# Does the stationary object deform more than the moving one after a collision?

Given two identical clay disks on an air track, one is stationary and another is moving at "high" speed. After colliding, does the stationary disk deform more than the moving one?

If it matters, the reference frame is with the stationary disk.

Edit: Please include in your answer if it matters whether or not the speed approaches the speed of light.

• Photonic/Chris: so the moving disk having more energy (kinetic) makes no diff? – AlJo Jan 4 '15 at 2:11
• According to Einstein, no. – Hot Licks Jan 4 '15 at 14:30
• Kinetic energy is based on velocity and the discs have the same velocity, relative to each other. Their velocity relative to you, who is not involved in the collision, is not relevant and therefore your judgement of which has more K.E. is more or less meaningless in this context. – Nagora Jan 4 '15 at 15:19
• @Nagora Has it right (and this was known to be true many centuries before Einstein). By the way, AlJo, the way comments ping people is complicated, but note I only saw your message above coincidentally. – user10851 Jan 5 '15 at 16:07

## 3 Answers

They must necessarily deform the same amount, otherwise you would violate Galilean invariance -- the idea that physics works no matter what reference frame you are in.

Suppose the stationary object $A$ deformed more. While you sit still in $A$'s reference frame, watching it deform more, have your friend run alongside the moving object $B$. In your friend's frame, $B$ is stationary, and so it should deform more than $A$. But this is a contradiction -- one cannot have the intrinsic properties of an object changing depending on who is looking at the object.

The reference frame doesn't matter. You cannot define a reference frame the way you did. Their deformation should be the same. The reason for this is that you can always transform to a different reference frame, i.e the centre of mass frame and physics should be the same as in any other inertial frame.

Having established this, in the centre of mass frame everything is symmetrical so its easier to see why both objects should deform the same. Both clay disks appear to be moving with the same momentum in opposite direction, thus there is no difference between them. Since this should hold in all inertial reference frames, you can see now why none of the 2 objects is special in any sense.

Addressing the comment made above: The moving disk has more Kinetic energy in the frame that you have defined. I on the other hand can equally calculate the two body's energies in the centre of mass frame where I will see both objects moving with equal but opposite momentum and their kinetic energies will be the same. Since the laws of physics shouldn't matter on the frame of reference that we chose, then both frames are valid. Hence by transforming to the CoM frame you can verify that no one of the two bodies has more energy content than the other, i.e energy content is a frame-dependent quantity.

• What do you mean I cannot define a ref frame the way I did? – AlJo Jan 4 '15 at 2:09
• @AlJo, I was basically trying to emphasise the importance of frame independence. You are free to choose the frame you will be working with yourself. Switching to the centre of mass frame is equally valid. You can even switch to a frame where you previously "moving" ball is now at rest and the other one is moving. – PhotonBoom Jan 4 '15 at 2:12
• @AlJo I have made an edit to answer your above comment. – PhotonBoom Jan 4 '15 at 2:20

If the point of the air track is to eliminate friction from consideration, let's make the situation even simpler:

Imagine a completely empty universe. Total blackness, no objects, no light, nothing.

Now add two clay lumps, and an invisible observer (you).

One clay lump appears (to you) to be motionless. Another clay lump appears (to you) to be moving towards the first clay lump at high speeds (feel free to make this speed as close to the speed of light as you like).

Now ask yourself these three questions:

1. If you (the observer) were to zoom over to the 2nd clay lump as it approaches and match its speed and direction so you were gliding next to it, how would the 2nd clay lump appear to be moving to you?

2. How would the 1st clay lump then appear to be moving to you?

3. If you were suddenly put into this situation, how would you tell if you were floating next to clay lump 1 or 2 (assuming they look identical)?

That should give you your answer.

• You answered the question with a whole new setup AND 3 questions. Hrmmm... never seen that before. – AlJo Jan 4 '15 at 3:05
• You'll find it's a setup that preserves the important parts of your setup, while dispensing with the distracting, irrelevant parts, like the walls, windows, ceiling, "air track", trees in the background, gravitational pull of the Earth, etc. – Brionius Jan 4 '15 at 3:16