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One way to find the
amount of work done is by using the formula
Fd cosine theta. But this number for
the amount of work done represents the amount of energy
transferred to an object. For instance, if you
solve for the work done and you get positive
200 joules, it means that the force gave
something 200 joules of energy. So if you have a
way of determining the amount of energy that
something gains or loses, then you have an alternate
way of finding the work done, since the work done on an
object is the amount of energy it gains or loses. For instance, imagine a
50-kilogram skateboarder that starts at rest. If a force starts the
skateboarder moving at 10 meters per
second, that force did work on the skateboarder
since it gave the skateboarder energy. The amount of kinetic energy
gained by the skateboarder is 2,500 joules. That means that the work done
by the force on the skateboarder was positive 2,500 joules. It's positive because the
force on the skateboarder gave the skateboarder
2,500 joules. If a force gives
energy to an object, then the force is doing
positive work on that object. And if a force takes away
energy from an object, the force is doing negative
work on that object. Now imagine that the
skateboarder, who's moving with 10
meters per second, gets stopped because he
crashes into a stack of bricks. The stack of bricks
does negative work on the skateboarder because
it takes away energy from the skateboarder. To find the work done
by the stack of bricks, we just need to figure out
how much energy it took away from the skateboarder. Since the skateboarder
started with 2,500 joules of kinetic energy and ends with
zero joules of kinetic energy, it means that the work done by
the bricks on the skateboarder was negative 2,500 joules. It's negative because the
bricks took away energy from the skateboarder. Let's say we instead
lift the bricks, which are 500 kilograms, upwards
a distance of four meters. To find the work that
we've done on the bricks, we could use Fd cosine theta. But we don't have to. We could just figure
out the amount of energy that we've given to the bricks. The bricks gain energy here. And they're gaining
gravitational potential energy, which is given by
the formula mgh. If we solve, we
get that the bricks gained 19,600 joules of
gravitational potential energy. That means that the work
we did on the bricks was positive 19,600 joules. It's positive because our
force gave the bricks energy. This idea doesn't just work with
gravitational potential energy and kinetic energy. It works for every
kind of energy. You can always find the work
done by a force on an object if you could determine the
energy that that force gives or takes away from that object. [MUSIC PLAYING]