# Work, Energy & Momentum Homework Packet Worksheet 1: This is a lot of work!

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1 Work, Energy & Momentum Homework Packet Worksheet 1: This is a lot of work! 1. A student holds her 1.5-kg psychology textbook out of a second floor classroom window until her arm is tired; then she releases it. a. How much work is done on the book by the student in simply holding it out the window? b. How much work is done by the force of gravity during the time it falls 3.0 m? 2. You are carrying a backpack across campus. What is the work done by your vertical-carrying force on the backpack? Explain. 3. A 500. kg light-weight helicopter ascends from the ground with an acceleration of 2.00 m/s 2. Over a 5.00 sec interval, what is a. The distance the helicopter traveled? b. The work done by the lifting force? c. The work done by the gravitational force? d. The net work done on the helicopter? 4. A 0.75-kg block slides with a uniform velocity down a 20.0 o inclined plane of horizontal length 1.2 m, as shown. a. Calculate the length of the ramp. b. How much work is done by the force of friction on the block as it slides the total length of the plane? c. What is the net work done on the block? (Explain/show work) L = 1.2m θ 5. (Challenge Problem) A worker pulls a 40.0-kg crate with a rope at the 30.0 o angle to the horizontal. The coefficient of sliding friction between the crate and the floor is If he moves the crate with a constant velocity a distance of 7.00 m, how much work does the worker do on the crate? (hint: make 2 equations for 2 unknowns) KINETIC ENERGY & THE WORK ENERGY THEOREM 6. You want to decrease the kinetic energy of an object by as much as you can. You can do so by reducing the mass by half or reducing the speed by half. Which should you do and why? 7. A 1200-kg automobile travels at 90.0 km/h. a. What is its kinetic energy? b. What net work would be required to bring it to a stop? 8. A 2.5 g bullet traveling at 350 m/s hits a tree and slows uniformly to a stop while penetrating a distance of 12 cm into the tree s trunk. What force was exerted on the bullet in bringing it to rest? 9. An 88-g arrow is fired from a bow whose string exerts an average force of 110 N on the arrow over a distance of 78 cm. a. What is the speed of the arrow as it leaves the bow? b. How far down range will the arrow go if it is released horizontally from the bow and 1.5 m from the ground?

2 Worksheet 2: Conservation of Energy (w/ nonconservative forces) KE i + PE i = KE f + PE f 1. A 50.0 kg block at rest is dropped from a height of 20.0 m. a. Find PEi b. Find KEi c. What is the total energy of the system? d. Find PE when the block has been dropped down to the 5.0 m level. e. Find KE when the block has dropped to the 5.0 m level. f. Find the velocity when the block has dropped to the 5.0 m level. g. Find PE the instant before hitting the ground. h. Find KE the instant before hitting the ground. i. Find the velocity the instant before hitting the ground. 2. A 3.0 kg physics book at rest is accidentally dropped from the top of a very tall building (60.0 m) a. Find PEi b. Find KEi c. Find total energy of the system. d. Find PE when the book has dropped 10.0 m (not down to the 10m level) e. Find KE when the book has dropped 10.0 m f. Find the velocity when the book has dropped 10.0m g. Find the PE at the 20. m level. h. Find the KE at the 5.0 m level i. Find the velocity of the book at the 5.0 m level. Enter Nonconservative Forces: KE i + PE i + E added = KE f + PE f + E lost 3. A 4.0 kg block initially at rest is pushed on a level, frictionless surface with a constant force of 10. N for 6.0 m a. Find the speed of the block at 6.0 m b. Find the speed of the block at 2.0 m 4. A 20. kg crate at rest on a 10. m high ramp, requires a 100. J push to get it moving down the ramp. The ramp and crate experience 20. J of friction. What is the kinetic energy of the block at the bottom of the ramp? 5. A 5.0 kg block, initially at rest, slides down a 30.0 o ramp with a constant frictional force of 2.0 N. The top of the ramp is 6.0 m vertically from the bottom. a. How much energy does the block loose because of friction? b. How fast is the block going when it reaches the bottom? 6. Block A and block B have masses of 4.0 kg each. Block A is dropped from a 15 m building and block B slides down a frictionless ramp from the top of the same building. a. Which block is going fastest at the bottom? b. What is that velocity?

3 Worksheet 3: You Have the POWER 1. A 60.0 kg jogger runs, at constant velocity, up a long flight of stairs in 4.0 sec. The vertical height of the stairs is 4.5 m. a. If the only force the jogger has to overcome is her weight, calculate the jogger s power output in watts and horsepower. b. How much energy did this require? 2. A girl consumes 8.4x10 6 J (2000 food calories) of energy in one day while maintaining a constant weight. What is the average power she produces in a day? 3. Calculate the power required on a 1400 kg car while climbing a 10. o hill (a fairly steep hill) at a steady 80.0 km/h. Resistive forces on the car are 700. N. 4. A car generates 18 hp when traveling at a steady 88 km/h. a. What is the average retarding force exerted on the car? b. What are some things this force could be due to? 5. A shot putter accelerates a 7.3 kg shot from rest to 14 m/s. If this motion takes 1.5 sec, what average power was developed? 6. Does efficiency describe how fast work is done? Explain. 7. Does a more powerful machine always perform more work than a less powerful one? Explain

4 Worksheet 4: Momentum, Impulse, and Conservation of Energy Momentum and Impulse 1. A fast athlete, of mass 70. kg, can run at 10. m/s. At what speed would the following have the same momentum: a. A 20. g bullet? b. A 1500 kg car? 2. A 1.0x10 4 kg truck moves at 30. m/s. At what speed would a 1200 kg car have the same value of a. linear momentum? b. kinetic energy? 3. A ball of mass kg is dropped from rest from a height of 1.25 m. It rebounds from the floor to reach a height of m. What impulse was given to the ball by the floor? 4. A 0.10 kg ball is thrown straight up into the air with an initial speed of 15 m/s. Find the momentum of the ball a. at it s maximum height? b. halfway to its maximum height? 5. A pitcher claims he can throw a kg baseball with as much momentum as a 3.00 g bullet moving with a speed of 1500 m/s. a. What is the baseball s speed if the pitcher s claim is valid? b. Which has greater kinetic energy, the ball or the bullet? Explain. 6. A 3.0 kg steel ball strikes a massive wall at 10.0 m/s at an angle of 60. o with the plane of the wall. If bounces off the wall with the same speed and angle. If the ball is in contact with the wall for 0.20 s, what is the average force exerted by the wall on the ball? Conservation of Energy 7. A 20 kg child starts from rest and reaches 4 m/s at the bottom of a 20 o slide of length 4 m. What is the coefficient of kinetic friction? 8. A 60 g tennis ball thrown vertically up at 24 m/s rises to a maximum height of 26 m. What was the work done by resistive forces? 9. A 0.30 kg block is pushed against a spring (k = 8 N/m) thereby compressing it by 24 cm. After it is released the lock travels a total distance of 52 cm before coming to rest. What is the coefficient of kinetic friction for the surface? 10. A 2 kg block starts from rest at an initial height of 40 cm and slides down a frictionless circular ramp. It slides for 83 cm on the horizontal surface before coming to a stop. What is the coefficient of kinetic friction?

5 Worksheet 5: Playing with Momentum 1. Kim holds a 2.0 kg air rifle loosely and fires a bullet of mass 1.0 g. The muzzle velocity of the bullet is 150 m/s. a. What is the recoil speed of the gun? b. Now the girl, with a mass of 48 kg, holds the gun tightly against her body. What is the new recoil speed? c. Why is this speed so much less then before? 2. An astronaut of mass 80. kg caries an empty oxygen tank of mass 10. Kg. He throws the tank away from himself with a speed of 2.0 m/s. With what speed does he start to move off into space? 3. In a freight yard, a train is being put together from freight cars. An empty freight car, coasting at 10. m/s strikes a loaded car that is stationary, and the cars couple (stick) together. Each of the cars has a mass of 3.0 x 10 3 kg when empty, and the loaded car contains 12,000 kg of canned soda (a year s supply for the physics class). Which what speed does the combination of the two cars move? 4. A tennis player returns a 30. m/s serve straight back at 25 m/s after making contact with the ball for 0.50 sec. If the ball has a mass of 0.20 kg, what is the force she exerted on the ball? 5. Two students are fighting with snowballs. Each throws a snowball in such a way that the two balls collide inelastically. Snowball A is 1.0 kg and snowball B is 7.0 x 10 2 g. Each snowball has a speed of 12 m/s. What is the speed and direction of the combined snow mass? 6. As the snowball fight continues, one 70. kg student launches the other 70. kg student across the frozen frictionless pond at 8.0 m/s towards a tree on the other side. The sliding student goes through a snowman which reduces his speed to 3.0 m/s. a. What is the change in momentum for the sliding student? b. If it takes the student 0.30 seconds to go through the snowman, what is the average force applied by the snowman? c. If it takes just 0.10 seconds to stop at the tree, what is the average force experienced by the previously sliding student? 7. One of the student s mom sees them fighting and tells them to hug and say they are sorry. Student A skating at 5.0 m/s east is caught in a bear hug by student B who is skating 8.0 m/s north. a. What is the final velocity and direction of the hugging students? b. Together the two boys slide 4.2 m before coming to a rest. What is the coefficient of friction of the ice?

6 Worksheet 6: Mixed Review - Energy & Momentum 1. A 150-g baseball reaches a batter with a speed of 25 m/s. After it has been struck, it leaves the bat at 35 m/s in the opposite direction. If the ball was in contact with the bat for.001 s, find the average force exerted on it during this period. (9 kn) 2. A 30.0 kg girl who is running at 3.0 m/s jumps on a stationary 10.0 kg sled on a frozen lake. How fast does the sled then move? (2.3 m/s) 3. A 0.5 kg stone moving north at 4 m/s collides with a 4 kg lump of clay moving west at 1 m/s. The stone becomes embedded in the clay. What is the velocity of the composite body after the collision? (1 m/s) 4. A 1.0 kg block, starting from 5.0 m high slides without friction down the slope as shown. At the bottom, it collides inelastically with a 5.0 kg block that is initially at rest. To what height (h) will the two block combo slide up the slope? (0.14m) 5m h 5. A kg bullet traveling at 300. m/s hits a 5.0 kg block of wood and becomes imbedded in the block. The block then slides without friction into a spring. If the spring is compressed.25 m, calculate its spring constant. (65,000 N/m) 6. A 20.0 kg block moving at 5.0 m/s hits a stationary 5.0 kg bock. The stick together and hit a spring with a spring constant of 200. N/m. How far is the spring compressed? (1.4 m) 7. A 5.0 kg football hits is caught by a 55 kg kid. Knocked off balanced by the catch, the kid then falls and slides down a frictionless 1.0 m tall hill. At the bottom of the hill, the kid slides 1.4 m on the pavement, where the coefficient of kinetic friction is How fast was the football initially thrown? (12m/s; answers may vary depending on rounding) 8. A 20. kg crate at rest on a 10. m high ramp, requires a 100. J push to get it moving down the ramp. The ramp and crate experience 20. J of friction. What is the kinetic energy of the block at the bottom of the ramp? (2.0x10 3 J) 9. A worker pulls a 40.0-kg crate with a rope at the 30.0 o angle to the horizontal. The coefficient of sliding friction between the crate and the floor is If he moves the crate with a constant velocity a distance of 7.00 m, how much work does the worker do on the crate? (1150J) 10. A 35 g superball hits a wall at 10.0 m/s. If bounces off the wall with a speed of 8.0 m/s and the ball is in contact with the wall for 0.20 s, what is the average force exerted by the wall on the ball? (3.2 N) 11. A 2.5 kg block starts from rest at an initial height of 35 cm and slides down a frictionless circular ramp. It slides for 83 cm on a horizontal friction-filled surface before coming to a stop. What is the coefficient of kinetic friction? (0.42) 12. A 70. kg skier is pulled 60. m up a 30. degree frictionless slope at 2.0 m/s. How much work is done & what is the power of the motor? (21,000 J; 690 W)

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