A 60.0 kg woman stands at one end of a 120 kg raft that is 6mlong. The other end

Question

A 60.0 kg woman stands at one end of a 120 kg raft that is 6mlong. The other end of the raft is 0.5m from a pier. a) The woman walks toward the pier until she gets to the otherend of the raft and stops there. Now what is the distance betweenthe raft and the pier? b) In a), how far did the woman walk (relative to thepier)? A 60.0 kg woman stands at one end of a 120 kg raft that is 6mlong. The other end of the raft is 0.5m from a pier. a) The woman walks toward the pier until she gets to the otherend of the raft and stops there. Now what is the distance betweenthe raft and the pier? b) In a), how far did the woman walk (relative to thepier)?

Explanation / Answer

m = 60.0 kg, M = 120 kg, d = 6 m, a) Let the pier be the origin. The coordinate of the center of theraft is 3.5 m, that of the woman is 6.5 m The center of the system is at (120*3.5 + 60*6.5)/(120 + 60) When she stopped working at the other end of the reft, hercoordinate is x (where x is the distance of her and the pier), thecoordinate of the center of the raft is 3 + x then the center of the system is at [120*(3 + x) + 60*x)/(120 +60) The center of the system doesn't change, so 120*3.5 + 60*6.5 = 120*(3 + x) + 60*x x = 2.5 m b) The coordinate of the woman changed from 6.5 to x, so she moved6.5 - x = 4 m, relative to the pier.

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