Man on a plank- Center of Mass pb.

AI Thread Summary
A man stands on one end of a 10 m plank on a frictionless surface, with a total system mass of 340 kg, including a rock at the other end. The center of mass is initially calculated to be 6.5 m from the man's end. When the man walks to the rock, the plank must move to maintain the center of mass. The correct calculation shows that the plank moves 2.9 m in the opposite direction as the man moves forward. Understanding the relationship between the movement of the man and the plank is crucial for solving the problem.
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Homework Statement



A man is standing at one end of a plank of length L = 10 m. The man has mass Mman = 100 kg and the plank has mass Mplank = 40 kg and the plank is atop a frictionless sheet of ice. At the other end of the plank sits a large rock of mass Mrock = 200 kg. The center of mass of the man+plank+rock is 6.5 m from the end of the plank where the man is standing.

The man walks to the other end of the plank and sits down on the rock. How far did the plank move along the ice?

Homework Equations




Xcm= m1x1+m2x2\divm1+ m2


The Attempt at a Solution



SO I added one more mass and plugged in the numbers, solving for Xplank

Xcm= m1x1+m2 x2+m3x3\divm1+ m2+m3

6.5=((100)(10)+(40)(Xplank)+(200)(0))\div(340 kg)

And... I wasn't even close. Help
 

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If it helps... the answer is 2.9 m, but I have no idea why.
 
When man moves forward, to keep the CM constant, the whole plank with man must back. So Man*L = Total mass*x.
Find x.
 
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