-
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.