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>> Work means a lot of things
to a lot of people.
In physics, work has
a specific meaning.
Work equals force
times displacement.
I'm using my force
to move this cell phone
across the table.
That's work.
Moving a product
to market is work.
Moving a rocket into
space is work, too.
How much energy do you need to
propel that rocket into space?
How much gas, which possesses
stored chemical energy,
do you need to drive across
the United States in your car?
Or how much energy do you need
to keep this manufacturing plant
assembly line in operation?
That's what the
Work-Energy Theorem
helps you figure out.
It took about 2,000 years
to figure out that forces
are what make objects
move and stop.
When I roll this ball
on the table,
do you think it'll stop?
Greek philosopher,
Aristotle, did.
In Aristotle's days,
around 320 B.C.,
he thought objects would just
naturally slow down and stop.
It wasn't until Sir Isaac Newton
came along almost
2,000 years later
that he figured out that
forces like friction that
are harder to see and measure
are acting on the ball
and slowing it down,
or other forces speeding it up.
It's Newton's
First Law of Motion.
An object at rest
will stay at rest
and an object in motion
will stay in motion
at a constant velocity,
unless acted upon
by a net force.
So without friction,
this ball would just
keep on rolling.
Newton understood
forces acting on masses,
but he didn't really take
into account energy's impact
on how things move.
That took years more
to figure out.
And in the world
we're living in,
with industry and technology,
energy is critical.
The key to the Work-Energy
Theorem is understanding that
the work you do on an object
will either add energy
to that object
or take energy away.
Remember, work equals
force times displacement.
So let's say I want to
move this box two meters.
If I exert 20 newtons of force
on the box to move it 2 meters,
then I'm doing 40 joules
of work on the box.
By pushing the box
and increasing its velocity,
the box gains 40 joules
of kinetic energy.
Kinetic energy is the energy
of a moving object.
That's the Work-Energy
Theorem in a nutshell.
Work is equal to the change in
that object's kinetic energy.
Kinetic energy is equal
to 1/2 your mass times
its velocity squared.
The delta symbol
means a change in.
That means work is equal
to the final kinetic energy
minus the initial
kinetic energy.
The key is,
it has to be displaced.
If you move it,
then return it to the same spot,
no work is done.
Why are forces like
friction important?
Well, if you want to know
how much friction slows down
a runner sliding into base,
or how big a parachute you need
to slow down this shuttle,
or how fast a train
can safely take a curve
without flying off the tracks,
the Work-Energy Theorem
can help you figure out
those problems.
And in each of those instances,
friction is a key force.
Friction is one of those forces
that's difficult to measure.
It takes away from
kinetic energy.
In the case of someone
sliding into base,
it takes kinetic energy
and turns it into heat.
The same way when you rub
your hands together real fast,
you can feel the heat.
You can calculate the energy
lost due to friction
in problems by using physics
that we've already learned.
How much work does friction do
if an 85 kilogram base runner
travels at an initial velocity
of 8 meters per second
and slides into second base
and then stops?
So, let's write down our knowns
and our unknowns.
Mass is equal to 85 kilograms.
Our initial velocity
is 8 meters per second.
Our final velocity
is 0 meters per second.
And we're solving for
the work done by friction.
And here's the equation
that we need to know.
Work is equal to the final
kinetic energy minus
the initial kinetic energy.
That means that work is
equal to 1/2 the mass times
the final velocity squared,
minus 1/2 mass times
the initial velocity squared.
We then plug in the values
we know and get work
due to friction equal to
1/2 times 85 kilograms times
0 meters per second squared
minus 1/2 times 85 kilograms
times 8 meters
per second squared.
Now, the first part of
the equation will be
equal to 0,
since 0 times anything is 0.
And that leaves us with
1/2 times 85 kilograms
times 8 meters
per second squared.
When we multiply that out,
we get the work done
by friction to be
negative 2,720 joules.
So friction takes energy
away from the kinetic energy
of the base runner, right?
Why are we getting
a negative answer?
Work is a scalar quantity.
How can it be negative?
Well, that negative sign
tells us that energy was taken
away from our base runner.
A positive number for work
would tell us that energy
was added to the base runner.
Does that make sense?
When you think of
the total work done,
that is the change in energy.
It's also the work
to overcome forces that
are hard to measure,
like friction.
That's what the
Work-Energy Theorem
allows us to solve.
The Work-Energy Theorem
is at the heart of
understanding physics.
And once you understand it,
you have a much better sense
of how the world works.
That's it for this segment
of "Physics in Motion",
and we'll see you next time.
>> For more practice problems,
lab activities,
and note-taking guides,
check out the
"Physics in Motion" toolkit.