# 1-D Elastic Collision

## Homework Statement

A cart with mass 340 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 0.66 m/s.
(a) What is the mass of the second cart?
(b) What is its speed after impact?
(c) What is the speed of the two-cart center of mass?

## Homework Equations

I'll use this space to organize variables:
m1 = 0.34 [kg]
v1i = 1.2 [m/s]
v1f = 0.66 [m/s]

## The Attempt at a Solution

Okay using the Conservation of Momentum model, I have:

m1v1i = m1v1f + m2v2f

So in order to find the mass of the second cart, I have:

(m1(v1i - v1f))/v2f = m2

And now I'm stuck because I don't have the final velocity of the second cart in order to compute its mass.

Last edited:

Delphi51
Homework Helper
Welcome to PF, Palerider.
You are in a common situation - two unknowns and only one equation.
You must find a second equation before you can solve for the two unknowns. The word "elastic" in the question is your clue. If you don't know what it means, look it up! "elastic collision" in Wikipedia will likely work.

Thank you for the welcome.
Okay so an elastic collision means that K is conserved throughout the collision.

Therefore:
(.5)m1v1i2 = (.5)m1v1f2 + (.5)m2v2f2

But that leaves me in the same situation as before doesn't it?

Delphi51
Homework Helper
Looks good. Now you have two equations with two unknowns. You should be able to solve for both the unknown mass and unknown final velocity. Solve the simpler equation for m2, then sub that into the other equation.