- Good morning.
We have already learned about
conservation of mechanical energy.
♫ Flipping Physics ♫
Remind me, Billy, when can we use
the conservation of mechanical energy equation?
- I actually don't remember.
- Mechanical energy is conserved
when there's no work done by friction and--
- There is no work done by the force applied.
- Thank you.
- Now we are going to discuss
how to solve problems
with a work done by friction.
We will leave problems with
a work done by force applied for later.
When the work done by the force applied
and an object is equal to zero,
the work done by friction
is equal to the change in mechanical energy.
Bo, what is the equation
for the work done by friction?
- Well, work is the force doing the work,
which in this case is the force of friction
times the displacement of the object
times the cosine of the angle between the force
and the displacement.
- Remember to use the magnitude of the force
and the magnitude of the displacement
because it is the cosine of the angle
that determines if the work is positive or negative.
- And Bobby,
what equation does ΔME
or the change in mechanical energy work out to be?
- I'm not sure what you mean by equation.
- You know, change in time,
change in velocity.
- Change in position.
Change in displacement.
- Bo, change in position is displacement.
There's no such thing as change in displacement.
- Yeah.
- Okay, "change in" means final minus initial
so change in mechanical energy
equals mechanical energy final
minus mechanical energy initial.
- Therefore, the equation we use
when the work done on an object by the force applied
is equal to zero,
and there's work done by the force of friction
on an object,
is the force of friction
times the displacement
times the cosine of theta
is equal to mechanical energy final
minus mechanical energy initial.
Remind me, Bo,
what are the three things I asked you to remember
about the direction of the force of friction?
- The force of friction is always parallel to the surfaces,
opposes sliding motion
and is independent of the direction
of the force applied.
- And the angle in the work due to friction equation
is the angle between the direction of the force of friction
and the direction of the displacement of the object.
Therefore, the angle theta
in your work due to friction equation
is always 180 degrees.
- That makes sense.
If an object is sliding to the left,
the force of friction is to the right
and the displacement of the object is to the left.
Therefore, the angle between
the direction of the force of friction
and the direction of the displacement
is 180 degrees.
- And if the object is moving to the right,
the force of friction points left
and the displacement of the object points right
and the angle between the force of friction
and the displacement is still 180 degrees.
Sure, I got it.
- I want my two dollars.
- Now, I do want to be careful with this always
because it actually isn't quite always true.
There are a few examples
where the force of friction
is actually in the same direction the object is moving.
One example is if a hockey puck
is on top of a block of wood.
As we pull the block to the right,
the hockey puck is accelerated to the right
by the force of friction.
In this case,
the force of friction acting on the hockey puck
and the displacement of the hockey puck
are both in the same direction.
Therefore, the angle in the work due to friction equation
actually works out to be zero degrees.
Now this is a bit of an unusual situation.
However, I did want to make sure that I mentioned it
because as you get further in to your physics careers,
it will come up more and more often.
Now let's take a look at what happens
to our work due to friction equation
if the work due to friction is equal to zero.
If the work done by the force of friction
is equal to zero,
that means zero equals
the change in mechanical energy,
which means zero is equal to mechanical energy final
minus mechanical energy initial.
Adding mechanical energy initial to both sides
gives us mechanical energy initial
equals mechanical energy final
or conservation of mechanical energy,
which means conservation of mechanical energy
is just a special case
of the work due to friction equation
equals change in mechanical energy
where the work done by friction
is equal to zero.,
which means, class,
when we use the work done by friction
equals change in mechanical energy equation,
we need to?
- Clearly identify the locations
of our initial and final points.
- And identify the location
of the horizontal zero line.
- Absolutely.
Thank you very much for learning with me today.
I enjoyed learning with you.