- [Instructor] 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 five kilogram mass is 49 newtons.
If the mass moves downwards
by an amount of six meters,
the work done by gravity
is going to be 294 joules.
Now, let's start over.
Say the mass again moves down six meters
but then, it moves up six meters,
then, down again six 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's
gonna 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 gonna 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 energies
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 it's now randomly distributed
along the ground and into the block.
