Answer to Question #162842 in Mechanics | Relativity for Benjamin

Question

Suppose that we have a collision between two carts on an air track and the carts stick together. One cart has a mass of 3M and is initially stationary. The second cart has a mass M and is moving with a momentum p⃗0 in the positive x-direction before the collision. a Which cart exerts the bigger force on the other? Explain (diagrams, expressions, etc will help here). b Which cart has the bigger change in momentum? Explain (diagrams, expressions, etc will help here). c What is the momentum of the second cart after the collision? Express in terms of p0.

Answer 1

One cart has a mass of 3M and is initially stationary.

$m_1 = 3M \space\space\space\space\space v_1 = 0$

The second cart has a mass M and is moving with a momentum p⃗0 in the positive x-direction before the collision

$m_2 = m \space\space\space P_2 = P_o \to P_2 = m_2v_2 \to v_2 = \large\frac{P_o}{m}$

Of course second cart exerts to first one bigger force because the first cart velocity is 0.

$P_1 + P_2 = P_1'+P_2'$

$P_0= (3M+M)U \to U = \large\frac{P_o}{4M}$