# 1-d Elastic Collision

1. Oct 18, 2007

### ace214

A 10.0 g object moving to the right at 22.0 cm/s makes an elastic head-on collision with a 15.0 g object moving in the opposite direction at 32.0 cm/s. Find the velocity of each object after the collision.

First, I converted the masses to kg and the velocities to m/s.
I used m1v1i + m2v2i = m1v1f + m2v2f and solved for v1f in terms of v2f and plugged this into
v1i - v2i = v2f - v1f to attempt to get v2f first (yes, I am converting back to cm/s) and I'm not getting the right answer... I don't understand what I'm doing wrong...

Here's my numbers:
.01(.22) + .015(.32) = .01v1f + (.015)v2f
.007 = .01v1f + .015v2f
v1f = (.007 - .015v2f)/.01 = .7 - 1.5v2f

(.22) - (-.32) = v2f - v1f
.54 = v2f - (.7 - 1.5v2f)
.54 = v2f -.7 + 1.5v2f
.61 = 2.5v2f
v2f = .244 m/s = 24.4 cm/s

This is due at 8:30 AM. EST tomorrow.

Last edited: Oct 18, 2007
2. Oct 18, 2007

### ace214

I have also tried v2i - v1i = v1f - v2f with positive numbers and v1i +v2i = v1f + v2f with properly-signed numbers... Someone please help...

Last edited: Oct 18, 2007
3. Oct 18, 2007

### Dick

So far, you have one equation in two unknowns, v1f and v2f. There is no way you can solve that for either one. You need another equation. In an elastic collision the kinetic energy is conserved as well as the momentum. Use that to get another equation.

4. Oct 18, 2007

### ace214

No there's two equations.... I already said that.

I used m1v1i + m2v2i = m1v1f + m2v2f and solved for v1f in terms of v2f and plugged this into v1i - v2i = v2f - v1f

Last edited: Oct 18, 2007
5. Oct 18, 2007

### TMM

I solved it by writing an equation for the total momentum and for the total kinetic energy. From there you can just substitute.

6. Oct 18, 2007

### ace214

When I did that, I got imaginary numbers from the quadratic.

7. Oct 18, 2007

### Dick

Ok, then the problem is that the second equation isn't true. Use KE.

8. Oct 18, 2007

### TMM

I didn't.

I wrote:

mv(2) + mv(1) = -260

.5mv(2)^2 + .5mv(1)^2 = 11000

Then I just substituted momentum one into the energy one and solved .

I got 12.3 cm/s to the right for the larger particle and 44.4 cm/s to the left for the smaller one, which is correct.

If you're getting lost in the conversion, just leave it in cgs.

9. Oct 18, 2007

### ace214

Also, the book says that that equation is supposed to work.

10. Oct 18, 2007

### Dick

Something like v1i + v2i = v2f + v1f will only work if the two masses are equal.

Last edited: Oct 18, 2007
11. Oct 18, 2007

### ace214

Ok, I redid the KE equation and got 32 and 24 for the larger mass. I've tried 24 already as I got it from the equation with just velocities above and it wasn't right..... Gaaaaaah.....

12. Oct 18, 2007

### ace214

Ok, I was an idiot and didn't use a negative velocity in the original momentum equation..... Wish somebody had caught it but oh well. Also the v1 - v2 = v2 - v1 does work for objects with different masses.