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.
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