Accelerating a cart example 35
If you push on a cart and accelerate it, there are two forces acting
on the cart: your hand’s force, and the static frictional force of the
ground pushing on the wheels in the opposite direction.
Applying the work theorem to your force tells us how to calculate
the work you do.
Applying the work theorem to the floor’s force tells us that the
floor does no work on the cart. There is no motion at the point
of contact, because the atoms in the floor are not moving. (The
atoms in the surface of the wheel are also momentarily at rest
when they touch the floor.) This makes sense, because the floor
does not have any source of energy.
The kinetic energy theorem refers to the total force, and because
the floor’s backward force cancels part of your force, the total
force is less than your force. This tells us that only part of your
work goes into the kinetic energy associated with the forward mo-
tion of the cart’s center of mass. The rest goes into rotation of the
wheels.
Discussion Questions
A Criticize the following incorrect statement: “A force doesn’t do any
work unless it’s causing the object to move.”
B To stop your car, you must first have time to react, and then it takes
some time for the car to slow down. Both of these times contribute to the
distance you will travel before you can stop. The figure shows how the
average stopping distance increases with speed. Because the stopping
distance increases more and more rapidly as you go faster, the rule of
one car length per 10 m.p.h. of speed is not conservative enough at high
speeds. In terms of work and kinetic energy, what is the reason for the
more rapid increase at high speeds?170 Chapter 3 Conservation of Momentum