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Energy and Circular Motion Exercises

Complete the following exercises.

1. A rifle with a longer barrel can fire bullets with a larger velocity than a rifle with a shorter barrel.
2. Explain this using the impulse-momentum theorem.

The force exerted on the expanding gases from the gunpowder for the long barrel is able to push for more time or has more time to be stabilized on the bullet so long as the bullet is in the barrel before hitting the resistance force hence the larger velocity.

1. Explain this using the work-energy theorem

The bullet is pushed through a longer distance hence more work is done due to the greater KE.

2. Use physics terms to explain the benefits of crumple zones in modern cars.

They help to reduce the impact of traffic collision on the car occupants against injury by controlled deformation by absorbing crash energy. The travelers have inertia when in a moving car and the crumple zones reduce the collision by balancing the speeds of the occupants and the vehicle. The crumple zones act as a cushion by absorbing the severe impact of collision and blowing some off in the form of sound and energy hence enabling the vehicle to attain a complete stop in a slow manner and exerting less pressure on the occupants hence saving lives.

3. When a gun is fired at the shooting range, the gun recoils (moves backward).

Explain this using the law of conservation of momentum.

The gun is heavier than the bullet and as it is being fired, it is forced to change the motion as it resists hence recoiling in the opposite direction so as to balance the forward momentum of the bullet and the ejector.

4. Rank the following in terms of increasing inertia:
   1. A 10,000 kg train car at rest
   2. A 100 kg person running at 5 m/s
   3. A 1200 kg car going 15 m/s
   4. A 15 kg meteor going at a speed of 1000 m/s

A.

D.

B.

C.

5. Rank the following in terms of increasing momentum:
   1. A 10,000 kg train car at rest
   2. A 100 kg person running at 5 m/s
   3. A 1200 kg car going 15 m/s
   4. A 15 kg meteor going at a speed of 1000 m/s

A.

B.

D.

C.

6. Rank the following in terms of increasing kinetic energy:
   1. A 1200 kg car going 15 m/s
   2. A 10,000 kg train car at rest
   3. A 15 kg meteor going at a speed of 1000 m/s
   4. A 100 kg person running at 5 m/s

D.

B.

A.

C.

7. Ben (55 kg) is standing on very slippery ice when Junior (25 kg) bumps into him. Junior was moving at a speed of 8 m/s before the collision and Ben and Junior embrace after the collision.  Find the speed of Ben and Junior as they move across the ice after the collision.  Give the answer in m/s.  Describe the work you did to get the answer.

Momentum dog initial = Momentum Combination after

(25×8) = (55 kg + 25 kg) v

200 = (80) v

200/80 = 80v/80

V = 2.5 m/s

To get the speed of the combination of Ben and the dog, their total mass and the speed should equal to the speed and mass of the dog alone.

8. Identical marbles are released from the same height on each of the following four frictionless ramps.

Compare the speed of the marbles at the end of each ramp. Explain your reasoning.

All the marbles have the same speed. They all have the same fall from the same height and have the same initial gravitational force hence on reaching the end of the ramp, they have equal kinetic energy hence the same speed.

9. A force of only 150 N can lift a 600 N sack of flour to a height of 0.50 m when using a lever as shown in the diagram below.
10. Find the work done on the sack of flour (in J).

W = F x D

(150 N + 600 N) x 0.50 m

= 750 x 0.50 = 375 J

1. Find the distance you must push with the 150 N force on the left side (in m).

D = W/F

375 J /150

= 2.50 m

1. Briefly explain the benefit of using a lever to lift a heavy object.

The lever magnifies effort by reducing the amount of force required to lift an object hence making the work easier.

10. Rank the following in terms of increasing power.
    1. Doing 100 J of work in 10 seconds.
    2. Doing 100 J of work in 5 seconds.
    3. Doing 200 J of work in 5 seconds.
    4. Doing 400 J of work in 30 seconds.

A.

D.

B.

C.

11. A student lifts a 25 kg mass a vertical distance of 1.6 m in a time of 2.0 seconds.
    1. Find the force needed to lift the mass (in N).

F = mass x gravity

25 kg x 9.8 m/s^2 = 245 N

1. Find the work done by the student (in J).

W = F x D

245 N x 1.6 m

= 392 J

1. Find the power exerted by the student (in W).

P = Work/Time

292/2.0

P = 146 W

12. A satellite is put into an orbit at a distance from the center of the Earth equal to twice the distance from the center of the Earth to the surface. If the satellite had a weight at the surface of 4000 N, what is the force of gravity (weight) of the satellite when it is in its orbit? Give your answer in newtons, N.

D = ½ x ½ = 1/4

¼ x 4000 = 1000 N

13. Consider a satellite in a circular orbit around the Earth.
    1. Why is it important to give a satellite a horizontal speed when placing it in orbit?

Because the horizontal speed is the tangential speed to the earth which enhances the circular motion and is necessary for compensating the downward fall.

2. What will happen if the horizontal speed is too small?

The centripetal force will be minimal hence the motion of the satellite will be at constant speed and direction.

1. What will happen if the horizontal speed is too large?

The centripetal force will increase hence accelerating the satellite which changes its direction.

14. If you drop an object from a distance of 1 meter above the ground, where would it fall to the ground in the shortest time: Atop Mt. Everest or in New York?

Atop Mt. Everest.

15. Why do the astronauts aboard the space station appear to be weightless?

Because they are in a free fall where they are not in contact with any force hence experience less effects of the gravitational force.

16. Why do the passengers on a high-flying airplane not appear weightless, similar to the astronauts on the space station?

The airplane does not fly too high such that the force of gravity cannot affect it and the speed it travels at is not fast enough to orbit the earth.

17. A ranger needs to capture a monkey hanging on a tree branch. The ranger aims his dart gun directly at the monkey and fires the tranquilizer dart.  However, the monkey lets go of the branch at exactly the same time as the ranger fires the dart.  Will the monkey get hit or will it avoid the dart?

The monkey will get hit.

The remaining questions are multiple-choice questions:

18. Compared to its weight on Earth, a 5 kg object on the moon will weigh
    1. The same amount.

B: Less

19. Compared to its mass on Earth, a 5 kg object on the moon will have
    1. The same mass.
    2. Less mass.
    3. More mass.

A: The same mass

20. The reason padded dashboards are used in cars is that they
    1. Look nice and feel good.
    2. Decrease the impulse in a collision.
    3. Increase the force of impact in a collision.
    4. Decrease the momentum of a collision.
    5. Increase the time of impact in a collision.

E: Increase the time of impact in a collision

1. Suppose you are standing on a frozen lake where there is no friction between your feet and the ice. What can you do to get off the lake?
   1. Bend over touching the ice in front of you and then bring you feet to your hands.
   2. Walk very slowly on tiptoe.
   3. Get on your hands and knees and crawl off the ice.
   4. Throw something in the direction opposite to the way you want to go.
2. Throw something in the direction opposite to the way you want to go.
3. A car travels in a circle with constant speed. Which of the following is true?
4. The net force on the car is zero because the car is not accelerating.
5. The net force on the car is directed forward, in the direction of travel.
6. The net force on the car is directed inward, toward the center of the curve.
7. The net force on the car is directed outward, away from the center of the curve.

C: The net force on the car is directed inward, toward the center of the curve.

23. A job is done slowly, and an identical job is done quickly. Which of the following is true?
    1. They require the same amount of force, but different amounts of work.
    2. They require the same amount of work, but different amounts of power.
    3. They require the same amounts of power, but different amounts of work.
    4. They require the same amounts of work, but different amounts of energy.

B: They require the same amount of work, but different amounts of power.

24. How many joules of work are done on a box when a force of 60 N pushes it 5 m in 3 seconds?
    1. 300 J
    2. 12 J
    3. 100 J
    4. 36 J
    5. 4 J

A: 300 J

25. A 1 kg cart moving with a speed of 3 m/s collides with a 2 kg cart at rest. If the carts stick together after the collision, with what speed will they move after the collision?
    1. 3 m/s
    2. 5 m/s
    3. 1 m/s
    4. 2 m/s

A: 3 m/s