#### Transcript Physics 111 Problem Set 8, Chapter 9

Physics 111 Practice Problem Solutions 08 Linear Momentum, Collisions, Systems of Particles SJ 8th Ed.: Chap 9.1 – 9.7 Contents (8A): 9-3, 9-4, 9-13*, 9-22, 9-27, 9-28, 9-39*, 9-40, 9-46, 9-54 Contents (8B) 10-2, 10-5, 10-8*, 10-14P, 10-20E, 10-33, 10-35*, 10-39, 10-40, 10-49*, 10-52 • • • • • • • New Concepts - Overview Linear Momentum, Isolated and Non-Isolated systems Newton’s Second Law in terms of the Momentum Conservation of Linear Momentum Impulse-Momentum Theorem What is a Collision? Momentum and Kinetic Energy in Collisions – – – • Center of Mass – • 8/8/2011 Inelastic Collisions in One Dimension Elastic Collisions in One Dimension Collisions in Two Dimensions Systems of Particles & Solid Bodies Linear Momentum for a System of Particles – – Newton’s Second Law for a System Momentum Conservation Problem 9 - 3E: What are (a) the x coordinate and (b) the y coordinate of the center of mass of the three-particle system shown in the figure? (c) What happens to the center of mass as the mass of the topmost particle is gradually increased? 8/8/2011 Problem 9 - 4E: Three thin rods, each of length L, are arranged in an inverted U, as shown in the figure. The two rods on the arms of the U each have mass M; the third rod has mass 3M. Where is the center of mass of the assembly? 8/8/2011 Problem 9 – 13P*: A stone is dropped at t = 0. A second stone, with twice the mass of the first, is dropped from the same point at t = 100 ms. (a) How far below the release point is the center of mass of the two stones at t = 300 ms? (Neither stone has yet reached the ground.) (b) How fast is the center of mass of the two-stone system moving at that time? 8/8/2011 Problem 9 – 22E: A 0.70 kg ball is moving horizontally with a speed of 5.0 m/s when it strikes a vertical wall. The ball rebounds with a speed of 2.0 m/s. What is the magnitude of the change in linear momentum of the ball? 8/8/2011 Problem 9 – 27E: A 91 kg man lying on a surface of negligible friction shoves a 68 g stone away from him, giving it a speed of 4.0 m/s. What velocity does the man acquire as a result? 8/8/2011 Problem 9 – 28E: Two blocks of masses 1.0 kg and 3.0 kg are connected by a spring and rest on a frictionless surface. They are given velocities toward each other such that the 1.0 kg block travels initially at 1.7 m/s toward the center of mass, which remains at rest. What is the initial velocity of the other block? 8/8/2011 Problem 9 – 39P*: A vessel at rest explodes, breaking into three pieces. Two pieces, having equal mass, fly off perpendicular to one another with the same speed of 30 m/s. The third piece has three times the mass of each other piece. What are the magnitude and direction of its velocity immediately after the explosion? 8/8/2011 Problem 9 – 40P: An 8.0 kg body is traveling at 2.0 m/s with no external force acting on it. At a certain instant an internal explosion occurs, splitting the body into two chunks of 4.0 kg mass each. The explosion gives the chunks an additional 16 J of kinetic energy. Neither chunk leaves the line of original motion. Determine the speed and direction of motion of each of the chunks after the explosion. 8/8/2011 Problem 9 – 46E: A railroad car moves at a constant speed of 3.20 m/s under a grain elevator. Grain drops into it at the rate of 540 kg/min. What is the magnitude of the force needed to keep the car moving at constant speed if friction is negligible? 8/8/2011 Problem 9 – 54E*: An automobile with passengers has weight 16,400 N and is moving at 113 km/h when the driver brakes to a stop. The frictional force on the wheels from the road has a magnitude of 8230 N. Find the stopping distance. Modification: Find the stopping time. 8/8/2011 Problem 9 – 54E* Continued: Find the stopping time. 8/8/2011 PROBLEM 10-2: The National Transportation Safety Board is testing the crash-worthiness of a new car. The 2300 kg vehicle, moving at 15 m/s, is allowed to collide with a bridge abutment, which stops it in 0.56 s. What is the magnitude of the average force that acts on the car during the impact? 8/8/2011 PROBLEM 10-5: A force that averages 1200 N is applied to a 0.40 kg steel ball moving at 14 m/s in a collision lasting 27 ms. If the force is in a direction opposite the initial velocity of the ball, find the final speed and direction of the ball. 8/8/2011 PROBLEM 10-8*: Bullets and other missiles fired at Superman simply bounce off his chest (Fig. 1027). Suppose that a gangster sprays Superman's chest with 3 g bullets at the rate of 100 bullets/min, and the speed of each bullet is 500 m/s. Suppose too that the bullets rebound straight back with no change in speed. What is the magnitude of the average force on Superman's chest from the stream of bullets? 8/8/2011 PROBLEM 10-14P The figure shows an approximate plot of force magnitude versus time during thecollision of a 58 g Superball with a wall. The initial velocity of the ball is 34 m/s perpendicular to the wall; it rebounds directly back with approximately the same speed, also perpendicular to the wall. What is Fmax, the maximum magnitude of the force on the ball from the wall during the collision? 8/8/2011 PROBLEM 10-20: A 5.20 g bullet moving at 672 m/s strikes a 700 g wooden block at rest on a frictionless surface. The bullet emerges, traveling in the same direction with its speed reduced to 428 m/s. (a) What is the resulting speed of the block? (b) What is the speed of the bullet–block center of mass? 8/8/2011 8/8/2011 8/8/2011 8/8/2011 8/8/2011 8/8/2011 8/8/2011