# The Linear Momentum of a System of Particles

Hello All, I have a question that i cant seem to get.

If someone could help me get started on part a that would be great.

So far i have tryed using P =m1v1 and cant seem to find any other equations that would help with the problem.

Any help is great!
Thank You

Problem:
A cart with mass 390 g moving on a frictionless linear air track at an initial speed of 1.2 m/s undergoes an elastic collision with an initially stationary cart of unknown mass. After the collision, the first cart continues in its original direction at 0.57 m/s.

(a) What is the mass of the second cart?
grams
(b) What is its speed after impact?
m/s
(c) What is the speed of the two-cart center of mass?
m/s

## Answers and Replies

Elastic means kinetic energy is conserved. You have two conservation equations:
$$m_1 v_{1i}= m_1v_{1f} + m_2v_{2f}$$ and
$$m_1 v_{1i}^2 = m_1 v_{1f}^2 + m_2v_{2f}^2$$
You can use these to determine the unknowns.

but how would i solve out for m2 or v2 when the equation has both in it?

Does v2f = v1i - v1f ?

Edit: I got it now thanks a lot !

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