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AP Physics: CON‑5.A (EU), CON‑5.A.2 (EK), CON‑5.A.2.1 (LO), CON‑5.B (EU), CON‑5.B.3 (EK), CON‑5.B.3.1 (LO), INT‑3.E (EU), INT‑3.E.1 (EK)

What's a conservative force? Conservative forces
are any force wherein the work done by
that force on an object only depends on the initial and
final positions of the object. In other words, the work done by
a conservative force on a mass does not depend on the
path taken by that mass. If the work done by a
force follows this rule, then we call it a
conservative force. For instance, the gravitational
force on a 5 kilogram mass is 49 newtons. If the mass moves downwards
by an amount of 6 meters, the work done by gravity
is going to be 294 joules. Now let's start over. Say the mass again
moves down 6 meters. But then it moves up 6 meters,
then down again 6 meters. The work done by gravity
for the first downwards trip was 294 joules. Then for the upwards trip,
since the gravitational force is pointing in the opposite
direction of the motion of the mass, the
work done by gravity is going to be
negative 294 joules. Then for the last
trip downwards, the work again is
positive 294 joules. That means that the total work
done on the mass from gravity is still 294
joules, just like it was when the mass was
lowered only once. In other words, the work done
by the gravitational force doesn't depend on the specifics
of the path taken by the mass. The work done by
gravity only depends on the initial and final
position of the mass. In fact, you could
allow the mass to take any path from
this initial point to the final point, and
the work done by gravity is still just going
to be 294 joules. Because the work done
by gravity doesn't depend on the path
taken, we call gravity a conservative force. The force exerted by a
spring is another example of a conservative force. The total work done
on a mass by a spring does not depend on the
path taken by the mass. It only depends on the
initial and final positions of the mass. The term conservative
comes from the fact that conservative forces
conserve mechanical energy, whereas non-conservative
forces do not conserve mechanical energy. Mechanical energy is kinetic
energy and potential energy. An example of a non-conservative
force is friction. If I move a mass along a
table from point A to point B, friction does a certain
amount of negative work on the mass, which creates
some thermal energy. If instead of going
straight from A to B, I make the block go from A to B
back to A over and over again, the work done by friction
will become larger and larger. And it'll generate more
and more thermal energy. Because the work
done by friction depends on the path
taken, friction is not a conservative force. Similarly, air resistance
is not a conservative force since the work done
by air resistance depends on the specifics
of the path taken. It's useful to note that
if a force is conservative, you could define a potential
energy for that force. That's why conservative forces
like gravity and spring forces have potential energies
associated with them. And non-conservative
forces like friction do not have potential
energy associated with them. This makes sense
because if you do work against the
gravitational force by lifting a mass
in the air, you can get that energy back out
by letting the mass fall down, turning potential energy
into kinetic energy. Similarly, if you do work
against the spring force by compressing a spring,
you can get that energy back out by letting the
spring decompress, which turns the stored potential
energy into kinetic energy. But if you do work against
the force of friction, you'll have a hard time trying
to get that energy back out. The energy's been dissipated
into the form of thermal energy and is now randomly
distributed along the ground and into the block.

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