# Elastic Collision (Urgent)

1. Oct 23, 2012

### johnhuntsman

A cart with a mass of 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 rst cart
continues in the same direction at 0.66 m/s. (a) What is the mass of the
second cart? (b) What is its speed after the collision?

I have two equations: Conservation of Momentum and Conservation of KE (since this is elastic).

m1vi = m1v1 + m2v2

.5m1vi2 = .5m1v12 + .5m2v22

I've solved for v2 using the equation for Conservation of Momentum, and plugged that into the equation for Conservation of KE and my answer is wrong (used up about a page of algebra, please don't expect me to type it out all on here). The correct answer can be found using the method in the PDF below.

http://www.physics.ucc.ie/py1052_ps6.pdf (problem 8)

My issue is that they solve for v1f (or as I called it in the equations above, v1) and yet v2f (or v2) is nowhere to be found on the side opposite of their v1f. I don't see how their algebra makes any sense. All I want is someone to explain this to me as this is supposed to be a straightforward question.

Last edited: Oct 23, 2012
2. Oct 23, 2012

### haruspex

You missed a 0.5 there. Is it as simple as that?
They used the momentum equation to get v2f in terms of the other variables, then substituted that in the KE equation.

3. Oct 23, 2012

### johnhuntsman

v2f = [m1vi - m1vf] / m2

Substitute that into cons. of KE:

.5m1vi2 = .5m1v12 + .5m2[(m1vi - m1v1) / m2]2

Which still doesn't look like what they have. This is what I solved and I ended up getting .127 kg. What mistake have I made at this point that I'm not seeing?

P.S. Eqn. for conservation of KE is fixed.

4. Oct 23, 2012

### haruspex

Work with that some. You should find vi - v1 cancels, getting rid of the quadratic.

5. Oct 23, 2012

### TamuNinja

use this after you get the numbers from momentum equation of:

ƩPi=ƩPf

(you have the break down of the above correct?)

Now plug into this

0=ΔKE+ΔPEg+ΔPEspring
=1/2mv2f-1/2mv2f+mghf-mghi+1/2kx2f-1/2kx2f

Now just place you values in the equation and remove things that you dont use for example the spring.

6. Oct 24, 2012

### johnhuntsman

Alrighty, thanks. That did it. I appreciate it : D