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. Two identical objects traveling in opposite directions with the same speed $V$ make a head-on collision. Find the speed of each object after the collision if (a) they stick together and (b) if the collision is perfectly elastic.

a) $v^{\prime}=0$b) $\vec{V}$

Physics 101 Mechanics

Chapter 8

Momentum

Physics Basics

Kinetic Energy

Potential Energy

Energy Conservation

Moment, Impulse, and Collisions

Cornell University

University of Michigan - Ann Arbor

Hope College

McMaster University

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So in this case, we have two objects off. Mask him more towards each other with the same velocity. Really, For our for our day. We want to see what happens if the stick together after the collision. Let's say after the collision this stick together and become a massive two m on move with velocity you let's say no. The initial Wyndham off the system is every for object on DH minus envy for object Giving us Cyril on the final moment. Um off the system would be simply the mass times velocity for the last stop for the only object after the collision. Just do him dance you because initial metaphysical to finally window as that there are no external forces. In this case we get toe emu is equal to zero which gives us you is equal to zero that he's after the two book. After the two objects stick to each other, they just stay there. Their final velocity becomes Cyril now for option B. I'm sorry. The party we want to see what happens if this election is perfectly elastic. Not that we have just finished the perfectly in Elastic is on now. We want to do the perfectly elastic is in this case we have the same situation and then going with Elastics re MP. But after the collision, we have our two masters with moving toe, possibly different velocities. So let's call this week, eh? Let's call her B b. The final velocities off objects A and B notice that their masters are still the same. No, Our initial momentum as seen here zero on our final moment on will simply be the sums often Momenta off the two objects which would be m i a this damn vehbi. Now we know that initial and fight along with them. Are you the same for an object without external forces and hands MBA less M V B is equal to zero which gives us we et les we b is equal to zero dividing both sides by I. Now I know that we have this equation because the other equation as usual from the from the part perfectly elastic condition be initial minus we be initial is equal to me a final minus will be final but with the minus sign they're related. Velocity of approach is equal in magnitude to the relative velocity ofthe separation. This gives us initially the velocities. Are we on minus B Nor that is in the opposite direction. And hence but that would be minus we when we substitute in tow the equations and B I is we on v B I It's like a sweet and this will be equal to the final velocities. We should simply be b A minus V b excuse us to be his equal We a minus. We'd be where we can forget the minus Sign here that says this. So we a minus Wee Bey is minus duty. Now that we have these two equations, we simply need to solve them for me and the baby nor that if we are toa thestreet patients be people be cancelled and they get to be a is equal to zero minus story on dividing vortex By two we get we a is equal to minus. We on now, substituting this back into this equation we get V B Is it called Hence the two objects come with velocities fi what each other And after the collision, they simply call back with the last six weeks, which is what you would expect from a perfectly elastic collision

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