Question

Suppose an asteroid ejects a small chunk of mass. Let the small chunk after the separation have a mass m1, and the new mass of the asteroid be m2. Assumed that initial velocity of the asteroid is zero. Let the final velocities of the small chunk and asteroid be v1’ and v2’ respectively. (a) Show thatthe speed of the main asteroid after the separation is v2’ = (m1/m2) v1’ (b) if we observe v1’ = 100m/s, and v2’ = 1m/s, and estimate that m1 = 1000kg, what is m2?

Answer #1

(a)

Since the net external force on asteroid is zero, momentum can be conserved.

Initial momentum

Final momentum

Since velocities and are in opposite directions,

Hence

(b)

Speeds are and

Mass of ejected part

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