Simple Nature - Light and Matter

K. DifferentiatingKcm, we have

dKcm=mtotalvcmdvcm

=mtotalvcm

dvcm

dt

dt

dxcm

dxcm [chain rule]

=mtotal

dvcm

dt

dxcm [dt/dxcm= 1/vcm]

=

dptotal

dt

dxcm [ptotal=mtotalvcm]

=Ftotaldxcm

I’ll call this thekinetic energy theorem— like the work theorem, it
has no standard name.

An ice skater pushing off from a wall example 32

The kinetic energy theorem tells us how to calculate the skater’s

kinetic energy if we know the amount of force and the distance

her center of mass travels while she is pushing off.

The work theorem tells us that the wall does no work on the

skater, since the point of contact isn’t moving. This makes sense,

because the wall does not have any source of energy.

Absorbing an impact without recoiling? example 33

. Is it possible to absorb an impact without recoiling? For in-
stance, if a ping-pong ball hits a brick wall, does the wall “give” at
all?
.There will always be a recoil. In the example proposed, the wall
will surely have some energy transferred to it in the form of heat
and vibration. The work theorem tells us that we can only have
an energy transfer if the distance traveled by the point of contact
is nonzero.
Dragging a refrigerator at constant velocity example 34
The fridge’s momentum is constant, so there is no net momen-
tum transfer, and the total force on it must be zero: your force
is canceling the floor’s kinetic frictional force. The kinetic energy
theorem is therefore true but useless. It tells us that there is zero
total force on the refrigerator, and that the refrigerator’s kinetic
energy doesn’t change.
The work theorem tells us that the work you do equals your hand’s
force on the refrigerator multiplied by the distance traveled. Since
we know the floor has no source of energy, the only way for the
floor and refrigerator to gain energy is from the work you do. We
can thus calculate the total heat dissipated by friction in the re-
frigerator and the floor.
Note that there is no way to find how much of the heat is dissi-
pated in the floor and how much in the refrigerator.

Section 3.2 Force in one dimension 169