Video Transcript
Each of the following figures
shows two rocks in outer space. Which figure correctly shows
the direction of the gravitational force exerted on each rock? (a), (b), (c), (d), or (e).
Okay, so here we’re told that
we have two rocks in outer space. That means there are no other
masses anywhere nearby these rocks. Therefore, we can assume that
the gravitational force exerted on each rock is due only to the other of the two
rocks. In order to figure out which of
these five diagrams correctly shows the direction of the forces acting on each
rock, we can recall a principle about gravitational force. That is, gravitational force is
always attractive.
This means that if we have two
masses, say one mass here and the other mass here, the force of gravity will
cause this mass to be attracted to the other one. And this second mass to be
attracted to the first. That is, the force vectors we
could show on each mass lie along a line between the two masses. This is always true when
objects exert gravitational forces on one another. Those attractional forces lie
along a line between the two objects’ respective centers of mass.
Looking at our answer options,
we see option (a) agreeing with the rule we just described. If the center of mass of the
reddish-brown rock is here and the center of mass of the yellowish rock is right
here, then we can see that the two gravitational force vectors lie along the
line between these points. And what’s more, they point in
such a way that indicates these forces as attractive. That is, the rocks will tend to
move toward one another.
Before we confirm that option
(a) is the correct answer, let’s look at the remaining choices. For option (b), if we draw a
straight line between the two centers of mass, we see the forces don’t lie along
this line. So, that means option (b) won’t
be our choice. Then, looking at option (c),
here the force vectors do lie along this line. But we notice that the force on
the reddish-brown rock is pointed in the wrong direction. The implication here is that
the golden-colored rock is somehow repelling the reddish-brown one. But we know that gravity
doesn’t act that way. We’ll cross off option (c) then
as well.
Looking at option (d), this
fails for the same reason option (b) did. The force vectors do not lie
along the line connecting these rocks’ centers of mass. And lastly, for option (e), the
vectors are along this line. But now, they both imply a
repulsive force rather than an attractive one. But gravity is always
attractive. So, we’ll cross out option (e)
too.
This confirms our earlier
assessment that it’s figure (a) that correctly shows the direction of the
gravitational force exerted on each rock.
