General physics

1. Jun 21, 2004

robyfan

Two people, one of mass 65kg and the other of mass 40kg, sit in a rowboat of mass 85kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat, 4.0m apart from each other, exchange seats.
How far will the boat move?
and in what direction will the boat move?

I know it's related to center of mass thing, but couldn't figure out....

2. Jun 21, 2004

HallsofIvy

Staff Emeritus
Since you know "it's related to center of mass thing", did you try calculating the center of mass? Taking the end at which the 65kg person is sitting to be 0 (let's call that the "bow"), we have a total mass of 65+ 40+ 85= 190 kg, with the 85 kg mass at 2 m (the center of the boat) and the 40 kg mass at 4 m. Taking x to be the center of mass, we have
190x= 0*65+ 2*85+ 4*40= 330 so x= 330/190= 1.74 m from the bow.

After they change places, the 40 kg person is at 0 and the 65 kg person is at 4 m.
Now 190x= 0*40+ 2*85+ 4*65= 430 so x= 430/190= 2.26 m from the bow.

Since there is no external force here, the center of mass of the boat actually stays in the sae place- it is the boat that moves: 2.26-1.74= 0.52 m in the direction of the bow.