# Energy and Momentum Review Problems

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1 Energy and Momentum Review Problems NAME 1. In which one of the following situations is zero net work done? A) A ball rolls down an inclined plane. B) A physics student stretches a spring. C) A projectile falls toward the surface of Earth. D) A box is pulled across a rough floor at constant velocity. E) A child pulls a toy across a rough surface causing it to accelerate. 2. An elevator supported by a single cable descends a shaft at a constant speed. The only forces acting on the elevator are the tension in the cable and the gravitational force. Which one of the following statements is true? A) The magnitude of the work done by the tension force is larger than that done by the gravitational force. B) The magnitude of the work done by the gravitational force is larger than that done by the tension force. C) The work done by the tension force is zero joules. D) The work done by the gravitational force is zero joules. E) The net work done by the two forces is zero joules. 3. A block is dropped from a high tower and is falling freely under the influence of gravity. Which one of the following statements is true concerning this situation? Neglect air resistance. A) As the block falls, the net work done by all of the forces acting on the block is zero joules. B) The kinetic energy increases by equal amounts over equal distances. C) The kinetic energy of the block increases by equal amounts in equal times. D) The potential energy of the block decreases by equal amounts in equal times. E) The total energy of the block increases by equal amounts over equal distances. 4. A concrete block is pulled 7.0 m across a frictionless surface by means of a rope. The tension in the rope is 40 N; and the net work done on the block is 247 J. What angle does the rope make with the horizontal? 5. A 5.00-kg block of ice is sliding across a frozen pond at 2.00 m/s. A 7.60-N force is applied in the direction of motion. After the ice block slides 15.0 m, the force is removed. The work done by the applied force is? 6. Larry's gravitational potential energy is 1870 J as he sits 2.20 m above the ground in a sky diving airplane before it takes off. What is Larry's gravitational potential energy when he begins to jump from the airplane at an altitude of 923 m?

2 For #7 and 8. A 2.0-kg projectile is fired with initial velocity components v ox = 30 m/s and v oy = 40 m/s from a point on the earth's surface. Neglect any effects due to air resistance. 7. What is the kinetic energy of the projectile when it reaches the highest point in its trajectory? 8. How much work was done in firing the projectile? 9. How much power is needed to lift a 75-kg student vertically upward at a constant speed of 0.33 m/s? 10. An engineer is asked to design a playground slide such that the speed a child reaches at the bottom does not exceed 6.0 m/s. Determine the maximum height that the slide can be. 11. Jennifer is walking at 1.22 m/s. If Jennifer weighs 552 N, what is the magnitude of her momentum? 12. A projectile is launched with a momentum of 200 kg m/s and 1000 J of kinetic energy. What is the mass of the projectile? 2

3 13. A stationary bomb explodes in space breaking into a number of small fragments. At the location of the explosion, the net force due to gravity is zero newtons. Which one of the following statements concerning this event is true? A) Kinetic energy is conserved in this process. B) All of the fragments must have equal kinetic energies. C) The sum of the kinetic energies of the fragments must be zero. D) The vector sum of the linear momenta of the fragments must be zero. E) The mass of any one fragment must be equal to the mass of any other fragment. 14. In which one of the following situations is linear momentum not conserved? A) A bomb suspended by a string explodes into one hundred fragments. B) A bowling ball collides with a set of ten pins. C) A golf ball is struck by a club. D) An astronaut floating in space throws a hammer away and subsequently moves in the opposite direction. E) A tree limb is struck by lightning and falls to the ground. 15. Two objects constitute an isolated system. In an elastic collision between the two objects, which one of the following statements is a false statement? A) The total kinetic energy is conserved. B) The kinetic energy of each object is the same before and after the collision. C) The total momentum is conserved. D) The magnitude of the force exerted by each object on the other object is equal. E) The total kinetic energy before the collision is equal to the total kinetic energy after the collision. 16. A 100-kg cannon at rest contains a 10-kg cannon ball. When fired, the cannon ball leaves the cannon with a speed of 90 m/s. What is the recoil speed of the cannon? 17. While on an interplanetary mission, a 58.5-kg astronaut is floating toward the front of her ship at 0.15 m/s, relative to the ship. She wishes to stop moving, relative to the ship. She decides to throw away the 2.50-kg book she's carrying. What should the approximate speed and direction of the book be to achieve her goal? 18. A 3.0-kg cart moving to the right with a speed of 1.0 m/s has a head-on collision with a 5.0-kg cart that is initially moving to the left with a speed of 2.0 m/s. After the collision, the 3.0-kg cart is moving to the left with a speed of 1.0 m/s. What is the final velocity of the 5.0-kg cart? 3

4 19. A 50.0-kg boy runs at a speed of 10.0 m/s and jumps onto a cart as shown in the figure. The cart is initially at rest. If the speed of the cart with the boy on it is 2.50 m/s, what is the mass of the cart? 20. In the game of billiards, all the balls have approximately the same mass, about 0.17 kg. In the figure, the cue ball strikes another ball such that it follows the path shown. The other ball has a speed of 1.5 m/s immediately after the collision. What is the speed of the cue ball after the collision? 21. A physics student shoves a 0.50-kg block from the bottom of a frictionless 30.0 inclined plane. The student performs 4.0 J of work and the block slides a distance s along the incline before it stops. Determine the value of s. 4

5 22. A 45kg boy is standing on a 2.0kg skateboard which is at rest on the ground. The boy jumps off the front of the skateboard with a horizontal speed of 0.50 m/s. What is the maximum possible speed of the skateboard? Which way does it move? 23. The graph shows the force component along the displacement as a function of the magnitude of the displacement. Determine the work done by the force during the interval from 2 to 10 m. 24. A 7.30-kg bowling ball strikes a 1.60-kg pin at rest head-on. Before the collision, the velocity of the ball is m/s. After the collision, the velocity of the ball is m/s. What is the velocity of the pin after the collision? 25. A 2.5-kg ball and a 5.0-kg ball have an elastic collision. Before the collision, the 2.5-kg ball was at rest and the other ball had a speed of 3.5 m/s. What is the kinetic energy of the 2.5-kg ball after the collision? 5

6 26. A tennis player returns a 30 m/s serve straight back at 25m/s, after making contact with the ball for 0.50 s. The ball has a mass of 0.20 kg. How much force does the racket exert on the ball? 27. You pull a 15.0 kg crate up a ramp with a 30 o incline at constant speed. How much work do you have to do to move the crate 4.0 m? There is friction ( = 0.2). 28. A dam is used to block the passage of a river and to generate electricity. Approximately kg of water fall each second through a height of 19.6 m. If 85 % of the gravitational potential energy of the water were converted to electrical energy, how much power would be generated? 6

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