Answer to Question #151713 in Physics for Jules

Question

A rocket and payload are moving through space with a constant velocity of 5000 m/s relative to the Earth. The mass of the rocket is 4000 kg and the mass of the payload is 1000 kg. The rocket and payload are then separated by a spring that pushes them apart so that they have a relative velocity of 100 m/s.

What are the velocities of the rocket and payload relative to the earth after separation?
What is the change in kinetic energy before and after the separation?
The spring that separated the rocket and payload has a spring constant of 4.0 x 106 N/m. How much was the spring compressed before separation?
What was the maximum force of the spring on the rocket?

Answer 1

1)

$$(m+M)v=MV-m(V-v')\\(1000+4000)5000=4000V+1000(V-100)\\v_r=V=5020\frac{m}{s} \\v_p=V-100=4920\frac{m}{s}$$

2)

$$\Delta K=0.5(1000+5000)5000^2-0.5(1000)(4920)^2\\-0.5(4000)(5020)^2=1.25\cdot10^{10}\ J$$

3)

$$\Delta K=0.5kx^2\\1.25\cdot10^{10}=0.5(4\cdot10^{6})x^2\\x=79\ m$$

4)

$$F=kx=(4\cdot10^{6})(79)=3.16\cdot10^{8}N$$