Physics 2002, Peter Orland, Spring 2014 Homework Set 5. 1. Two skaters, each of mass M are standing a slight distance apart on a nearly frictionless horizontal surface of ice (for example, a skating rink). Initially at rest, they throw a ball of mass m, back and forth between them. Each time, the ball has a speed of v (assume it travels horizontally). a. What is the velocity of the first skater immediately after she throws the ball for the first time? b. What is the velocity of the second skater, immediately after she catches the ball. c. Just after the second skater throws the ball back, for the first time, what is her velocity? d. After the ball has made 10 complete round trips, and the first skater is holding the ball, what is the velocity of each skater? What is the total momentum of the system of the two skaters and the ball? 2. A rocket of total mass M, contains fuel of mass m. Thus the rocket without any fuel would have a mass of M −m. The fuel is discharged as exhaust gasses with an average speed v (relative to the earth). How fast will the rocket be traveling when the fuel is used up? Neglect gravity and air resistance. 3. A bullet of mass m traveling with velocity v strikes and lodges in a wooden block of mass M. The block is initially at rest. a. What is the final velocity of the block and bullet after the collision? b. How much kinetic energy is lost as heat? c. Suppose the block is suspended from a vertical cable. The block will therefore swing as a pendulum, increasing its height. What is the maximum height the block will reach? 4. A ball of mass m bounces horizontally back and forth between two heavy vertical walls, each of mass M m. The separation between the walls is L and the kinetic energy of the ball is K (assume that it does not decrease, i.e. that the collisions are always elastic). Find the average force on each wall. HINTS: It will help to first answer two questions. What is the impulse given to a wall during one bounce? How many bounces occur in a given amount of time t? 5. A neutron in a reactor makes and elastic head-on collision with a carbon atom at rest. The mass of the carbon atom is roughly twelve times that of the neutron. HINT: Assume that twelve is a very large number. 1 a. What is the final kinetic energy of the nucleus? What fraction of the neutron’s kinetic energy K, is transferred to the carbon nucleus? b. What is the final kinetic energy of the neutron? 2

Physics 2002, Peter Orland, Spring 2014 Homework Set 5. 1. Two skaters, each of mass M are standing a slight distance apart on a nearly frictionless horizontal surface of ice (for example, a skating rink). Initially at rest, they throw a ball of mass m, back and forth between them. Each time, the ball has a speed of v (assume it travels horizontally). a. What is the velocity of the first skater immediately after she throws the ball for the first time? b. What is the velocity of the second skater, immediately after she catches the ball. c. Just after the second skater throws the ball back, for the first time, what is her velocity? d. After the ball has made 10 complete round trips, and the first skater is holding the ball, what is the velocity of each skater? What is the total momentum of the system of the two skaters and the ball? 2. A rocket of total mass M, contains fuel of mass m. Thus the rocket without any fuel would have a mass of M −m. The fuel is discharged as exhaust gasses with an average speed v (relative to the earth). How fast will the rocket be traveling when the fuel is used up? Neglect gravity and air resistance. 3. A bullet of mass m traveling with velocity v strikes and lodges in a wooden block of mass M. The block is initially at rest. a. What is the final velocity of the block and bullet after the collision? b. How much kinetic energy is lost as heat? c. Suppose the block is suspended from a vertical cable. The block will therefore swing as a pendulum, increasing its height. What is the maximum height the block will reach? 4. A ball of mass m bounces horizontally back and forth between two heavy vertical walls, each of mass M m. The separation between the walls is L and the kinetic energy of the ball is K (assume that it does not decrease, i.e. that the collisions are always elastic). Find the average force on each wall. HINTS: It will help to first answer two questions. What is the impulse given to a wall during one bounce? How many bounces occur in a given amount of time t? 5. A neutron in a reactor makes and elastic head-on collision with a carbon atom at rest. The mass of the carbon atom is roughly twelve times that of the neutron. HINT: Assume that twelve is a very large number. 1 a. What is the final kinetic energy of the nucleus? What fraction of the neutron’s kinetic energy K, is transferred to the carbon nucleus? b. What is the final kinetic energy of the neutron? 2