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The following is another example in which we can profit by checking
against our physical intuition for what should be happening.
Example
As shown in the figure below, Cindy is rappelling down a cliff. Her downward motion is at constant speed, and
she takes little hops off of the cliff, as shown by the dashed line. Analyze the forces in which she participates
at a moment when her feet are on the cliff and she is pushing off.
force acting on Cindyforce related to it by Newton’s third law
planet earth’s downward gravitational force on CindyCindy’s upward gravitational force on earth
ropes upward frictional force on Cindy (her hand)Cindy’s downward frictional force on the rope
cliff’s rightward normal force on CindyCindy’s leftward normal force on the cliff
The two vertical forces cancel, which is what they should be doing if she is to go down at a constant rate. The
only horizontal force on her is the cliff’s force, which is not canceled by any other force, and which therefore
will produce an acceleration of Cindy to the right. This makes sense, since she is hopping off. (This solution is
a little oversimplified, because the rope is slanting, so it also applies a small leftward force to Cindy. As she
flies out to the right, the slant of the rope will increase, pulling her back in more strongly.)
I believe that constructing the type of table described in this section is
the best method for beginning students. Most textbooks, however, prescribe
a pictorial way of showing all the forces acting on an object. Such a picture
is called a free-body diagram. It should not be a big problem if a future
physics professor expects you to be able to draw such diagrams, because the
conceptual reasoning is the same. You simply draw a picture of the object,
with arrows representing the forces that are acting on it. Arrows represent-
ing contact forces are drawn from the point of contact, noncontact forces
from the center of mass. Free-body diagrams do not show the equal and
opposite forces exerted by the object itself.
Discussion questions
A. In the example of the barge going down the canal, I referred to a “floating”
or “hydrostatic” force that keeps the boat from sinking. If you were adding a
new branch on the force-classification tree to represent this force, where would
it go.
B. A pool ball is rebounding from the side of the pool table. Analyze the forces
in which the ball participates during the short time when it is in contact with the
side of the table.
C. The earth’s gravitational force on you, i.e. your weight, is always equal to
mg, where m is your mass. So why can you get a shovel to go deeper into the
ground by jumping onto it. Just because you’re jumping, that doesn’t mean
your mass or weight is any greater, does it.
Discussion question C.
Chapter 5Analysis of Forces