# Momentum and Collisions

1. Oct 27, 2008

### nastassja

1. The problem statement, all variables and given/known data

A particle p traveling with a speed of vpi = 3 m/s hits and scatters elastically from another particle N, initially at rest. Particle p is deflected through 90°, leaving with a speed of vpf = 2.3 m/s, and a mass mp = 2 kg.
a) What angle (in degrees) does the recoiling N make to the incident-p direction?

b) What is the magnitude of the momentum of the recoiling N?

c) What is the change in the energy of the p?

d) What is the speed of the recoiling N?

e) What is the mass of the N?

2. Relevant equations
mv=p
mpv0p + mNv0N=mpvfp + mNvfN

(for x and y directions)

3. The attempt at a solution

a) Since N is at rest at first, and p is perpendicular to the x-axis after the collision, I assumed that the pfNx would equal the initial momentum of p, or 2kg*3m/s or 5kg*m/s.

For the y direction, the momentum of N has to be equal and opposite p's momentum, so it is = -4.6kg*m/s.

I used inverse tangent to get the angle = -47.4 which is wrong. Where did I go wrong?

b)
c)
d)
e)

I have c) and I am sure I know how to do the rest if I can get a) right. Thanks.

2. Oct 28, 2008

### alphysicist

Hi nastassja,

This should be 6 kg m/s.

Also, you performed the inverse tangent incorrectly. The initial particle is moving along the x axis; since they want the angle with the incident direction of the p particle, that means they are asking for the angle relative to the x-axis.

But you calculated -47.4 by using:

$$\tan^{-1} \left( \frac{5}{-4.6} \right)$$

If you want the angle from the x-axis, you have to use y/x in the inverse tangent; but you used x/y.

3. Oct 28, 2008

### nastassja

I can't believe I made such a stupid mistake. Thanks.