Can someone help me with this?

Imagine we have a system composed of three spheres 1, 2 and 3.

1 is connected to a wall on its left side with a spring and to sphere 2 with another spring, the sphere 2 is connected with 3 with another one and 3 is connected to a wall on its right side also with a spring. All springs have constant $k$.

1st Doubt. Now, if we have $m_{1}->∞$ what changes in this system? What I really what to know is if the sphere 1 moves at all.

Here's what I thought: It can't move, because if it does the energy of the system would be infinite. I drew this conclusion from:


and since $m_{1}$ is considered infinite, the energy would have to be infinite if sphere 1 moved. Therefore, for the energy NOT to be infinite I concluded that sphere 1 couldn't move.

2nd Doubt. If the previous thinking was correct we can simplify the system to just the spheres 2 and 3 now can't we? And consider the sphere 1 to be like... a wall, or something. Am I right?

If I wrote this too hard to understand please let me know. I'll try to explain better. Thanks very much.


One can always transform to the rest frame of reference of an arbitrarily large inertial mass and eliminate your first doubt; kinetic energy is frame dependent.

For you second doubt, note that as the inertial mass of sphere 1 becomes much larger than the others, assuming no other changes, the acceleration of sphere 1 becomes much smaller than the other spheres and is thus insignificant. In the limit of "infinite" inertial mass, the acceleration of sphere 1 goes to zero.

Thus, as you correctly conclude, only the dynamics of spheres 2 and 3 need be considered.

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