Three small spaceships are traveling in a common direction, say to the right. Sh

Question

Three small spaceships are traveling in a common direction, say to the right. Ship A is a distance L from ship B and ship B is a distance 2L from ship C. Ship A is twice the mass of ship B and ship C, which are both equal masses, m. At this instant, ship C is traveling twice the speed of ship A and ship B, both of which are traveling at the same speed, v.

A.) What is the Velocity of the center of mass at the instant described?

B.) An engine in ship B kicks on and exerts a force F naught on it to the right. After t seconds, what is the velocity of the center of mass of the 3 ships?

-I am horrible at center of mass problems!

Explanation / Answer

A) x=0 @ ship A A = 2m , B+C = 2m CM(B+C) is half way between B and C which is at 2L for 0 now we have 2m @ 0 and 2m @ 2L Averaging these we find the CM for the system to be at L. B) F= ma a = F/m v = at = Ft/4m Each craft is moving with velocity at least 'v' Craft C is moving with 1/4 the mass with an additional 1v Craft B is accelerating at a rate Ft/4m over time t v(t) = v + v/4 + Ft/4m =5/4v + Ft/4m

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