Two manned satellites approaching one another at a relative speed of 0.500 m/s i

Question

Two manned satellites approaching one another at a relative speed of 0.500 m/s intend to dock. The first has a mass of 4.50 103 kg, and the second a mass of 7.50 103 kg. Assume that the positive direction is directed from the second satellite towards the first satellite.

a) Calculate the final velocity after docking, in the frame of reference in which the first satellite was originally at rest.
_____________ m/s

(b) What is the loss of kinetic energy in this inelastic collision?
__________________ J

(c) Repeat both parts, in the frame of reference in which the second satellite was originally at rest.
final velocity
____________ m/s
loss of kinetic energy
_____________________ J

Explain why the change in velocity is different in the two frames, whereas the change in kinetic energy is the same in both.

Explanation / Answer

a)final velocity =m2v2/(m1+m2) =7.5 x1000 x0.5/(12 x1000) =0.312m/s

b)loss in ke =(1/2)m2v22-(1/2)(m1+m2)v2 =-(1/2) (12000)(0.3122) + (1/2)(7500)0.52 =353.43J

c)

final velocity =m1v1/(m1+m2) =4.5 x1000 x0.5/(12 x1000) =0.187m/s

b)loss in ke =(1/2)m1v22-(1/2)(m1+m2)v2 =-(1/2) (12000)(0.1872) + (1/2)(4500)0.52 =352.68J

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