Introduction to SAT II Physics

relative to the other. In this cases, it is important to remember that the center of mass of the system
as a whole doesn’t move.
EXAMPLE

A fisherman stands at the back of a perfectly symmetrical boat of length L. The boat is at rest in the

middle of a perfectly still and peaceful lake, and the fisherman has a mass^1 / 4 that of the boat. If the

fisherman walks to the front of the boat, by how much is the boat displaced?

If you’ve ever tried to walk from one end of a small boat to the other, you may have noticed that
the boat moves backward as you move forward. That’s because there are no external forces acting
on the system, so the system as a whole experiences no net force. If we recall the equation

, the center of mass of the system cannot move if there is no net force acting on the

system. The fisherman can move, the boat can move, but the system as a whole must maintain the
same center of mass. Thus, as the fisherman moves forward, the boat must move backward to
compensate for his movement.
Because the boat is symmetrical, we know that the center of mass of the boat is at its geometrical
center, at x = L/ 2. Bearing this in mind, we can calculate the center of mass of the system
containing the fisherman and the boat:

Now let’s calculate where the center of mass of the fisherman-boat system is relative to the boat
after the fisherman has moved to the front. We know that the center of mass of the fisherman-boat
system hasn’t moved relative to the water, so its displacement with respect to the boat represents
how much the boat has been displaced with respect to the water.
In the figure below, the center of mass of the boat is marked by a dot, while the center of mass of
the fisherman-boat system is marked by an x.