Question

A compressed spring is compressed between a 5kg and 3 kg cart, respectively. When the spring is released, what will be the same for the carts?

Answer 1

The momentum of the two carts will be the same

Explanation:

First of all, we notice that the system consisting of the two carts + the spring is an isolated system: this means that there are no external forces acting on it.

As a result, the total momentum of the system must be conserved.

Since the spring is at rest, the total momentum of the system after the two carts are released is:

$p_f = p_1 + p_2$

where

$p_1$ is the momentum of the 1st cart

$p_2$ is the momentum of the 2nd cart

The total momentum of the system at the beginning, when the spring is compressed, is zero:

$p_i=0$

Since the total momentum must be conserved, we have:

$p_i = p_f\\0 = p_1 + p_2\\\rightarrow p_2 = -p_1$

Which means that the two carts will have equal and opposite momenta.

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