Question

1. Two manned satellites approaching one another, at a relative speed of 0.250 m/s, intending to dock. The first has a mass of 4.0010³ kg , and the second a mass of 7.5010³ kg .

a) Consider the frame of reference in which the first satellite was originally at rest. Determine the momentum of the satellites before docking.

2. Determine the Kinetic energy of the satellites before docking.

3. Using conservation of momentum determine the velocity of the satellites after docking.

4. Determine the final Kinetic energy of the system.

5. What is the loss of kinetic energy in this inelastic collision (docking process)?

6. Repeat the calculation by using the frame of reference in which the second satellite was originally at rest. Explain why the change in velocity is different in the two frames, whereas the change in kinetic energy is the same in both.

Answer 1

a) Considering the first satellite at rest, then the second approaches with a speed of 0.25 m/s:

Since the docking is in one dimension:

b) The kinetic energy of the system before docking is:

c) Conservation of momentum means that the momentum of the system before docking must equal the momentum of the system after docking. We consider that the system after docking is a single mass M = m1 + m2 with a speed V (inelastic collision):

d) The final kinetic energy of the system is:

e) The loss of kinetic energy is just the difference between the final and the initial:

f) If we repeat the calculation considering the second satellite at rest, now we assign the approaching speed to the first, and we get:

We have to consider that momentum is speed times mass. The momentum of the system is not the same because the masses of the satellites are different, if the masses were the same, the change of velocity would be the same in the two frames. The change in KE on the other hand depends on the approach velocity and the total mass of the system only, therefore it's the same for both reference frames.