# Momentum with 3 masses

1. Jun 28, 2010

### mandy9008

1. The problem statement, all variables and given/known data
A space probe, initially at rest, undergoes an internal mechanical malfunction and breaks into three pieces. One piece of mass m1 = 41.8 kg travels in the position x-direction at 12.0 m/s, and a second piece of mass m2 = 62.0 kg travels in the xy-plane at an angle of 105° at 12.0 m/s. The third piece has mass m3 = 112 kg.

(a) Sketch a diagram of the situation, labeling the different masses and their velocities. (Do this on paper. Your instructor may ask you to turn in this work.)

(b) Write the general expression for conservation of momentum in the x- and y-directions in terms of m1, m2, m3, v1, v2, and v3 and the sines and cosines of the angles, taking θ to be the unknown angle. (Do this on paper. Your instructor may ask you to turn in this work.)

(c) Calculate the final x-components of the momenta of m1 and m2.

(d) Calculate the final y-components of the momenta of m1 and m2.

(e) Substitute the known momentum components into the general equations of momentum for the x- and y-directions, along with the unknown mass m3. (Do this on paper. Your instructor may ask you to turn in this work.)

(f) Solve the two-momentum equations for v3 cos θ and v3 sin θ, respectively, and use the identity cos2 θ + sin2 θ = 1 to obtain v3.

(g) Divide the equation for v3 sin θ by v3 cos θ to obtain tan θ, then obtain the angle by taking the inverse tangent of both sides.

(h) In general, would three such pieces necessarily have to move in the same plane? Why?

2. Relevant equations
p=mv

3. The attempt at a solution
c. p=mv
p=(41.8 kg) (12.0 m/s)
p=5016 kg m/s

p=(62.0 kg)(12.0 m/s)cos 10
p=-192.6 kg m/s

d. mass 1 p=o
mass 2 p= )(12.0 m/s) sin 105
p=718.6 kg m/s

I have done all but the last 3. I cannot figure out f g and h

2. Jun 28, 2010

### Dick

What about e)? What kind of equations do you get from the sum of the three momentum vectors?