table K:1 186. Earth's mass is approximately 81 times the mass of the Moon. If Earth exerts a gravitational force of magnitude F on the Moon, the magnitude of the gravitational force of the Moon on Earth is1. F 3. 9F2. F/81 4. 81F1 Newton's third law states that if object A exerts a force on object B, then object B exerts an equal and opposite force on object A. The relative masses of the objects do not affect these action-reaction pairs of forces.4 187. A 0.50-kilogram object moves in a horizontal circular path with a radius of 0.25 meter at a constant speed of 4.0 meters per second. What is the magnitude of the object's acceleration?1. 8.0 m/s2 3. 32 m/s2

2. 16 m/s2 4. 64 m/s2

4 The centripetal acceleration does not depend on the mass. Use the speed, the radius, and Equation ME18 on Reference Table K:3 188. The accompanying diagram shows two bowling balls, A and B, each having a mass of 7.00 kilograms, placed 2.00 meters apart.

What is the magnitude of the gravitational force exerted by ball A on ball B?

1. 8.17 × 10-9 N 3. 8.17 × 10-10 N2. 1.63 × 10-9 N 4. 1.17 × 10-10 N3 Use Reference Table A and Equation ME10 on Reference Table K:1 189. A force of 1 newton is equivalent to 1

1 Use Equation ME8 on Reference Table K, and substitute the appropriate units into this equation:2 190. Base your answer on the information below.

A stream is 30. meters wide and its current flows southward at 1.5 meters per second. A toy boat is launched with a velocity of 2.0 meters per second eastward from the west bank of the stream.

What is the magnitude of the boat's resultant velocity as it crosses the stream?1. 0.5 m/s 3. 3.0 m/s2. 2.5 m/s 4. 3.5 m/s2 Refer to the accompanying diagram, and use Equation GT4A on Reference Table K:

The velocity of the boat and the stream are at right angles to one another. Therefore, the magnitude of the resultant velocity can be calculated using the Pythagorean theorem (see image):3 191. Base your answer on the information below.

A stream is 30. meters wide and its current flows southward at 1.5 meters per second. A toy boat is launched with a velocity of 2.0 meters per second eastward from the west bank of the stream.

How much time is required for the boat to reach the opposite bank of the stream?1. 8.6 s 3. 15 s2. 12 s 4. 60. s3 The time needed to travel east across the stream is determined solely by the magnitude of the velocity in the eastern direction (2.0 m/s). Use Equation ME1 on Reference Table K:3 192. An observer recorded the data in the accompanying chart for the motion of a car undergoing constant acceleration.

What was the magnitude of the acceleration of the

1. 1.3 m/s2 3. 1.5 m/s2

2. 2.0 m/s2 4. 4.5 m/s2

3 Since the acceleration is constant, we need to choose only two pairs of data (for example, the first and third) and apply Equation ME2 on Reference Table K:4 193. Which graph best represents the relationship between the velocity of an object thrown straight upward from Earth's surface and the time that elapses while it is in the air? [Neglect friction.]

4 The acceleration of the object is constant (-9.81 m/s2). Therefore, the graph of velocity versus time must be a straight line with a negative slope. The object rises with decreasing speed, stops for an instant, and falls with increasing speed. Of the choices given, only the graph in choice (4) displays all of these properties.

Wrong Choices Explained:(1) This graph is one in which the velocity is constant; the acceleration is 0 m/s2.(2), (3) These graphs display accelerations that are not constant.2 194. In the accompanying diagram, scaled vectors represent the momentum of each of two masses, A and B, sliding toward each other on a frictionless, horizontal surface.

Which scaled vector best represents the momentum of the system after the masses collide?

2 Refer to the accompanying diagram:Momentum is a vector quantity that is conserved when a collision occurs. In other words, the total momentum before the collision must be equal to the total momentum after the collision. In order to find the total momentum, add these vector quantities as shown in the diagram.1 195. The speedometer in a car does not measure the car's velocity because velocity is a1. vector quantity and has a direction associated with it

3. scalar quantity and has a direction associated with it

2. vector quantity and does not have a direction associated with it

4. scalar quantity and does not have a direction associated with it

1 Velocity is a vector quantity and must have both magnitude and direction associated with it. A speedometer measures only the magnitude of the velocity, that is, the speed.1 196. A projectile launched at an angle of 45o above the horizontal travels through the air. Compared to the projectile's theoretical path with no air friction, the actual trajectory of the projectile with air friction is1. lower and shorter 3. higher and shorter2. lower and longer 4. higher and longer1 The presence of air friction will reduce both the horizontal and vertical components of the projectile's initial velocity. Since the time of flight and the (horizontal) range of the projectile depend on these components, the actual path will be lower in height and shorter in duration.1 197. In which diagram do the field lines best represent the gravitational field around Earth?

1 The direction of the gravitational field lines are determined by the path that a test mass takes as it approaches Earth. Any mass will be directed on a line toward the center of Earth. This arrangement is given by the diagram in choice (1).1 198. A 100.0-kilogram boy and a 50.0-kilogram girl, each holding a spring scale, pull against each other as shown on the accompanying diagram.

The accompanying graph shows the relationship between the magnitude of the force that the boy applies on his spring scale and time.

Which graph best represents the relationship between the magnitude of the force that the girl applies on her spring scale and time?

1 As a result of Newton's third law, the boy's force will always equal the girl's force since the spring scales are connected to one another. Therefore, the graph of the boy's force versus time will be identical to the graph of the girl's force versus time. (Their body masses are irrelevant to this problem.)4

199. Which term identifies a scalar quantity?1. displacement 3. velocity2. momentum 4. time4 A scalar quantity has magnitude but not direction. Time is never associated with a direction and is therefore a scalar quantity.

Wrong Choices Explained:(1), (2), (3) Displacement, momentum, and velocity are all associated with both magnitude and direction. They are vector quantities.1 200. Two 20.-newton forces act concurrently on an object. What angle between these forces will produce a resultant force with the greatest magnitude?1. 0o 3. 90.o

2. 45o 4. 180.o

1 When two forces act at the same point, they produce the maximum resultant force (40.0 newtons) when the angle between them is 0o.

Wrong Choice Explained:(4) When the angle between the two forces is 180o, they will produce the minimum resultant force (0.0 newton).1 201. A car traveling west in a straight line on a highway decreases its speed from 30.0 meters per second to 23.0 meters per second in 2.00 seconds. The car's average acceleration during this time interval is1. 3.5 m/s2 east 3. 13 m/s2 east2. 3.5 m/s2 west 4. 13 m/s2 west1 Assume that east is positive and west is negative. Use Equation ME2 on Reference Table K:(see image)2 202. In a race, a runner traveled 12 meters in 4.0. seconds as she accelerated uniformly from rest. The magnitude of the acceleration of the runner was1. 0.25 m/s2 3. 3.0 m/s2

2. 1.5 m/s2 4. 48 m/s2

2 Use Equation ME4 on Reference Table K:(see image)1 203. A projectile is launched at an angle above the ground. The horizontal component of the projectile's velocity, vx, is initially 40. meters per second. The vertical component of the projectile's velocity, vy, is initially 30. meters per second. What are the components of the projectile's velocity after 2.0. seconds of flight? [Neglect friction.]1. vx = 40. m/s and vy = 10. m/s 3. vx = 20. m/s and vy = 10. m/s2. vx = 40. m/s and vy = 30. m/s 4. vx = 20. m/s and vy = 30. m/s

1 When a projectile is in motion, the horizontal component of its velocity, vx, does not change. So vx remains 40. m/s. The vertical component, however, does change because of the influence of gravity. In order to find the final value of vy, use Equation ME3 on Reference Table K:(see image)4 204. A stone on the end of a string is whirled clockwise at constant speed in a horizontal circle as shown on the accompanying diagram.

Which pair of arrows best represents the directions of the stone's velocity, v, and acceleration, a, at the position shown?

4 Refer to the accompanying diagram:

When an object undergoes uniform circular motion, its acceleration at every point in its path is directed to the center of the circle and its velocity is tangent to the circle. In the position shown on the diagram, the acceleration points to the left and the velocity points down.2 205. On a small planet, an astronaut uses a vertical force of 175 newtons to lift an 87.5-kilogram boulder at constant velocity to a height of 0.350 meter above the planet's surface. What is the magnitude of the gravitational field strength on the surface of the planet?1. 0.500 N/kg 3. 9.81 N/kg2. 2.00 N/kg 4. 61.3 N/kg

2 Since the boulder is lifted at constant velocity, the force applied by the astronaut is equal to the gravitational force on the boulder. Use Equation ME11 on Reference Table K:(see image)2 206. Which quantity has both a magnitude and a direction?1. energy 3. power2. impulse 4. work2 Vector quantities have both magnitude and direction. Of the choices given, only choice (2), impulse, is a vector quantity. The other choices are scalar quantities and have magnitude only.2 207. The length of a football field is closest to1. 1000 cm 3. 1000 km2. 1000 dm 4. 1000 mm2 A football field is 100 yards long. Since 1 yard is equal to approximately 1 meter, the length of the field is approximately 100 meters or 1000 decimeters.

Wrong Choices Explained:(1) 1000 centimeters is equal to approximately 30 feet.(3) 1000 kilometers is equal to approximately 600 miles.(4) 1000 millimeters is equal to approximately 3 feet.3 208. A student on an amusement park ride moves in a circular path with a radius of 3.5 meters once every 8.9 seconds. The student moves at an average speed of1. 0.39 m/s 3. 2.5 m/s2. 1.2 m/s 4. 4.3 m/s3 The distance traveled by the student is the circumference of the circular path. Use Equations GT3B and ME1 on Reference Table K:(see image)3 209. When a 1.0-kilogram cart moving with a speed of 0.50 meter per second on a horizontal surface collides with a second 1.0-kilogram cart initially at rest, the carts lock together. What is the speed of the combined carts after the collision? [Neglect friction.]1. 1.0 m/s 3. 0.25 m/s2. 0.50 m/s 4. 0 m/s3 This problem involves the conservation of linear momentum. Use Equations ME12 and ME13 on Reference Table K:(see image)4 210. Which graph represents the relationship between the magnitude of the gravitational force exerted by Earth on a spacecraft and the distance between the center of the spacecraft and center of Earth? [Assume constant mass for the spacecraft.]

4 Refer to Equation ME10 on Reference Table K. The gravitational force between two masses varies inversely as the square of the distance between the masses. As the distance increases, the force decreases but never reaches zero. When graphed, this type of relationship produces a curve known as a hyperbola and is illustrated in choice (4).2 211. The accompanying diagram represents a setup for demonstrating motion.

When the lever is released, the support rod withdraws from ball B, allowing it to fall. At the same instant, the rod contacts ball A, propelling it horizontally to the left. Which statement describes the motion that is observed after the lever is released and the balls fall? [Neglect friction.]

1. Ball A travels at constant velocity. 3. Ball B hits the tabletop before ball A.2. Ball A hits the tabletop at the same time as ball B. 4. Ball B travels with an increasing acceleration.

2 Both balls fall at the same rate, a rate that is determined by the acceleration of gravity (g). Therefore, they will both reach the tabletop at the same time.1 212. A container of rocks with a mass of 65.0 kilograms is brought back from the Moon's surface where the acceleration due to gravity is 1.62 meters per second2. What is the weight of the container of rocks on Earth's surface?1. 638 N 3. 105 N2. 394 N 4. 65.0 N

1 The mass of the rocks is 65.0 kg whether they are on the Moon or on Earth. Use Equation ME11 on Reference Table K:3 213. An astronaut drops a hammer from 2.0 meters above the surface of the Moon. If the acceleration due to gravity on the Moon is 1.62 meters per second2, how long will it take for the hammer to fall to the Moon's surface?1. 0.62 s 3. 1.6 s2. 1.2 s 4. 2.5 s3 The hammer is dropped from rest (vi = 0.0 m/s). Use Equation ME4 on Reference Table K:1 214. A satellite weights 200 newtons on the surface of Earth. What is its weight at a distance of one Earth radius above the surface of Earth?1. 50 N 3. 400 N2. 100 N 4. 800 N1 See Equation ME10 on Reference Table K. When the gravitational force (weight) of an object on the surface of Earth is calculated, r is the distance between the object and the center of Earth, that is, one Earth radius. When the object is placed one radius above the surface of the Earth, it is two Earth radii from the center of Earth (2r). Since the gravitational force depends on the factor 1/r 2, doubling the distance will cause the gravitational force to be reduced to one-quarter of its initial value: 50 N.4 215. Which cart has the greatest inertia?1. a 1-kilogram cart traveling at a speed of 4 m/s 3. a 3-kilogram cart traveling at a speed of 2 m/s2. a 2-kilogram cart traveling at a speed of 3 m/s 4. a 4-kilogram cart traveling at a speed of 1 m/s4 Inertia is a property of matter that is measured solely by its mass: the greater the mass, the greater the inertia.1 216. The accompanying diagram shows a 5.00-kilogram block at rest on a horizontal, frictionless table.

Which diagram best represents the force exerted on the block by the table?

1 Since the object is in equilibrium, it must be subject to two equal and opposite forces: its weight (5.00 kg • 9.81 m/s2 = 49.1 N), which points downward, and the normal force exerted on the block by the table, which is also 49.1 N but points upward.Wrong Choice Explained: (3) This diagram displays the mass of the object and not its weight.4 217. Two positively charged masses are separated by a distance, r. Which statement best describes the gravitational and electrostatic forces between the two masses?

1. Both forces are attractive. 3. The gravitational force is repulsive and the electrostatic force is attractive.

2. Both forces are repulsive. 4. The gravitational force is attractive and the electrostatic force is repulsive.

4 Gravitational forces are always attractive. Electrical forces are attractive if the masses have opposite electrical charges and are repulsive if they have the same type of electrical charge. Since both masses are charged positively, the electrical force between them is repulsive.2 218. The approximate height of a 12-ounce can of root beer is1. 1.3 x 10-3 m 3. 1.3 x 100 m2. 1.3 x 10-1 m 4. 1.3 x 101 m2 1 meter is about 39 inches. 1.3 × 10-1 meter is about 5 inches, a reasonable height for a can of root beer.

Wrong Choices Explained:(1) 1.3 × 10-3 meter is approximately equal to 0.05 inch.(3) 1.3 × 100 meter is approximately equal to 50 inches.(4) 1.3 × 101 meter is approximately equal to 500 inches.

4 219. Which physical quantity is correctly paired with its unit?1. power and watt(dot notation)seconds 3. electric current and amperes/coulomb

2. energy and newton(dot notation)seconds 4. electric potential difference and joules/coulomb

4 Refer to Equation EL3 on Reference Table K. Electric potential difference is defined as the work done on an electric charge (in joules) divided by the magnitude of the charge (in coulombs): joules/coulomb.

Wrong Choices Explained:(1) Power is measured in watts; a watt•second measures energy or work.(2) Energy is measured in joules; a newton•second is the unit associated with impulse.(3) Electric current is measured in amperes; an ampere/coulomb reduces to the inverse of time (1/t).2 220. An object is dropped from rest and falls freely 20. meters to Earth. When is the speed of the object 9.8 meters per second?1. during the entire first second of its fall 3. during its entire time of fall2. at the end of its first second of fall 4. after it has fallen 9.8 meters2 We need to find the time at which the speed of the object is 9.8 m/s. Use Reference Table A and Equation ME3 on Reference Table K. When an object falls freely from rest, vi = 0.0 m/s and a = g = 9.8 m/s2:

Therefore, the speed of the object is 9.8 m/s at the end of its first second of fall.

Wrong Choices Explained:(1), (3) Since the object is accelerated by gravity, its speed is continuously changing during its fall.(4) Using Equation ME5 on Reference Table K shows that when the object has fallen 9.8 meters, its final speed will be 14 m/s.3 221. A 2.0-kilogram body is initially traveling at a velocity of 40. meters per second east. If a constant force of 10. newtons due east is applied to the body for 5.0 seconds, the final speed of the body is1. 15 m/s 3. 65 m/s2. 25 m/s 4. 130 m/s3 First we need to solve for the acceleration of the object. Use Equation ME8 on Reference Table K:

Second, we need to insert the information into Equation ME3 on Reference Table K:3 222. A 5.0-newton force and a 7.0-newton force act concurrently on a point. As the angle between the forces is increased from 0° to 180°, the magnitude of the resultant of the two forces changes from1. 0.0 N to 12.0 N 3. 12.0 N to 2.0 N2. 2.0 N to 12.0 N 4. 12.0 N to 0.0 N

3 When the concurrent forces act at an angle of 0°, they act in the same direction. The resultant is the sum of the two forces, in this case 12.0 N. When the forces act at an angle of 180°, they act in opposite directions. The resultant is the difference of the two forces, in this case 2.0 N. Therefore, as the angle is changed from 0° to 180°, the resultant varies from 12.0 N to 2.0 N.3 223. A 5.0-newton force could have perpendicular components of1. 1.0 N and 4.0 N 3. 3.0 N and 4.0 N2. 2.0 N and 3.0 N 4. 5.0 N and 5.0 N3 Let F1 and F2 be two components of a force F. If the components are perpendicular, then the force and its components must form a right triangle as shown in the accompanying diagram:

Moreover, the force and its components would have to obey the Pythagorean theorem: F2 = F12 + F

22. (See

Equation GT4A on Reference Table K.) Of the choices given, only choice (3), 3.0 N and 4.0 N, obeys this relationship: (5.0 N)2 = (3.0 N)

2 + (4.0 N)

2.

2 224. A golf ball is hit at an angle of 45° above the horizontal. What is the acceleration of the golf ball at the highest point in its trajectory? [Neglect friction.]1. 9.8 m/s2 upward 3. 6.9 m/s2 horizontal2. 9.8 m/s2 downward 4. 0.0 m/s2

2 The acceleration due to gravity is constant: 9.8 m/s2 downward for the entire trajectory of the golf ball.3 225. At the circus, a 100.-kilogram clown is fired at 15 meters per second from a 500.-kilogram cannon. What is the recoil speed of the cannon?1. 75 m/s 3. 3.0 m/s2. 15 m/s 4. 5.0 m/s3 Since momentum is conserved, the final momentum of the clown will be equal and opposite to the final momentum of the cannon. Use Equations ME12 and ME13 on Reference Table K:3 226. A ball is thrown horizontally at a speed of 24 meters per second from the top of a cliff. If the ball hits the ground 4.0 seconds later, approximately how high is the cliff?1. 6.0 m 3. 78 m2. 39 m 4. 96 m3 The initial vertical speed of the ball is zero. The distance that it falls can be found from Equation ME4 on Reference Table K:

The horizontal speed of the ball is not needed to solve this problem since gravity affects only the downward speed of the ball.3 227. A 0.2-kilogram red ball is thrown horizontally at a speed of 4 meters per second from a height of 3 meters. A 0.4-kilogram green ball is thrown horizontally from the same height at a speed of 8 meters per second. Compared to the time it takes the red ball to reach the ground, the time it takes the green ball to reach the ground is

1. one-half as great 3. the same2. twice as great 4. four times as great3 The vertical speed of both objects depends on only the acceleration due to gravity and the height of the objects above the ground. The masses of the objects and their horizontal speeds do not matter in this case. Since both objects fall from the same height, they will reach the ground at the same time.3 228. The diagram (see image) represents the path of an object after it was thrown.

What happens to the object's acceleration as it travels from A to B? [Neglect friction.]

1. It decreases. 3. It remains the same.2. It increases.3 After the object is thrown, the only force acting on the object is the gravitational force (that is, its weight). Since the object's weight is constant near the surface of Earth, the object's acceleration due to gravity is also constant.1 229. The acceleration due to gravity on the surface of planet X is 19.6 meters per second2. If an object on the surface of this planet weighs 980. newtons, the mass of the object is 1. 50.0 kg 3. 490. N2. 100. kg 4. 908 N1 Use Equation ME11 on Reference Table K and solve for mass.2 230. A basketball player jumped straight up to grab a rebound. If she was in the air for 0.80 second, how high did she jump?1. 0.50 m 3. 1.2 m2. 0.78 m 4. 3.1 m2 Since the player was in the air for a total of 0.80 second, she rose for 0.40 second and then fell the same distance for 0.40 second. Solving this problem is easier when considering the time interval in which she fell. Use Reference Table A and Equation ME4 on Reference Table K.2 231. The force required to start an object sliding across a uniform horizontal surface is larger than the force required to keep the object sliding at a constant velocity. The magnitudes of the required forces are different in these situations because the force of kinetic friction

1. is greater than the force of static friction 3. increases as the speed of the object relative to the surface increases

2. is less than the force of static friction 4. decreases as the speed of the object relative to the surface increases

2 When objects in contact are at rest, attractive forces are present between the objects. In order to start one of the objects sliding, these forces (that is, the force of static friction) must be overcome.

Once the object is in motion, these attractive forces are reduced and less force is needed to overcome (kinetic) friction.1 232. A 50.-kilogram student threw a 0.40-kilogram ball with a speed of 20. meters per second. What was the magnitude of the impulse that the student exerted on the ball?

1 We assume that the ball was initially at rest. Use Equations ME12 and ME14 on Reference Table K.4 233. A man is pushing a baby stroller. Compared to the magnitude of the force exerted on the stroller by the man, the magnitude of the force exerted on the man by the stroller is 1. zero 3. larger2. smaller, but greater than zero 4. the same4 According to Newton's third law, when object A (in this case, the man) exerts a force on object B (in this case, the baby stroller), object B exerts an equal and opposite force on object A.4 234. A constant unbalanced force is applied to an object for a period of time. Which graph best represents the acceleration of the object as a function of elapsed time?

4 Refer to Equation ME8 on Reference Table K. A constant net (or unbalanced) force gives rise to a constant acceleration. The graph in choice (4) shows that the acceleration is constant over time.

Wrong Choices Explained:(1) This graph shows acceleration constantly increasing.(2) This graph shows acceleration constantly decreasing.(3) This graph shows acceleration increasing at an increasing rate.3 235. The diameter of a United States penny is closest to1. 100 m 3. 10-2 m2. 10-1 m 4. 10-3 m3 10-2 meter (1 centimeter) is approximately equal to 0.4 inch, a reasonable estimation of the diameter of a United States penny.

Wrong Choices Explained:(1) 100 meter is approximately equal to 3 feet.(2) 10-1 meter is approximately equal to 4 inches.(4) 10-3 meter is approximately equal to 0.04 inch.

2 236. A car initially traveling at a speed of 16 meters per second accelerates uniformly to a speed of 20. meters per second over a distance of 36 meters. What is the magnitude of the car's acceleration?1. 0.11 m/s2 3. 0.22 m/s2

2. 2.0 m/s2 4. 9.0 m/s2

4 237. A ball is thrown at an angle of 38 degrees to the horizontal. What happens to the magnitude of the ball's vertical acceleration during the total time interval that the ball is in the air?1. It decreases, then increases. 3. It increases, then decreases.2. It decreases, then remains the same. 4. It remains the same.

1 238. A man standing on a scale in an elevator notices that the scale reads 30 newtons greater than his normal weight. Which type of movement of the elevator could cause this greater-than-normal reading?1. accelerating upward 3. moving upward at constant speed2. accelerating downward 4. moving downward at constant speed

2 239. A vector makes an angle, theta , with the horizontal. The horizontal and vertical components of the vector will be equal in magnitude if angle theta is1. 30 degrees 3. 60 degrees2. 45 degrees 4. 90 degrees

3 240. Projectile A is launched horizontally at a speed of 20. meters per second from the top of a cliff and strikes a level surface below, 3.0 seconds later. Projectile B is launched horizontally from the same location at a speed of 30. meters per second. The time it takes projectile B to reach the level surface is1. 4.5 s 3. 3.0 s2. 2.0 s 4. 10. s

2 241. Projectile A is launched horizontally at a speed of 20. meters per second from the top of a cliff and strikes a level surface below, 3.0 seconds later. Projectile B is launched horizontally from the same location at a speed of 30. meters per second. Approximately how high is the cliff?1. 29 m 3. 60. m2. 44 m 4. 104 m

4 242. A 60-kilogram skydiver is falling at a constant speed near the surface of Earth. The magnitude of the force of air friction acting on the skydiver is approximately1. 0 N 3. 60 N2. 6 N 4. 600 N

2 243. An astronaut weighs 8.00 X 102 newtons on the surface of Earth. What is the weight of the astronaut 6.37 X 106 meters above the surface of Earth?1. 0.00 N 3. 1.60 X 103 N2. 2.00 X 102 N 4. 3.20 X 103 N

3 244. When a 12-newton horizontal force is applied to a box on a horizontal tabletop, the box remains at rest. The force of static friction acting on the box is1. 0 N 3. 12 N2. between 0 N and 12 N 4. greater than 12 N

3 245. Ball A of mass 5.0 kilograms moving at 20. meters per second collides with ball B of unknown mass moving at 10. meters per second in the same direction. After the collision, ball A moves at 10. meters per second and ball B at 15 meters per second, both still in the same direction. What is the mass of ball B?1. 6.0 kg 3. 10. kg2. 2.0 kg 4. 12 kg

4 246. A 1.5-kilogram lab cart is accelerated uniformly from rest to a speed of 2.0 meters per second in 0.50 second. What is the magnitude of the force producing this acceleration?1. 0.70 N 3. 3.0 N2. 1.5 N 4. 6.0 N

1 247. Which person has the greatest inertia?1. a 110-kg wrestler resting on a mat 3. a 70-kg long-distance runner traveling at 5 m/s2. a 90-kg man walking at 2 m/s 4. a 50-kg girl sprinting at 10 m/s

4 248. A child is riding on a merry-go-round. As the speed of the merry-go-round is doubled, the magnitude of the centripetal force acting on the child1. remains the same 3. is halved2. is doubled 4. is quadrupled

2 249. Forces A and B have a resultant R. Force A and resultant R are represented in the accompanying diagram.

Which vector best represents force B?

2 250. Which graph best represents the motion of an object that is not in equilibrium as it travels along a straight line?

4 251. Three forces act on a box on an inclined plane as shown in the accompanying diagram. [Vectors are not drawn to scale.]

If the box is at rest, the net force acting on it is equal to

1. the weight 3. friction2. the normal force 4. zero

4 252. Velocity is to speed as displacement is to1. acceleration 3. momentum2. time 4. distance

4 Velocity is the vector quantity that includes speed and direction. Displacement is the vector quantity that includes distance and direction.1 253. The diagram (see image) shows a resultant vector, R.

Which diagram best represents a pair of component vectors, A and B, that would combine to form resultant vector R?

1 When component vectors are added head-to-tail, they produce a resultant vector. The diagram (see image) shows how choice (1) produces the vector R (see image).

Wrong Choices Explained:(2) Since vectors A and B are pointing in opposite directions, they would produce a resultant of zero.(3) see image(4) see image4 254. A person is standing on a bathroom scale in an elevator car. If the scale reads a value greater than the weight of the person at rest, the elevator car could be moving1. downward at constant speed 3. downward at increasing speed2. upward at constant speed 4. upward at increasing speed4 If the person accelerates upward, a net force acts on the person in the upward direction. In this case, the force supplied by the bottom of the elevator (that is, the scale) must be greater than the person's weight. As a result of Newton's third law, the person will exert a (downward) force on the scale that is greater than the person's weight.

Wrong Choices Explained:(1), (2) Since the person is not accelerating in either case, no net force is acting on the person. As a result, the scale will read the actual weight of the person.(3) If the person is accelerating downward, the net force on the person is in the downward direction. As a result, the scale will read less than the person's weight.3 255. The diagram shows a student seated on a rotating circular platform, holding a 2.0-kilogram block with a spring scale. The block is 1.2 meters from the center of the platform. The block has a constant speed of 8.0 meters per second. [Frictional forces on the block are negligible.]

The reading on the spring scale is approximately

1. 20. N 3. 110 N2. 53 N 4. 130 N

2 256. The diagram shows a horizontal 8.0-newton force applied to a 4.0-kilogram block on a frictionless table.

What is the magnitude of the block's acceleration?

1. 0.50 m/s2 3. 9.8 m/s2

2. 2.0 m/s2 4. 32 m/s2

2 257. A 0.10-kilogram model rocket's engine is designed to deliver an impulse of 6.0 newton-seconds. If the rocket engine burns for 0.75 second, what average force does it produce?1. 4.5 N 3. 45 N2. 8.0 N 4. 80. N

1 258. The diagram shows a student seated on a rotating circular platform, holding a 2.0-kilogram block with a spring scale. The block is 1.2 meters from the center of the platform. The block has a constant speed of 8.0 meters per second. [Frictional forces on the block are negligible.]

Which statement best describes the block's movement as the platform rotates?

1. Its velocity is directed tangent to the circular path, with an inward acceleration.

3. Its velocity is directed perpendicular to the circular path, with an inward direction.

2. Its velocity is directed tangent to the circular path, with an outward acceleration.

4. Its velocity is directed perpendicular to the circular path, with an outward acceleration.

1 259. Base your answer on the information below and on the diagram shown.

The diagram shows a compressed spring between two carts initially at rest on a horizontal frictionless surface. Cart A has a mass of 2 kilograms and cart B has a mass of 1 kilogram. A string holds the carts together.

What occurs when the string is cut and the carts move apart?

1. The magnitude of the acceleration of cart A is one-half the magnitude of the acceleration of cart B.

3. The magnitude of the force exerted on cart A is one-half the magnitude of the force exerted on cart B.

2. The length of time that the force acts on cart A is twice the length of time the force acts on cart B.

4. The magnitude of the impulse applied to cart A is twice the magnitude of the impulse applied to cart B.

1 260. Base your answer on the information below and on the diagram shown.

The diagram shows a compressed spring between two carts initially at rest on a horizontal frictionless surface. Cart A has a mass of 2 kilograms and cart B has a mass of 1 kilogram. A string holds the carts together.

After the string is cut and the two carts move apart, the magnitude of which quantity is the same for both carts?

1. momentum 3. inertia2. velocity 4. kinetic energy

2 261. The displacement-time graph shown represents the motion of a cart initially moving forward along a straight line.

During which interval is the cart moving forward at constant speed?

1. AB 3. CD2. BC 4. DE

1 262. What is the approximate mass of a pencil?1. 5.0 X 10-3 kg 3. 5.0 X 100 kg2. 5.0 X 10-1 kg 4. 5.0 X 101 kg

4 263. A force vector was resolved into two perpendicular components, F1 and F2, as shown in the diagram.

Which vector best represents the original force?

4 264. The accompanying diagram shows a 50.-kilogram crate on a frictionless plane at angle theta to the horizontal. The crate is pushed at constant speed up the incline from point A to point B by force

F.

If angle theta were increased, what would be the effect on the magnitude of force F and the total work W done on the crate as it is moved from A to B?

1. W would remain the same and the magnitude of F would decrease.

3. W would increase and the magnitude of F would decrease.

2. W would remain the same and the magnitude of F would increase.

4. W would increase and the magnitude of F would increase.

2 265. Base your answer on the information and accompanying diagram.A ball is thrown horizontally with an initial velocity of 20.0 meters per second from the top of a tower 60.0 meters high.What is the horizontal velocity of the ball just before it reaches the ground? [Neglect air resistance.]

1. 9.81 m/s 3. 34.3 m/s2. 20.0 m/s 4. 68.6 m/s

3 266. Base your answer on the information and accompanying diagram.A 60.-kilogram car travels clockwise in a horizontal circle of radius 10. meters at 5.0 meters per second.The centripetal acceleration of the car at the position shown is directed toward point

1. A 3. C2. B 4. D

2 267. Base your answer on the information and accompanying diagram.A 60.-kilogram car travels clockwise in a horizontal circle of radius 10. meters at 5.0 meters per second.The magnitude of the centripetal force acting on the car is

1. 590 N 3. 30. N2. 150 N 4. 2.5 N

4 268. Which is a vector quantity?1. distance 3. power2. speed 4. force

4 269. The diagram shows a granite block being slid at constant speed across a horizontal concrete floor by a force parallel to the floor.

Which pair of quantities could be used to determine the coefficient of friction for the granite on the concrete?

1. mass and speed of the block 3. frictional force and speed of the block2. mass and normal force on the block 4. frictional force and normal force on the block

1 270. An object with an initial speed of 4.0 meters per second accelerates uniformly at 2.0 meters per second2 in the direction of its motion for a distance of 5.0 meters. What is the final speed of the object?1. 6.0 m/s 3. 14 m/s2. 10. m/s 4. 36 m/s

3 271. After a model rocket reached its maximum height, it then took 5.0 seconds to return to the

launch site. What is the approximate maximum height reached by the rocket? [Neglect air resistance.]1. 49 m 3. 120 m2. 98 m 4. 250 m

2 272. The diagram shows a student throwing a baseball horizontally at 25 meters per second from a cliff 45 meters above the level ground.

Approximately how far from the base of the cliff does the ball hit the ground? [Neglect air resistance.]

1. 45 m 3. 140 m2. 75 m 4. 230 m

2 273. A projectile is fired from a gun near the surface of Earth. The initial velocity of the projectile has a vertical component of 98 meters per second and a horizontal component of 49 meters per second. How long will it take the projectile to reach the highest point in its path?1. 5.0 s 3. 20. s2. 10. s 4. 100 s

2 274. A 70.-kilogram astronaut has a weight of 560 newtons on the surface of the planet Alpha. What is the acceleration due to gravity on planet Alpha?1. 0.0 m/s2 3. 9.8 m/s2

2. 8.0 m/s2 4. 80. m/s2

1 275. When a satellite is a distance R from the center of Earth, the force due to gravity on the satellite is F. What is the force due to gravity on the satellite when its distance from the center of Earth is 3R?1. F/9 3. F2. F/3 4. 9F

3 276. In the accompanying diagram, a box is on a frictionless horizontal surface with forces F1 and F2

acting as shown.If the magnitude of F1 is greater than the magnitude of F2, then the box is

1. moving at constant speed in the direction of F1 3. accelerating in the direction of F1

2. moving at constant speed in the direction of F2 4. accelerating in the direction of F2

2 277. Which two graphs represent the motion of an object on which the net force is zero?

3 278. The accompanying table lists the coefficients of kinetic friction for four materials sliding over steel.A 10.-kilogram block of each of these materials is pulled horizontally across a steel floor at constant velocity. Which block requires the smallest applied force to keep it moving at constant velocity?

1. aluminum 3. copper2. brass 4. steel

3 279. The magnitude of the force that a baseball bat exerts on a ball is 50. newtons. The magnitude of the force that the ball exerts on the bat is1. 5.0 N 3. 50. N2. 10. N 4. 250 N

2 280. A bullet traveling at 5.0 X 102 meters per second is brought to rest by an impulse of 50. newton•seconds. What is the mass of the bullet?1. 1.0 X 10-2 kg 3. 1.0 X 101 kg2. 1.0 X 10-1 kg 4. 2.5 X 104 kg

4 281. Which graph best represents the relationship between acceleration due to gravity and mass for

objects near the surface of Earth? [Neglect air resistance.]

2 282. What is an essential characteristic of an object in equilibrium?1. zero velocity 3. zero potential energy2. zero acceleration 4. zero kinetic energy

2 283. The accompanying diagram shows two carts that were initially at rest on a horizontal, frictionless surface being pushed apart when a compressed spring attached to one of the carts is released. Cart A has a mass of 3.0 kilograms and cart B has a mass of 5.0 kilograms.If the speed of cart A is 0.33 meter per second after the spring is released, what is the approximate speed of cart B after the spring is released?

1. 0.12 m/s 3. 0.33 m/s2. 0.20 m/s 4. 0.55 m/s

1 284. Base your answer on the information and accompanying diagram.A ball is thrown horizontally with an initial velocity of 20.0 meters per second from the top of a tower 60.0 meters high.What is the initial vertical velocity of the ball?

1. 0 m/s 3. 20.0 m/s2. 9.81 m/s 4. 60.0 m/s

4 285. Base your answer on the information and accompanying diagram.A ball is thrown horizontally with an initial velocity of 20.0 meters per second from the top of a tower 60.0 meters high.What is the approximate total time required for the ball to reach the ground? [Neglect air resistance.]

1. 12.2 s 3. 3.00 s2. 2.04 s 4. 3.50 s

2 286. What is the total displacement of a student who walks 3 blocks east, 2 blocks north, 1 block west, and then 2 blocks south?1. 0 3. 2 blocks west2. 2 blocks east 4. 8 blocks

1 287. A group of bike riders took a 4.0-hour trip. During the first 3.0 hours, they traveled a total of 50. kilometers, but during the last hour they traveled only 10. kilometers. What was the group's average speed for the entire trip?1. 15 km/hr 3. 40. km/hr2. 30. km/hr 4. 60. km/hr

4 288. A skier starting from rest skis straight down a slope 50. meters long in 5.0 seconds. What is the magnitude of the acceleration of the skier?1. 20. m/s2 3. 5.0 m/s2

2. 9.8 m/s2 4. 4.0 m/s2

2 289. An object falls freely from rest near the surface of Earth. What is the speed of the object after having fallen a distance at 4.90 meters?1. 4.90 m/s 3. 24.0 m/s2. 9.80 m/s 4. 96.1 m/s

4 290. Which two terms represent a vector quantity and the scalar quantity of the vector's magnitude, respectively?1. acceleration and velocity 3. speed and time2. weight and force 4. displacement and distance

1 291. A 4.0-kilogram rock and a 1.0-kilogram stone fall freely from rest from a height of 100 meters. After they fall for 2.0 seconds, the ratio of the rock's speed to the stone's speed is1. 1:1 3. 2:12. 1:2 4. 4:1

3 292. Two concurrent forces have a maximum resultant of 45 newtons and a minimum resultant of 5

newtons. What is the magnitude of each of these forces?1. 0 N and 45 N 3. 20. N and 25 N2. 5 N and 9 N 4. 0 N and 50. N

4 293. The accompanying diagram represents a block at rest on an incline.

Which diagram best represents the forces acting on the block? (Ff = frictional force, FN = normal force, and Fw = weight.)

4 The weight of the block (Fw) must point vertically downward. Since the block tends to slide down the plane, the frictional force (Ff) must act up the plane and parallel to it. The normal force (FN) is the "contact" force between the block and the plane; this force must be perpendicular to both the plane and the block. Of the choices given, only the force diagram given in choice (4) shows the three forces with their correct orientations.2 294. In the accompanying diagram, S is a point on a car tire rotating at a constant rate.

Which graph best represents the magnitude of the centripetal acceleration of point S as a function of time?

2 Refer to Equation ME18 on Reference Table K. As the tire rotates, neither the speed nor the radius (the distance of point S from the center of the axle) changes. Therefore, the centripetal acceleration will remain constant over time. This relationship is illustrated by the graph given in choice (2).1 295. A 1.0 × 103-kilogram car travels at a constant speed of 20. meters per second around a horizontal circular track. Which diagram correctly represents the direction of the car's velocity (v) and the direction of the centripetal force (Fc) acting on the car at one particular moment?

1 The direction of the velocity of the car will always be tangent to the circular track, while the centripetal force will always point to the center of the circle. This combination is correctly illustrated in the diagram given in choice (1).4 296. Which graph best represents the relationship between the magnitude of the electrostatic force and the distance between two oppositely charged particles?

4 See Equation EL1 on Reference Table K. The electrostatic force is inversely proportional to the square of the distance between the two charges. As the distance increases, the force between the charges decreases (and vice versa). However, neither the force nor the distance can ever be zero. According to the equation, a force of zero implies an infinite distance, and a distance of zero gives an undefined value for the force. The graph in choice (4) is the only graph to show this relationship correctly.3 297. A rock falls from rest off a high cliff. How far has the rock fallen when its speed is 39.2 meters per second? [Neglect friction.]1. 19.6 m 3. 78.3 m2. 44.1 m 4. 123 m3 The acceleration of the object is the acceleration due to gravity, 9.81 m/s2. See Reference Table A. The initial speed is 0 m/s, and the final speed is 39.2 m/s. Use Equation ME5 on Reference Table K:1 298. A rocket initially at rest on the ground lifts off vertically with a constant acceleration of 2.0 × 101 meters per second2. How long will it take the rocket to reach an altitude of 9.0 × 103 meters?1. 3.0 × 101 s 3. 4.5 × 102 s2. 4.3 × 101 s 4. 9.0 × 102 s1 The initial speed of the rocket is 0 m/s, the acceleration of the rocket is 2.0 × 101 m/s2, and the distance traveled by the rocket is 9.0 × 103 m. Use Equation ME4 on Reference Table K: