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 3.1m long and has mass 220kg . Burt has mass 42.5kg and Ernie has mass 42.0kg . 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.

Part A

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.

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Explanation / Answer

as total external force on the log is zero, the center of mass will remain the same.

now assume that one end of the log (where burt is ), has coordinate 0.(assuming x axis to be along the log, there by eliminating any change in y component)

other end be at 3.1 m

the center of mas of the log will be at 3.1/2=1.55 m
so cente rof mass will be at (1.55*220+42.5*0+42*3.1)/(220+42.5+42)=1.5475 m

now assume that the log has moved by d m.

log's center of mass will be at 1.55+d
burt and ernie both will be at d.

then center of mass of the system will be

(42.5*d+42*d+220*(1.55+d))/(220+42.5+42)

which should remain constant as before.

so (42.5*d+42*d+220*(1.55+d))/(220+42.5+42)=1.5475

d=0.4276 m

so the log has moved 0.4276 m relative to the shore. (in 2 significant figure, answer=0.43 m)

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