# Particles colliding

1. Oct 6, 2007

### kateman

1. The problem statement, all variables and given/known data
A neutron (m= 1.6 x10-27) moving with speed Vo strikes a stationary particle of unknown mass and rebounds elastically straight back along its path with a velocity of .7Vo. What is the mass of the struck particle?

2. Relevant equations
P initial = P final
Ke initial = Ke final

3. The attempt at a solution
alright i tried saying that the velocity imparted on the stationary particle was .3Vo but that gave me an answer of a mass of a neutron when the actual answer is 9.46 x 10-27.

i know: v1i = Vo
v2i = 0
v1f = .7Vo

2. Oct 6, 2007

### Vijay Bhatnagar

Let mass of the stationary particle be m and its velocity after collision be V. Write down the equations for conservation of momentum and kinetic energy (keep in mind the +/- sign of the velocities). Solve these to obtain m. [If you are able to write down the equations but do not know how to solve them to get m, post again writing down upto the step you are able to reach]

3. Oct 7, 2007

### kateman

yeah i understand what your saying:

1/2m1Vo^s = 1/2m1v1f^s+ 1/2m2 .7Vo^s

m1Vo = m1v1f + m2 .7Vo

what i have done is rearrange it for one value and then substitute it into the other equation but this still gives me the wrong answer. any ideas?

4. Oct 7, 2007

### Hootenanny

Staff Emeritus
You should recall that momentum is a vector quantity and hence, direction is important.

5. Oct 7, 2007

### kateman

1/2m1Vo^s = 1/2m1v1f^s - 1/2m2 .7Vo^s

ahhh well a negative in place of a positive might help :P
thanks hootenanny!

6. Oct 7, 2007

### Hootenanny

Staff Emeritus
Careful though, I'm sure 1/2m2(0.7v02) should be 1/2m1(0.7v02). Assuming that m1 is your known mass

7. Oct 7, 2007

### kateman

argh its these small errors that really throw me off
thanks again :)

8. Oct 7, 2007

### Hootenanny

Staff Emeritus
No problem

9. Oct 8, 2007

### kateman

alright so i used

m1Vo^2 = -m1 .7Vo^2 + m2 V2f

v2f = m1Vo^2 + m1 .7Vo^2/m2

then i subs the v2f into the kinetic formula equation and ended up with this:

m1Vo^2 + m1 .7Vo^2/m2 = (m1Vo^2 + m1 .7Vo^2/m2)^2

0 = m1Vo^2 + m1 .7Vo^2/m2

alright, have i gone wrong somewhere and if so, where?

10. Oct 8, 2007

### Hootenanny

Staff Emeritus
I'm not sure what you've done there, I think you may have got your equations mixed up. Kinetic energy is a scalar quantity; i.e. direction doesn't matter. And make sure you square the whole velocity. I'll start you off;

Momentum
$$m_1v_0 = m_1(-0.7\times v_0) + m_2v_2$$

Kinetic Energy
$$m_1v_0^2 =m_1(0.7\times v_0)^2 + m_2v_2^2$$

11. Oct 8, 2007

### kateman

hmm i see the directions with ke did stuff me up

if the .7Vo velocity is negative, could you not just say that m1.7Vo as a whole is negative, and then rearrange as such?

i try to rearrange it but keep stuffing it up.

what should i do, rearrange on for v2f and then substitute it in the other? if so i need some more guidance