# Homework Help: Man on a plank- Center of Mass pb.

1. Oct 28, 2009

### Footballer010

1. The problem statement, all variables and given/known data

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?

2. Relevant equations

Xcm= m1x1+m2x2$$\div$$m1+ m2

3. The attempt at a solution

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

Xcm= m1x1+m2 x2+m3x3$$\div$$m1+ m2+m3

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

And... I wasn't even close. Help

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2. Oct 28, 2009

### Footballer010

If it helps... the answer is 2.9 m, but I have no idea why.

3. Oct 29, 2009

### rl.bhat

When man moves forward, to keep the CM constant, the whole plank with man must back. So Man*L = Total mass*x.
Find x.