A man with mass m 1 = 64 kg stands at the left end of a uniform boat with mass m

Question

A man with mass m1 = 64 kg stands at the left end of a uniform boat with mass m2 = 174 kg and a length L = 3.3 m. Let the origin of our coordinate system be the man’s original location as shown in the drawing. Assume there is no friction or drag between the boat and water.

1)If the man now walks to the right edge of the boat, what is the location of the center of mass of the system?

2)After the man walks to the right edge of the boat, what is the new location the center of the boat?

3)

Now the man walks to the very center of the boat. At what location does the man end up?

Explanation / Answer

(1) if man wlaks to the right edge then also the COM of the body will remain same that is 1.206 m from its left end.
(2) when man walks toward right boat will move toward left.
So the combined centre will remain at same position but centre of boat changes.
x = 3.3/(1 + m(boat)/man) = 3.3 /(1 +(174/64)) = 0.887 m to the left of its original position
(3) New location of man
x = (3.3/2) / (1+64/174) = 1.206 m right of the origin

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