Two friends, Burt and Ernie, are standing at opposite ends of a uniform log that

Question

Two friends, Burt and Ernie, are standing at opposite ends of a uniform log that is floating in a lake. The log is 3.6 m long and has mass 260 kg . Burt has mass 35.5 kg and Ernie has mass 35.5 kg . Initially the log and the two friends are at rest relative to the shore. Burt then offers Ernie a cookie, and Ernie walks to Burt's end of the log to get it.

Relative to the shore, what distance has the log moved by the time Ernie reaches Burt? Neglect any horizontal force that the water exerts on the log and assume that neither Burt nor Ernie falls off the log.

Express your answer to two significant figures and include the appropriate units.

mm

mm

Explanation / Answer

Burt, who's at the left end of the log. So the center of mass is at

(35.5 x 0 + 260 x 1.8 + 35.5 x 3.6) / (35.5 + 260 + 35.5) = 9 / 5 = 1.8 m from the left end.

After Ernie walked, the center of mass is at

(295 x 0 + 260 x 1.8) / 331 = 1.4138 m from the left end.

The log moved 1.8 - 1.4138 = 0.3862 m = 386.2mm (Answer)

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