Understanding Momentum: Explained in a YouTube Video

[Marioqwe]

I was watching this video on youtube about momentum:



At 23:42 he says that the momentum in the ball has changed by an amount 2mv. I do not understand that part. Why is that the ball's momentum changes by that amount?

 

[cepheid]

Remember that momentum is a vector quantity, so direction is important. Before hitting the wall, the tennis ball has a momentum of +mv. After hitting bouncing off the wall, it has a momentum of -mv (its velocity is exactly the opposite of what it was before).

So, what is the difference between the final momentum and the initial momentum (i.e. the change in momentum)?

 

[Bhumble]

Momentum is mv. The velocity changed direction by 180 degrees which means that the ball came to a stop and then accelerated to v in the opposite direction. So the total momentum change is 2mv.

 

[cepheid]

Momentum is mv. The velocity changed direction by 180 degrees which means that the ball came to a stop and then accelerated to v in the opposite direction. So the total momentum change is 2mv.

Don't give away the answer! Much better if the original poster arrives at it him/herself and gains true understanding in the process.

 

[Marioqwe]

Oh I see.

So,

mv + 0 = -mv + MV
2mv = MV

meaning that the momentum on the wall is 2mv. And it seems that if I solve for V

V = 2mv/M and let the mass go to infinity because it is much more massive than the ball, V approaches 0 and its KE is almost zero.

Thanks for the help.

 

[Dickfore]

Although your conclusion about the limit of KE is true, your logic is flawed. Namely, when the mass of the wall tends to infinity the velocity tends to zero, but the kinetic energy is half product of the mass and velocity squared, so it is an indefinite form $0 \cdot \infty$.

 

[cepheid]

Does the resolution to the problem posed by the lecturer come about because the collision excites vibrations in the lattice structure of the wall that themselves carry momentum? (I know I'm being hypocritical when it comes to giving away answers, but I'm not sure if this is true and I genuinely would like to know).

 

[Marioqwe]

Should I then say that M >> m? Or is the whole limit approach wrong?

 

[Dickfore]

1. What is the velocity of the center of mass of the wall and the incoming ball:
   $$V_{\mathrm{C M}} = \frac{m v}{m + M} = \frac{v}{1 + M/m}$$
   if the mass of the wall $M$ is much bigger than the mass of the ball $m$, i.e. $M/m \rightarrow \infty$?
   
2. Find the velocities of the incoming ball and the wall in the CM frame!
   
3. During an elastic collision, the velocities of the incoming objects change sign in the CM frame. What are the velocities of the bounced ball and the wall in the CM frame?
   
4. Is it hard to go back to the so called LAB frame in this case? What are the velocities of the bounced ball and the wall in this frame?