A.P. Physics – 1

Unit 3

Work, Energy, & Momentum In-Class Example Problems

Work:

Fapp = 20N

35o

1. A 3kg block is sliding across a frictionless surface when a 20N applied force begins to act, as shown in the diagram. If the force acts as the block moves 3m to the right, calculate the work done by the applied force during the slide.

2. A 20kg block slides down a 30o incline at a constant velocity. Calculate the following, as the block slides through a distance of 2.1m down the incline. a. Work done by gravity.

b. Work done by the normal force.

c. Work done by friction.

d. Net work done on the block.

F (N) 3. The given graph shows force versus distance compressed for a pillow exerting a force on an egg in bringing it to a stop. Use the graph to calculate the work done by the pillow during the entire 15cm stopping distance.

40

20

0

d (cm) 3

9

15

Work and Kinetic Energy: 4. A 6kg block is initially sliding at 5m/s, and is later moving at 8m/s. a. Calculate the initial kinetic energy of the block.

b. Calculate the work done on the block to cause its increase in speed.

5. A 1200kg car is traveling at 18m/s when it applies its brakes. If the brakes allow friction to exert a 2000N force on the car, and the brakes are applied for 50m, how fast is the car moving when the brakes are released?

Potential Energy: 6. A 30kg mass is hung from a spring (k=200N/m), which has the effect of stretching the spring down a distance of 1.47m. a. Calculate the increase in the elastic potential energy of the spring.

b. Calculate the decrease in the gravitational potential energy of the mass.

Energy Conservation Basics: 7. A 3kg box is given a push up a frictionless incline, such that its initial speed is 8.6m/s. What is the maximum height that the box reaches above the incline’s base?

8. A ball is dropped from a rooftop that is 12 meters above the ground. How fast is the ball moving when it reaches a point only 3 meters above the ground?

Spring Energy Conservation: 9. A 230g block is attached to the end of a horizontal spring of negligible mass and spring constant 1900N/m. The spring is stretched back from equilibrium by a distance of 35cm and released from rest. What is the speed of the block when it has crossed through equilibrium and is now 10cm past equilibrium?

10. A vertically-oriented spring (k=2000N/m) is compressed a total of 20cm below its equilibrium position, by a 3kg block placed on top of it and also by an additional force used to get the spring ready to ‘launch’ the block. If the spring is released, calculate the launch speed of the block.

Pendulum Energy Conservation:

11. A 2.0m-long pendulum is released from rest when the support string is at an angle of 25o with the vertical. What is the speed of the pendulum bob at the bottom of its swing?

Energy Conservation with Friction: 12. A certain 3kg object is dropped from a height of 4.2 meters. If it strikes the ground with a speed of 6.5m/s, how much work is done by air resistance during the object’s fall?

13. A 5kg box is pressed against a horizontal spring (k=500N/m), compressing it 40cm from equilibrium. The spring is released from rest, pushing the box across a flat surface. If the coefficient of friction between the box and surface is 0.15, what is the speed of the box when it is measured 4 meters from the point of initial release?

Friction & Inclines & E-Conservation!

14. A boy on a sled, with a combined mass of 80kg, slides down a 34o hill that is 25m long. If the coefficient of friction between the sled and hill is 0.15, calculate the sled’s speed when it reaches the base of the hill.

Power: 15. How long will it take a 7hp motor to lift a 500kg crate upward by a distance of 4.2 meters?

16. A small motor uses a rope to pull a 3kg block up a 20o incline at a constant speed of 5.2m/s. If a frictional force of 7N impedes the block's motion, what power is required of the motor?

Momentum & Impulse: 17. A 2kg object is initially moving at 5m/s in the positive direction, and 3 seconds later it is moving at 7m/s in the negative direction. a. Calculate the initial momentum of the object.

b. Calculate the change in momentum of the object.

c. Calculate the average force that acted on the object during the 3s interval.

18. A 23 kg block is sliding across a frictionless floor at 4 m/s, when a 50 N force begins acting on it in the opposite direction of its motion. If the force acts for 2 seconds, determine the magnitude and direction of the block’s velocity after the force is done acting on it.

19. The only force acting on a 3kg object varies over time as shown in the given graph. Determine the speed of the object at the end of 10s, assuming the object started with a speed of 5 m/s at t=0s.

Force (N) 6 5 4 3 2 1 0

0 1 2 3 4 5 6 7 8 9 10 11

Basic Momentum Conservation: 20. A 3g marble, moving to the right at 8m/s, collides with a larger 5g marble, initially at rest. If the 3g marble is moving back to the left at 2m/s after the collision, what is the final velocity (speed and direction) of the 5g marble after the collision?

21. A 75kg man, initially at rest, throws a 750g baseball to the right at 22m/s. What is the man’s velocity (speed and direction) after he throws the ball?

Time (s)

Types of Collisions 22. A 300 gram block is sliding to the right across a frictionless floor at 4 m/s when it collides head-on with a 200 gram block that is sliding to the left at 3 m/s. After the collision, the 300 gram block is still moving to the right, but at a slower speed of 1.5 m/s. a. How fast is the 200 gram block moving after the collision?

b. Was the collision elastic or inelastic? Give specific numerical evidence.

23. A 75 kg man on ice-skates is initially standing still. But then he catches a 5 kg medicine ball that has been thrown to him, and the ball is moving at 3m/s when he catches it. How fast do the man and ball move together after the catch?

Elastic Collisions: 24. In a physics experiment, a cart with a mass of 2.5 kg is rolling to the right at some speed. The 2.5 kg cart then undergoes an elastic collision with a second cart, which is initially at rest. After the elastic collision the 2.5 kg cart is still moving to the right, at a speed that is 1/5 of its original speed. a. Write two equations that could be used to find the unknown mass of the second cart.

b. Use the two equations above to determine the mass of the second cart.

25. A block of mass M is moving to the right at a speed of 9 m/s, when it undergoes an elastic collision with a block of mass 2M, that is moving to the left at 3 m/s. After the elastic collision, both blocks are moving at new speeds. a. Write two equations that could be used to find the speeds of the blocks after the collision.

b. Use the two equations above to determine the speeds of the two blocks after the collision.

2-D Collisions 26. A 5 kg disk originally at rest is exploded apart into three pieces. A 2 kg piece moves off at 3 m/s in the positive x-direction, and a 1 kg piece moves off at 4 m/s in the negative y-direction. With what speed, and in what direction, does the third piece move?

27. As shown in the top-view diagram, a pool ball is initially rolling on a pool table at 4m/s, when it collides with an identical pool ball that is initially at rest. After the collision, the first ball is rolling at 3.6 m/s, at an angle of 27o from its original direction. In what direction, and with what speed, is the 2nd ball moving after the collision?

Before Collision

After Collision 3.6 m/s

4 m/s

27o

Multiple Steps w/Energy and Momentum! 28. Two objects, of mass 'M' and '2M' are hung next to each other from strings of the same length. The larger object is pulled back to a height 'h' and released to swing and collide with the other mass. If the larger object somehow stops due to the collision, find the max height to which the smaller object swings after the collision.

29. A 6.2g bullet is fired into a 3.1kg ballistic pendulum, where the block rises to a maximum angle of 62o from the vertical. If the length of the pendulum is 23cm, find the initial speed of the bullet.

30. A 3kg box is slid across a frictionless surface, traveling at 5.7m/s when it strikes a 7kg box, initially at rest. After the collision, the 3kg block bounces back at 1.3 m/s, and the 7kg block slides up a frictionless incline. What is the maximum height to which the 7kg block rises as it slides up the incline?