LECTURE 16 COLLISIONS

Lecture Instructor: Kazumi Tolich Lecture 16

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¨ Reading chapter 9-5 to 9-6 ¤ Collisions n Completely inelastic collisions n Elastic collisions Collisions

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¨ The total linear momentum of the colliding objects is always conserved during any collision. ¨ In an elastic collision, the total kinetic energy of the system remains the same. ¨ In an inelastic collision, the total kinetic energy changes. ¤ In an extreme case of a completely inelastic collision, all objects share a common velocity at the end of the collision. Quiz: 1

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¨ A compact car and a large truck collide head-on and stick together. Which undergoes the larger momentum change? A. Car B. Truck C. The momentum change is the same for both vehicles. D. Cannot tell without knowing the final velocity of combined mass. Quiz: 16-1 answer

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¨ The momentum change is the same for both vehicles.

¨ Conservation of momentum tells us that the changes in momentum must add up to

zero: ∆� = ∆� + ∆�= �

¨ So the change in the car’s momentum must be equal to the change in the truck’s momentum, and the two changes must be in the opposite directions. Quiz: 2

¨ Two cars of equal mass travel in opposite directions at equal speeds. They collide in a completely inelastic collision. Just after the collision, their velocities are A. zero. B. equal to their original velocities. C. equal in magnitude but opposite in direction from their original velocities. D. less in magnitude and in the same direction as their original velocities. Quiz: 16-2 answer

¨ zero.

¨ Since two cars of equal mass travel in opposite directions at equal speeds before the collision, the total momentum of the two-car system is zero.

¨ After the collision, the total momentum must remain zero.

¨ In a completely inelastic collision, the two colliding cars stick together.

¨ The only way the two-car combination after the collision to have a zero momentum is if it had a zero velocity. Demo: 1

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¨ Eleven Pool Balls ¤ Demonstration of kinetic energy and momentum conservations in elastic collisions

¨ Collisions with Air Track ¤ Demonstration of collisions n Inelastic collisions n Elastic collisions: � = � and � = �

Before After � = � � � � � � � Quiz: 3

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¨ A box sliding on a frictionless surface collides and sticks to a second identical box which is initially at rest. Compare the

initial kinetic energy (Kinitial) and final kinetic energy (Kfinal) of the system of two boxes.

Initial

Final Quiz: 16-3

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¨ � > �

¨ Since the boxes stick together after the collision, this is a completely inelastic collision.

¨ The kinetic energy usually decreases in an inelastic collision due to losses associated with sound, heat, and deformation. In every completely inelastic collision, internal kinetic energy always decreases.

¨ The kinetic energy sometimes increases if collision sets off an explosion, releasing chemical energy etc. Example: 1

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¨ A bullet with a mass � = 5.20 g moving at � = 672 m/s strikes a wooden block with a mass � = 0.700 kg at rest on a frictionless surface. The bullet emerges with its speed reduced to � = 428 m/s. a) What is the resulting speed of the block? b) How much kinetic energy was lost? Example: 2

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¨ Two titanium spheres approach each other head- on with the same speed and collide elastically. After the collision, one of the spheres, whose mass is 0.300 kg, remains at rest. What is the mass of the other sphere? Demo: 2

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¨ Astro-blaster ¤ The small ball is given a speed significantly larger than any of the initial speeds since the momentum is conserved. ¤ A similar process occurs in the collapse of a star during a supernova explosion. The resulting collision can send jets of material racing away from the supernova at nearly the speed of light. Quiz: 4

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¨ Suppose you are on a cart, initially at rest, which rides on a frictionless horizontal track. You throw a ball at a vertical surface that is firmly attached to the cart. If the ball bounces straight back as shown in the picture, will the cart be put into motion after the ball bounces back from the surface? A. Yes, to the right B. Yes, to the left C. No. Left Right Quiz: 16-4 answer

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¨ Yes, to the left

¨ Before you throw the ball, the total momentum of the cart/you/ball system is zero.

¨ After the ball bounces on the wall, the total momentum of the system remains zero.

¨ Since the ball has a momentum to the right, the rest of the system must have a momentum to the left. Example: 3

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¨ Two hockey players with identical mass, � = 75 kg, skating at � = 5.75 m/s collide and stick together. If the angle between their initial directions was � = 125º, what is their velocity after the collision?