a b c d g not - Angelfirelists the length (l) of the pendulum in meters and the square of the period (T2) of the pendulum in seconds2. a On a separate piece of graph paper, plot the

Test2-Per-Grav-Kep TEACHER ANSWER KEY January 20, 2004

'see explanation below' 1. Please Note: Parts a, b, c and d of this question are actually 4 consecutive questions on a Regents exam that needed to be grouped together as one here. Base your answers on the following information and accompanying table. In an experiment, a student measured the length and period of a simple pendulum. The data table lists the length (l) of the pendulum in meters and the square of the period (T2) of the pendulum in seconds2. a On a separate piece of graph paper, plot the data points for the square of period versus length. [1] b Draw the best-fit straight line. [1] c Using your graph, determine the time in seconds it would take this pendulum to make one complete swing if it were 0.200 meter long. [1] d The period of a pendulum is related to its length where g, in the accompanying formula, represents the acceleration due to gravity. Explain how the graph you have drawn could be used to calculate the value of g. [You do not need to perform any actual calculations.] [1]

1 2. Which orbit diagram best represents the relative motion of the planet Saturn and the Sun? [Points F1 and F2 represent foci.]

2 3. The comet Hyakutake, seen in the Earth's sky this year, will take more than 10,000 years to complete its orbit. Which object is at a focus of the comet's orbit?

1. Earth 3. Moon

2. Sun 4. Jupiter

No Explanation Available.

3 4. Which diagram best represents the orbit of the planet Pluto around the Sun?


2 5. As the distance between the Moon and the Earth increases, the Moon's orbital speed

1. decreases 3. remains the same

2. increases


4 6. Base your answer to the following question on the diagram which represents the orbit of a comet about the Sun. At which position in its orbit is the comet's speed greatest?

1. A 3. C

2. B 4. D

3 7. The diagram represents the path taken by the planet P as it moves in an elliptical orbit around sun S. The time it takes to go from point A to point B is , and from point C to point D is. If the two shaded areas are equal, then is

1. less than t2 3. the same as t2

2. greater than t2


3 8. The accompanying diagram shows four different locations of a satellite in its elliptical orbit about Earth. At which location is the magnitude of the satellite's velocity greatest?

1. A 3. C

2. B 4. D

4 9. Which statement is consistent with Kepler's laws of planetary motion?

1. The planets move at a constant speed around the Sun.

3. The more massive the planet, the slower the planet moves around the Sun.

2. The speed of a planet is directly proportional to the radius of the path of motion.

4. An imaginary line from a planet to the Sun sweeps out equal areas in equal time intervals.

1 10. What is the magnitude of the gravitational force between an electron and a proton separated by a distance of 1.0 X 10-10 meter?

1. 1.0 X 10-47 N 3. 1.0 X 10-37 N

2. 1.5 X 10-46 N 4. 1.5 X 10-36 N

3 11. A 3.0-kilogram mass weighs 15 newtons at a given point in the Earth's gravitational field. What is the magnitude of the acceleration due to the gravity at this point?

1. 45 m/s2 3. 5.0 m/s2

2. 9.8 m/s2 4. 0.20 m/s2


2 12. As the mass of a body increasess, its gravitational force of attraction on the Earth


2. increases


4 13. The magnitude of the gravitational force between two objects is 20. newtons. If the mass of

each object were doubled, the magnitude of the gravitational force between the objects would be

1. 5.0 N 3. 20. N

2. 10. N 4. 80. N


1 14. The gravitational force of attraction between two objects would be increased by

1. doubling the mass of both objects, only 3. doubling the mass of both objects and doubling the distance between the objects

2. doubling the distance between the objects, only

4. doubling the mass of one object and doubling the distance between the objects

2 15. Spacecraft S is traveling from planet P1 toward planet P2. At the position shown, the magnitude of the gravitational force of planet P1 on the spacecraft is equal to the magnitude of the gravitational force of planet P2 on the spacecraft. As the spacecraft moves from the position shown toward planet P2, the ratio of the gravitational force of P2 on the spacecraft to the gravitational force of P1 on the spacecraft will

1. decrease 3. remain the same

2. increase


3 16. What is the magnitude of the gravitational force between two 5.0-kilogram masses separated by a distance of 5.0 meters?

1. 5.0 X 100 N 3. 6.7 X 10-11 N

2. 3.3 X 10-10 N 4. 1.3 X 10-11 N

4 17. In an automobile collision, a 44-kilogram passenger moving at 15 meters per second is brought

to rest by an air bag during a 0.10-second time interval. What is the magnitude of the average force exerted on the passenger during this time?

1. 440 N 3. 4400 N

2. 660 N 4. 6600 N

1 18. The radius of Mars is approximately one-half the radius of Earth, and the mass of Mars is approximately one-tenth the mass of Earth. Compared to the acceleration due to gravity on the surface of Earth, the acceleration due to gravity on the surface of Mars is (note that this question has only three choices)

1. smaller 3. the same

2. larger

4 19. A 4.0 kilogram model airplane travels in a horizontal circular path of radius 12 meters at a constant speed of 6.0 meters/second. If the speed of the aiplane is doubled and the radius of the path remains unchanged, the magnitude of the centripetal force acting on the airplane would be

1. half as much 3. one-fourth as much

2. twice as much 4. four times as much


3 20. A convertible car with its top down is traveling at constant speed around a circular track, as shown in the diagram. When the car is at point A, if a passenger in the car throws a ball straight up, the ball could land at point

1. A 3. C

2. B 4. D


4 21. The diagram shows a 5.0 kilogram cart traveling clockwise in a horizontal circle of radius 2.0 meters at a constant speed of 4.0 meters/second. At the position shown, the velocity of the cart is directed toward point

1. P 3. R

2. Q 4. S


2 22. The diagram shows a 5.0 kilogram cart traveling clockwise in a horizontal circle of radius 2.0 meters at a constant speed of 4.0 meters/second. At the position shown, the centripetal acceleration of the cart is directed toward point

1. P 3. R

2. Q 4. S


1 23. The diagram shows a 5.0 kilogram cart traveling clockwise in a horizontal circle of radius 2.0 meters at a constant speed of 4.0 meters/second. If the mass of the cart was doubled, the maginitude of the centripetal acceleration of the cart would be

1. unchanged 3. halved

2. doubled 4. quadrupled


3 24. The diagram shows a 5.0 kilogram cart traveling clockwise in a horizontal circle of radius 2.0 meters at a constant speed of 4.0 meters/second. What is the maginitude of the centripetal force acting on the cart?

1. 8.0 N 3. 40 N

2. 20 N 4. 50 N


3 25. A 60.-kilogram adult and a 30.-kilogram child are passengers on a rotor ride at an amusement park. When the rotating hollow cylinder reaches a certain constant speed, v, the floor moves downward. Both passengers stay "pinned" against the wall of the rotor, as shown in the diagram.Compared to the magnitude of the acceleration of the adult, the magnitude of the acceleration of the child is

1. less 3. the same

2. greater


2 26. A satellite is moving at a constant speed in a circular orbit about the Earth, as shown in the diagram. The net force acting on the satellite is directed toward point

1. A 3. C

2. B 4. D


2 27. A vehicle travels at a constant speed of 6.0 meters per second around a horizontal circular curve with a radius of 24 meters.The mass of the vehicle is 4.4 x 103 kilograms.An icy patch is located at P on the curve.What is the magnitude of the frictional force that keeps the vehicle on its circular path?

1. 1.1 x 103 N 3. 4.3 x 104 N

2. 6.6 x 103 N 4. 6.5 x 104 N


1 28. As a cart travels around a horizontal circular track, the cart must undergo a change in

1. velocity 3. speed

2. inertia 4. weight

1 29. The diagram shows a satellite of mass m orbiting Earth in a circular path of radius R.

3 30. Base your answer on the diagram which shows a 2.0-kilogram model airplane attached to a wire. The airplane is flying clockwise in a horizontal circle of radius 20. meters at 30. meters per second. What is the magnitude of the centripetal acceleration of the airplane?

1. 0 m/s2 3. 45 m/s2

2. 1.5 m/s2 4. 90. m/s2


2 31. Base your answer on the diagram which shows a 2.0-kilogram model airplane attached to a wire. The airplane is flying clockwise in a horizontal circle of radius 20. meters at 30. meters per second. If the wires breaks when the airplane is at the position shown, the airplane will move toward point

1. A 3. C

2. B 4. D


2 32. A motorcycle travels around a flat circular track. If the speed of the motorcycle is increased, the force required to keep it in the same circular path


2. increases


3 33. Base your answer on the following information and the accompanying diagram. A 1.00 × 103-kilogram car is driven clockwise around a flat circular track of radius 25.0 meters. The speed of the car is a constant 5.00 meters per second. Which factor, when doubled, would produce the greatest change in the centripetal force acting on the car?

1. mass of the car 3. velocity of the car

2. radius of the track 4. weight of the car

1 34. Base your answer on the following information and the accompanying diagram. A 1.00 × 103-kilogram car is driven clockwise around a flat circular track of radius 25.0 meters. The speed of the car is a constant 5.00 meters per second. At the instant shown in the diagram, the car's centripetal acceleration is directed

1. toward E 3. toward W

2. toward N 4. clockwise

3 35. Base your answer on the information given and diagram shown. A 1200-kilogram car traveling at a constant speed of 9.0 meters per second turns at an intersection. The car follows a horizontal circular path with a radius of 25 meters to point P. The magnitude of the centripetal force acting on the car as it travels around the circular path is approximately

1. 1.1 X 104 N 3. 3.9 X 103 N

2. 1.2 X 104 N 4. 4.3 X 102 N

2 36. An amusement park ride moves a rider at a constant speed of 14 meters per second in a horizontal circular path of radius 10. meters. What is the rider's centripetal acceleration in terms of g, the acceleration due to gravity?

1. 1g 3. 3g

2. 2g 4. 0g

1 37. An athlete in a hammer-throw event swings a 7.0-kilogram hammer in a horizontal circle at a constant speed of 12 meters per second. The radius of the hammer's path is 2.0 meters. At the position shown, the centripetal force acting on the hammer is directed toward point

1. A 3. C

2. B 4. D

3 38. An athlete in a hammer-throw event swings a 7.0-kilogram hammer in a horizontal circle at a constant speed of 12 meters per second. The radius of the hammer's path is 2.0 meters. What is the magnitude of the centripetal acceleration of the hammer?

1. 6.0 m/s2 3. 72 m/s2

2. 24 m/s2 4. 500 m/s2

2 39. An athlete in a hammer-throw event swings a 7.0-kilogram hammer in a horizontal circle at a constant speed of 12 meters per second. The radius of the hammer's path is 2.0 meters. If the hammer is released at the position shown, it will travel toward point

1. A 3. C

2. B 4. D

1 40. The diagram shows the elliptical orbit of a comet around the Sun.

1. A 3. C

2. B 4. D

3 41. A 4.0 kilogram model airplane travels in a horizontal circular path of radius 12 meters at a constant speed of 6.0 meters/second. At the position shown, what is the direction of the net force acting on the airplane?

1. north 3. east

2. south 4. west


Documents

a b c d g not - Angelfirelists the length (l) of the pendulum in meters and the square of the period (T2) of the pendulum in seconds2. a On a separate piece of graph paper, plot the