10/11/11. Physics 101 Tuesday 10/11/11 Class 14" Chapter " Inelastic collisions" Elastic collisions" Center of mass"

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1 Consider the following situations and possible isolated systems: Physics 101 Tuesday Class 14" Chapter " Inelastic collisions" Elastic collisions" Center of mass" Two cars on an icy road collide. The two cars are an isolated system. One car travels on an icy road. The car is an isolated system. A car makes an emergency stop on a road. The car is an isolated system Adapted from Eric Mazur, "Peer Instruction" 1997 Consider the following situations and possible isolated systems: A ball drops to the Earth. The ball is an isolated system A billiard ball collides with another billiard ball on a pool table. The two balls are an isolated system Suppose the entire population of Earth gathers in one location and, at a pre-arranged signal, everyone jumps up. About a second later, 6 billion people land back on the ground. After the people have landed, the Earth s momentum is A) the same as before the people jumped. B) different than it was before the people jumped. C) impossible to know whether it changed. After the 6 billion people have passed the apex of their jump and are on the way down, the velocity of the Earth is A) away from the people B) toward them C) zero Adapted from Eric Mazur, "Peer Instruction"

2 Ball 1 strikes stationary Ball 2 in a 1D elastic collision. The initial momentum of Ball 1, p! 1 i, and the final momentum of Ball 2, p! 2 f, are shown on the graph. Ball 1 strikes stationary Ball 2 in a 2D elastic collision. The initial momentum of Ball 1, p! 1 i, and the final momentum of Ball 2, p! 2 f, are shown on the graph. p 2f p 1i p 2f p 1i What is the magnitude of the x-component of p! 1 f? A: 0 B: 1 C: 2 D: 3 E: None of these What is the x-component of p! 1 f? A: 0 B: 1 C: 2 C: 3 E: None of these In-elastic collisions! In-elastic collisions! 2

3 In-elastic collisions! A crazy person is driving right at you with the same kind of car. You have two choices, either hit him head on, or drive off the road into a wall. Which would be better? A) Drive into the wall B) Drive into the other person C) It doesn t matter In-elastic collision! A cart moving at velocity, v!, collides with an identical cart on an air track and the two carts stick together after the collision. What is their velocity after colliding? A: v! 1 v! 2 B: C: zero!! D: E:! v! 1 v 2 In-elastic collision! A compact car and a large truck collide head on and stick together. Which vehicle undergoes the larger acceleration during the collision? A: car B: truck C: Both experience the same acceleration. D: Can t tell without knowing the initial velocities. Eric Mazur, "Peer Instruction" 1997 In-elastic collision! A compact car and a large truck collide head on and stick together. Which vehicle has the largest momentum change? A: car B: truck C: Both experience the same change in momentum. D: Can t tell without knowing the initial velocities. Eric Mazur, "Peer Instruction"

4 Conservation of mechanical work! You are playing football (or a rough game of soccer), and an opponent with momentum exactly opposite yours runs right into you. Which scenario would you prefer? A: The opponent is small. B: The opponent is big. C: Makes no difference. Inelastic collision! Two masses m 1 and m 2 approach each other on a frictionless table and collide. Is it possible that, as a result of the collision, all of the kinetic energy of both masses is converted to heat. A: Yes B: No If so, under what circumstances? Elastic collisions worked example! Problem 9.37 (sort of) 700 kg car stopped and rear ended by 1400 kg truck going at 10 m/s. If collision is elastic (poor approximation) what is final speed of both? Elastic collisions! A small glider is gliding along an air track at some initial speed, hits a much larger glider, and is observed to bounce back with a final speed nearly equal to its initial speed. BEFORE AFTER The speed of the large glider after the collision is A) less than the initial speed of the small glider. B) larger than the initial speed of the small glider. C) necessarily zero. 4

5 Elastic collisions! You are given two carts, A and B. They look identical, and you've been told they are made of the same material. You place A at rest on an air track and give B a constant velocity to the right so that it collides elastically with A. After the collision, both carts move to the right, the velocity of B being smaller than what it was before the collision. What do you conclude? A: Cart A is hollow. B: The two carts are identical. C: Cart B is hollow. From E. Mazur, "Peer Instruction" Elastic collisions! A big ball, mass M=10m, speed v, strikes a small ball, mass m, at rest. Could the following occur: The big ball comes to a complete stop and the small ball takes off with speed 10v? 10 m v 10 M m m m 10v A: Yes, this can occur. B: No, it cannot occur because it would violate momentum conservation C: No, it cannot occur because it would violate conservation of energy. Collisions! Is it possible for a stationary object that is struck by a moving object to have a larger final momentum than the initial momentum of the incoming object? A:Yes. B: No Eric Mazur, "Peer Instruction" 1997 Two people on roller blades throw a ball back and forth. After a couple of throws, when the first thrower once again is holding the ball, they are (ignore friction) A: standing still, where they were initially. B: standing still, farther away from each other. C: standing still, closer together than initially. D: moving away from each other. E: moving toward each other. 5

6 Consider two elas.c collisions: 1) a golf ball with speed v hits a sta.onary bowling ball head- on. 2) a bowling ball with speed v hits a sta.onary golf ball head- on. In which case does the golf ball have the greater speed a>er the collision? a) situation 1 b) situation 2 c) both the same v at rest 1 v at rest 2 Carefully place a small rubber ball (mass m) on top of a much bigger basketball (mass M) and drop these from some height h. What is the velocity of the smaller ball a>er the basketball hits the ground, reverses direc.on, and then collides with the small rubber ball? a) zero b) v c) 2v D) 3v e) 4v Where is the center of mass of a baseball bat located? a) at the midpoint b) closer to the thick end c) closer to the thin end (near handle) d) it depends on how heavy the bat is 6

7 Two equal-mass particles (A and B) are located at some distance from each other. Particle A is held stationary while B is moved away at speed v. What happens to the center of mass of the two-particle system? a) it does not move b) it moves away from A with speed v c) it moves toward A with speed v d) it moves away from A with speed ½v e) it moves toward A with speed ½v The disk shown below in (1) clearly has its center of mass at the center. Suppose the disk is cut in half and the pieces arranged as shown in (2). Where is the center of mass of (2) as compared to (1)? (1) X CM a) higher b) lower c) at the same place d) there is no definable CM in this case (2) Center of Mass! Important point about center of mass: Reading Assignment! The net external force acting on an assembly of particles changes accelerates the center of mass of the system just like a force applied to a point particle. Thursday 10/ Tuesday 10/

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