You are standing at the very rear of a raft of length L = 5.6 m and mass M = 119

Question

You are standing at the very rear of a raft of length L = 5.6 m and mass M = 119 kg that is at rest in a lake with its prow only 0.50 m from the end of the pier. Your mass is m = 66 kg. Neglect frictional forces between the raft and the water.

(a) How far from the end of the pier is the center of mass of the you-raft system?
______ m

(b) You walk to the front of the raft and then stop. How far from the end of the pier is the center of mass now?
______ m

(c) When you are at the front of the raft, how far are you from the end of the pier?
______ m

Explanation / Answer

a)

use this equation: Xcm =(mp*xp + mr*xr) / (mp + mr)

=(66*6.1 + 119 * 3.3)/66+19

= 4.29 m

where mp is the mass of you (i decided on mp for "mass of person"), xp is distance of your position to the end of the pier (hint L+.5m), mr is the mass of the raft, and xr is the distance of the halfway point of the raft (aka center of the raft) + the distance between the raft and the pier.

b) Xcm does not change = 4.29 m

c) use Xcm = (mp*d + mr(d+distance to center of raft)) / (mp + mr), then just plug and chug to find d.

793.6=66d+119d+59.5

d=3.9 m

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