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Work/Energy theorem





Reading the answer given by Eugene P. Mosca to a question by
JMGreen, I cannot resist making the following comments:

I quote: "Imagine standing still on a frictionless surface and
then pushing off a wall to get yourself moving. Since the points
of application of either the force on you or the force on the wall
do not move, no work is done either on or by you. However you gain
kinetic energy as you slide away from the wall."

Some people came to the rescue of those who do not understand
this mistery, by inventing something called "pseudowork", thus adding
to the general confusion. No "pseudowork" is needed !

Replace the human body by a brick. Replace the hand and the
pushing arm by a compressed spring. Then let the spring expand.
If you want to understand the motion of *the brick*, you
must pay atention to all forces acting on *the brick* (You may
forget the force applied by the wall *on the spring*) It is the work
done by the force applied by *the spring on the brick*, that equals the
change of kinetic energy of the *brick*.

Now replace *spring* by the arms and muscles and replace *brick*
by the rest of your body. The top of the arms push on the rest
of the body and if you multiply this push while the arms stretch
by and appropiate (non zero) displacement, you will get a non
zero increase in kinetic energy.

This is closely related to the case of an oars boat. Some people
think that to predict the boat motion you must care about
the force that *the water applies to the boat* and they equate
this to the force applied by the water on the oars.
To predict the motion of the boat, we must use the *forces acting
on the boat*. The forces that the oars
apply to the boat at the points of contact bewteen oar and
boat (how do ou call them and the US Naval Academy ?) is the
important propelling force. Of course the friction with the water is
the other force of interest.

And once you really understand the oars boat, you understand many
other puzzles. By example how a car (supposely accelerated by
the force of friction with the road, forces "that make no
work"), can gain kinetic energy. You can see that it is not the
same *forces on the wheels* that *forces on the car*.

Dario Moreno.