Problem 8.91 Two friends, Burt and Ernie, are standing at opposite ends of a uni
ID: 1602458 • Letter: P
Question
Problem 8.91
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 270 kg . Burt has mass 25.0 kg and Ernie has mass 38.5 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.
Explanation / Answer
The center of mass of the system will be:
x = ([25 x 0] + [270 x 1.8] + [38.5 x 3.6]) / (25 + 38.5 + 270) = 1.873 m from the left end. [Assuming Burt to be at the left end].
After Ernie walked towards Burt, the center of mass will shift and will now be at
x = ([25+38.5 x 0] + 270 x 1.8) / (25 + 38.5 + 270) = 1.457 m from the left end.
So, the log moved a distance of 1.873 - 1.457 = 0.4157 m.