out normal forces. These forces are perpendicular to the surface
of contact. For simplicity, we show only two pairs of these normal
forces, as if the hand were a pair of pliers.
force acting on person force related to it by Newton’s
third law
rope’s static frictional force on
personperson’s static frictional force
on rope
rope’s normal force on
personperson’s normal force on
rope
rope’s normal force on
personperson’s normal force on
rope
(There are presumably other forces acting on the person as well,
such as gravity.)
If a rope goes over a pulley or around some other object, then
the tension throughout the rope is approximately equal so long as
the pulley has negligible mass and there is not too much friction. A
rod or stick can be treated in much the same way as a string, but
it is possible to have either compression or tension.
Discussion Question
A When you step on the gas pedal, is your foot’s force being transmitted
in the sense of the word used in this section?3.2.8 Work
Energy transferred to a particle
To change the kinetic energy,K= (1/2)mv^2 , of a particle mov-
ing in one dimension, we must change its velocity. That will entail a
change in its momentum,p=mv, as well, and since force is the rate
of transfer of momentum, we conclude that the only way to change
a particle’s kinetic energy is to apply a force.^6 A force in the same
direction as the motion speeds it up, increasing the kinetic energy,
while a force in the opposite direction slows it down.
Consider an infinitesimal time interval during which the particle
moves an infinitesimal distance dx, and its kinetic energy changes
by dK. In one dimension, we represent the direction of the force
and the direction of the motion with positive and negative signs for
F and dx, so the relationship among the signs can be summarized
as follows:(^6) The converse isn’t true, because kinetic energy doesn’t depend on the di-
rection of motion, but momentum does. We can change a particle’s momentum
without changing its energy, as when a pool ball bounces off a bumper, reversing
the sign ofp.
164 Chapter 3 Conservation of Momentum