Critical thinking physics problems

CRITICAL THINKING PHYSICS PROBLEM

clas Period Name

1 CRITICAL THINKING PHYSICS PROBLEM

1. Physics Toolkit

1 A solid wheel of mass m and radius r rotates around an axis. The moment of inertia, I, of the1

wheel is given by the equation I = ————mr2.2

What is the radius of a 5.1-kg wheel with a moment of inertia of 18 kg•m 2?

(a)

a. 2.7 m

b. 7.1 m

c. 180 m

d. 130 m

(b) Which is the correct plot of I versus r for a wheel with a mass of 10 kg?

a. c.Moment of Inertia of a 10-kg Object Moment of Inertia of a 10-kg Object

120250

200 100

150 80

100 60

50 40

200 10 20 30

Radius (m)

40 50

0 10 20 30

Radius (m)

40 50

b. d.Moment of Inertia of a 10-kg Object Moment of Inertia of a 10-kg Object

12,0002500

10,0002000

80001500

60001000

4000500

20000 10 20 30 40 50

Radius (m)0 10 20 30 40 50

Radius (m)

2. Two students make a pendulum of a small ball tied onto the end of a piece of string. They set thependulum in motion and use a stopwatch to measure the time taken for one complete swing; this is the period of the pendulum. To determine how the length of the string affects the period, the students change the length, L, of the string, and measure the period, T, of the pendulum for each string length. Their measurements are given in the table on the following page.

Mom

ent

of

iner

tia

(kg

•m2)

Mo

me

nt

of

ine

rtia

(k

g•m

2)

Mom

ent

of

iner

tia

(kg

•m2)

Mo

me

nt

of

ine

rtia

(k

g•m

2)

Name

continued

a. Plot the values given in the table, draw the curve that best fits all points, and describe the curve.

One of the students decides to investigate the relationship between the string length and thesquare of the period. She uses their previous measurements to prepare the following table.

b. Plot the values given in this new table, draw the best-fit curve, and describe the curve.

c. According to the graph, what is the relationship between the square of the period of the pen-dulum and the length of the string?

d. Use the graph to write an equation relating period squared to string length.

String Length L (m) Period Squared T 2 (s2) String Length L (m) Period Squared T 2 (s2)

0.07 0.28 0.55 2.22

0.10 0.40 0.70 2.82

0.20 0.81 0.90 3.61

0.40 1.61

String Length L (m) Period T (s) String Length L (m) Period T (s)

0.07 0.53 0.55 1.49

0.10 0.63 0.70 1.68

0.20 0.90 0.90 1.90

0.40 1.27

Name

John goes for a run. From his house, he jogs north for exactly 5.0 min at an average speed of 8.0 km/h. He continues north at a speed of 12.0 km/h for the next 30.0 min. He then turns around and jogs south at a speed of 15.0 km/h for 15.0 min. Then he jogs south for another 20.0 min at 8.0 km/h. He walks the rest of the way home.

1. How many kilometers does John jog in total?

a. 3.4 km

b. 12.5 km

c. 13.1 km

d. 785 km

2. How far will John have to walk to get home after he finishes jogging?

a. 0.0 km

b. 0.25 km

c. 5.58 km

d. 15.0 km

3. Which is the correct plot of total distance as a function of time for John’s jog?

a. c.Distance v. TimeGraph of John’s

Jog

Distance v. TimeGraph of John’s

Jog

6 12

5 10

4 8

3 6

2 4

1 2

0 05 10 15 20 25

Time (min)

30 5 10 15 20 25 30

Time (min)

b. d.Distance v. Time Graph of John’s Jog Distance v. Time Graph of John’s Jog

6 12

5 10

4 8

3 6

2 4

1 2

0 010 20 30 40 50

Time (min)

60 70 10 20 30 40 50 60 70

Time (min)

Dis

tanc

e (k

m)

Dis

tanc

e (k

m)

Dis

tanc

e (k

m)

Dis

tanc

e (k

m)

2. Represent ing Motion

Name continued

4. Two drivers (driver A and driver B) are traveling in opposite directions on a long, straight road atdifferent constant velocities. Their motions are represented by the position-time graphs of each, shown below.

Position-Time Graph for Two Drivers

80604020

0—20—40—60—80

—1000 1

Time (h)

2

a. How long had driver A already been driving when driver B started to drive?

b. How long had driver A been driving when she was 30 km away from her starting point?

c. Which driver is faster?

d. What happens at point P?

Pos

itio

n (

km)

B

P

A

Name

acceleration, skidding to a complete stop in 4.5 s.1. The driver of a car traveling at 110 km/h slams on the brakes so that the car undergoes a constant

(a) What is the average acceleration of the car during braking?

a. —0.041 m/s2

b. —0.15 m/s2

c. —6.9 m/s2

d. —24 m/s2

(b) If the car skids in a straight line for the entire length of the stopping distance, how long are itsskid marks?

a. 7.0X101 m

b. 1.4X102 m

c. 2.1X102 m

d. 2.5X102 m

(c) Which is the most accurate plot of velocity versus time for the braking car?

a. c.Velocity v. Time Graph for the Braking Car Velocity v. Time Graph for the Braking Car

30 30

25 25

20 20

15 15

10 10

5 5

0 00.5 1 1.5 2 2.5 3

Time (min)

3.5 4 4.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Time (s)

b. d.Velocity v. Time Graph for the Braking Car Velocity v. Time Graph for the Braking Car

30 30

25 25

20 20

15 15

10 10

5 5

0 00.5 1 1.5 2 2.5 3 3.5 4 4.5

Time (s)

0.5 1 1.5 2 2.5 3 3.5 4 4.5

Time (s)

2. A person is standing on the roof of a tall building. She throws a ball from the top of the buildingin such a way that when the ball passes a window cleaner who is 2.0 m from the top, it is falling at a speed of 7.0 m/s. It takes another 2.9 s to reach the ground.

a. How tall is the building?

b. How fast is the ball moving when it hits the ground?

5

Ve

loci

ty (

m/s

)V

elo

city

(m

/s)

Ve

loci

ty (

m/s

)V

elo

city

(m

/s)

3. Accelerated Motion

Name

continued

3. A 0.250-kg cart moves on a straight horizontal track. The graph of velocity, v, versus time, t, for themotion of the cart is given below.

Velocity-Time Graph for Cart

0.80.60.40.20.0

—0.2—0.4—0.6—0.8—1.0

0.0 5.0 10.0 15.0 20.0

Time (s)

a. Identify every time, t, for which the cart is at rest.

b. Identify every time interval for which the speed (the magnitude of the velocity) of the cart isincreasing.

c. Determine the horizontal position, x, of the cart at t = 8.0 s if the cart is located at x = 2.0 mat t = 0 s.

d. On the axes below, sketch the graph of acceleration, a, versus time, t, for the motion of the carfrom t = 0 s to t = 25 s.

Acceleration-Time Graph for Cart

0.80.60.40.20.0

—0.2—0.4—0.6—0.8—1.0

0.0 5.0 10.0 15.0 20.0

Time (s)

Ve

loci

ty (

m/s

)

Acc

ele

ratio

n

(m/s

2 )

Name

4. Forces in One Dimension

1. Which graph best describes the movement of an object on which no net force is exerted?

a. c.

0 0Time (s) Time (s)

b. d.

0 0Time (s) Time (s)

2. The relationship between force and acceleration is

a. direct linear.

b. inverse linear.

c. direct quadratic.

d. inverse quadratic.

3. A 6.0-kg wooden block is pulled across a carpet with a force of F = 36 N. The block begins at restand accelerates to a velocity of 0.25 m/s in 0.50 s. What is the force of friction acting on the block?

a. 3.0 N

b. 33 N

c. 36 N

d. 39 N

4. A 1500-kg car can accelerate from rest to 72 km/h in 8.0 s. What is the net force acting on the carto cause this acceleration?

a. 3.8 kN

b. 14 kN

c.

d.

15 kN

240 kN

Dis

tan

ce (

m)

Acc

ele

ratio

n

(m/s

2 )

Dis

tan

ce (

m)

Acc

ele

ratio

n

(m/s

2 )

Name continued

5. A model rocket of mass 0.350 kg is launched vertically. The rocket has an engine that is ignited attime t = 0, as shown below, and the engine fires for 2.50 s, providing a thrust of 14.6 N. When the rocket reaches its maximum height, a parachute is deployed, and the rocket then descendsvertically to the ground.

Ground

t = 0 sEngine ignites

t = 2.50 sEngine shuts

down

Maximum height;parachute deploys Rocket descends

a. On the figures below, draw and label a free-body diagram for the rocket during each of thefollowing intervals:

(i) while the engineis firing

(ii) after the engine shuts down,but before the parachute is deployed

(iii) the moment the parachuteis deployed

b. Determine the magnitude of the average acceleration of the rocket while the engine is firing.

c. Determine the velocity of the rocket at the end of the period when the engine fires.

d. A person stands on a bathroom scale in a full-sized rocket that is being launched vertically.Consider the time interval when the rocket engine is firing. Is the scale reading during this time interval less than, equal to, or greater than the scale reading when the rocket is at rest? Justify your answer.

Name

5. Forces in Two Dimensions

1. Which graph most accurately describes the relationship between the force of kinetic friction and the normal force?

a. c.

FN FN

b. d.

FN FN

2. Glaciers push rocks in front of them. Before a stationary rock starts moving as a result of the forceFglacier exerted on it, the static friction between the rock and the ground

a.

b.

c.

d.

decreases until it is smaller than Fglacier.

remains constant until it is smaller than Fglacier.

increases until it is equal to the product of s s and the normal force on the rock.

decreases until it is equal to the product of s s and the normal force on the rock.

3. You are pushing a rock along level ground and making the rock speed up. How does the size ofthe force you exert on the rock compare with the size of the force the rock exerts on you? The force you exert

a.

b.

c.

d.

is larger than the force the rock exerts on you.

is the same size as the force the rock exerts on you.

is smaller than the force the rock exerts on you.

could be any of the above; it depends on other factors.

Ff,

kin

eti

cF

f, k

ine

tic

Ff,

kin

eti

cF

f, k

ine

tic

Name continued

4. How does the size of the friction force exerted by the ground on the rock in the previous problemcompare with the size of the force the rock exerts on you? The force of friction

a.

b.

c.

d.

is larger than the force the rock exerts on you.

is the same size as the force the rock exerts on you.

is smaller than the force the rock exerts on you.

could be any of the above; it depends on other factors.

5. As shown below, two blocks on an inclined plane are connected to each other by a light string,and the upper block also is connected to a hanging ball by a light string passing over a frictionless pulley of negligible mass. The ball hangs over the top edge of the inclined plane. The blocks move with a constant velocity down the inclined plane.Block 1 has a mass of m1 = 6.00 kg and block 2 has a mass of m2 = 3.00 kg. The inclined plane makes an angle of 0 = 32 .0°

with the horizontal. The coefficient of kinetic friction betweeneach block and the inclined plane is 0.124. M

0a. In the space below, draw and label a free-body diagram of

all the forces acting on block 2.

b. Determine the magnitude of the force of kinetic friction acting on block 2.

c. Determine the mass of the hanging ball, M, that enables blocks 1 and 2 to move withconstant velocity down the inclined plane.

d. If the string between blocks 1 and 2 is cut, determine the acceleration of block 2 while it ismoving on the inclined plane.

m1

m2

Name

magnitude of the initial velocity is vi, the launch angle is 0, and

the horizontal and vertical components of the initial velocity are vxi and vyi.

1. The diagram at the right shows the trajectories of two balls. The

(a) Compare the values of 0i. The value for ball A

a.

b.

c.

d.

is greater than the value for ball B.

is equal to the value for ball B.

is less than the value for ball B.

Horizontal position (m)

cannot be compared with the value for ball B using only the information given.

(b) Compare the values of vi. The value for ball A

a.

b.

c.

d.




cannot be compared with the value for ball B using only the information given.(c) Compare the values of vxi. The value for ball A

a.

b.

c.

d.




cannot be compared with the value for ball B using only the information given.(d) Compare the values of vyi. The value for ball A

a.

b.

c.

d.




cannot be compared with the value for ball B using only the information given.

2. Two balls are thrown horizontally. Ball C is thrown with a force of 20 N, and ball D is thrownwith a force of 40 N. Assuming all other factors are equal, ball D will fall toward the ground

a.

b.

c.

d.

faster than ball C.

more slowly than ball C.

at the same rate as ball C.

at a rate that cannot be compared with that of ball C using the information given.

Ve

rtic

al

po

sitio

n

(m)

A

B

6. Motion in Two Dimensions

Name continued

3. A pilot wants to fly due north a distance of 125 km. The wind is blowing out of the west at aconstant 35 km/h. If the plane can travel at 175 km/h, how long will the trip take?

4. A boy ties a 58-g tennis ball to the end ofa light string that is 65 cm long and whirls the ball above his head in a horizontal circle, as shown at right. The boy exerts a force of 5.2 N on the string to keep theball moving in a circle at a height of 1.7 m above the ground.

(a) Determine the speed of the ball.

(b) Suppose that the string breaks as the ball swings in its circular path. Describe the motion ofthe ball

(i) the instant after the string breaks.

(ii) after the string breaks but before it hits the ground.

(c) How long will it take the ball to reach the ground?

(d) How far will the ball travel horizontally before it hits the ground?

Name

7 .Gravitation

1. According to Kepler’s second law of planetary motion,

a.

b.

c.

d.

planets maintain constant speed around the Sun.

planets maintain constant acceleration around the Sun.

the speed of a planet is greatest when it is closest to the Sun.

the area swept out by the orbit per time unit keeps changing.

2. A space probe is directly between two moons of a planet. If it is twice as far from moon A as it isfrom moon B, but the net force on the probe is zero, what can be said about the relative masses of the moons?

a.

b.

c.

d.

Moon A is twice as massive as moon B.

Moon A has the same mass as moon B.

Moon A is four times as massive as moon B.

Moon A is half as massive as moon B.

The Moon is receding from Earth by approximately 3.8 cm per year. Earth’s mass is 5.98X1024 kg, and its radius is 6.38X106 m. The Moon’s mass is 7.3X1022 kg, its radius is 1.79X106 m, and its orbital period around Earth is 27.3 days. The current average distance between the two surfaces is3.85X108 m. Assume that neither body gains or loses mass and that the recession continues at a

rate of 3.8 cm per year.

3.

a. Approximately how much will the gravitational attraction between the Moon and Earth changebetween now and 499 million years from now?

b. Approximately how long, in present Earth-days, will it take the Moon to orbit Earth 499million years from now?

Name continued

4. The mean distance of the planet Neptune from the Sun is 30.05 times the mean distance of Earthfrom the Sun.

a. Determine how many Earth-years it takes Neptune to orbit the Sun.

The mass of the Sun is 1.99X1030 kg, and the closest distance of Neptune from the Sun is4.44X109 km. What is the orbital speed of Neptune in km/s at this point?

b.

c. Without doing any numerical calculations, answer the following. Is the orbital speed of Earthless than, equal to, or greater than the orbital speed of Neptune? Explain your reasoning.

d. The radius of Neptune is 3.883 times that of Earth, and the mass of Neptune is 17.147 timesthat of Earth. From the surface of which planet (Earth or Neptune) would it be easier to launch a satellite? Explain your reasoning.

Name

It has 25 cars, holds 800 passengers, and each ride lasts 30 min. The London Eye’s moment of inertia is best estimated at between

1. The London Eye is a Ferris wheel with a circumference of 424 m and a total mass of 2,100,000 kg.

a. 2X109 and 3X109 kg•m 2

b. 4X109 and 5X109 kg•m 2

c. 5X109 and 10X109 kg•m 2

d. 2X1011 and 4X1011 kg•m 2

2. In 7.0 s, a car accelerates uniformly from rest to a velocity at which its wheels are turning at6.0 rev/s.

(a) What was the angular acceleration of the car’s wheels?

a. 0.14 rad/s2

b. 0.86 rad/s2

c. 5.4 rad/s2

d. 42 rad/s2

(b) If the tires of the car have a diameter of 42 cm, and they rolled on the ground withoutslipping, how far did the car go in those 7.0 s?

a. 4.4 m

b. 28 m

c. 110 m

d. 130 m

3. Consider two wheels with fixed hubs. The hub cannot move, but the wheel can rotate about it. Thehubs are fixed to a stationary object. The hubs and spokes are massless, so that the moment of inertia of each wheel is given by I = mr2, where r is the radius of the wheel. Each wheel starts from rest and has a force applied tangentially at its rim. Wheel A has a mass of 1.0 kg, a diameter of1.0 m, and an applied force of 1.0 N. Wheel B has a mass of 1.0 kg and a diameter of 2.0 m. The two wheels undergo identical angular accelerations. What is the magnitude of the force applied to wheel B?

a. 0.13 N

b. 2.0 N

c.

d.

4.0 N

8.0 N

8. Rotational Motion

Name

continued

4. A system consists of a steal beam of mass M = 68.4 kg and length L = 1.84 m, with a 39.0-kgbrass sphere attached at the right end of the rod, as shown below.

B A

a. Determine the moment of inertia of the system for rotation about an axis through the center ofthe steel beam (axis A).

b. Determine the moment of inertia of the system for rotation about an axis through one end ofthe beam (axis B).

c. Determine the constant horizontal force, F, that must be exerted on the brass sphere in orderto produce an angular acceleration of the system such that = 2r rads. F is exerted perpendic- ular to the steel beam, and the system rotates around axis B.

d. Consider part c. If the system started from rest, determine the linear velocity of the brasssphere after the force has been applied for 4.0 s.

Name continued

4. The following collisions take place on a flat, horizontal tabletop with negligible friction.

a.

A 2.1-kg cart, A, with frictionless wheels is moving at a constant speed of 3.4 m/s to the righton the tabletop, as shown above, when it collides with a second cart, B, that is initially at rest. The force acting on cart A during the collision is shown as a function of time in the graph below, where t = 0 is the instant of initial contact. Assume that friction is negligible. Calculate the magnitude and direction of the velocity of cart A after the collision.

0.0 0.5 1.0 1.5 2.0 2.5 3.0

—2.0

—4.0

Time (ms)

b. In another experiment on the same table, an incident ball, C, of mass 0.15 kg is rolling at1.3 m/s to the right on the tabletop. It makes a head-on collision with a target ball, D, of mass0.50 kg at rest on the table. As a result of the collision, the incident ball rebounds, rolling backward at 0.80 m/s immediately after the collision. Calculate the velocity of ball D immediately after the collision. (Ignore friction in your calculations.)

c. In a third experiment on the same table, an incident ball, E, of mass 0.250 kg rolls at 5.00 m/stoward a target ball, F, of mass 0.250 kg. The incident ball rolls to the right along the x-axis, and makes a glancing collision with a target ball, F, that is at rest on the table. The velocity of incident ball E immediately after the collision is 4.33 m/s at an angle of 30.0º above the x-axis. Calculate the magnitude and direction of target ball F’s velocity immediately after the collision. (Ignore friction.)

Fo

rce

(kN

)

A B

Education

Critical thinking physics problems