Cracking the SAT Physics Subject Test

Therefore, the center of mass is at

(xcm, ycm) = (1.5, −5)

relative to the midpoint of the bar.

Questions 7-8

A man of mass 70 kg is standing at one end of a stationary,

floating barge of mass 210 kg. He then walks to the other end

of the barge, a distance of 90 meters. Ignore any frictional

effects between the barge and the water.

7. How far will the barge move?


8. If the man walks at an average velocity of 8 m/s, what is the
   average velocity of the barge?

Here’s How to Crack It

7. Since there are no external forces acting on the man + barge system, the
   center of mass of the system cannot accelerate. In particular, since the system
   is originally at rest, the center of mass cannot move. Letting x = 0 denote the
   midpoint of the barge (which is its own center of mass, assuming it is
   uniform), we can figure out the center of mass of the man + barge system:

So the center of mass is a distance of 11.25 meters from the midpoint of

the barge, and since the man’s mass is originally at the left end, the center of

mass is a distance of 11.25 meters to the left of the barge’s midpoint.