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# Work example problems

Video transcript

I'm going to show you
some examples of how to solve problems
involving work. Imagine a 4 kilogram trashcan. The trashcan is disgusting. So someone ties a
string to it and pulls on the string with a
force of 50 newtons. The force of kinetic friction
on the trashcan while it slides is 30 newtons. The trash can slides
across the ground for a distance of 10 meters. Let's try to find the work done
by each force on the trash can as it slides across the ground. To find the work
done by each force, we should recall the
formula definition of work. Work equals Fd
cosine theta, where theta is the angle
between the force doing the work and the direction
the trashcan is moving. There are four forces
involved here-- tension, the normal force, the
gravitational force, and the force of
kinetic friction. In finding the work done
for all of these forces, the displacement is
going to be 10 meters. But the value of the
force and the angle between that force
and the displacement is going to differ for
each of the forces. For instance, to find the work
done by the force of tension, we'll plug in the size of the
tension, which is 50 newtons. The displacement is 10 meters. And since the tension
force is pointed in the same direction
as the displacement, the angle between the force of
tension and the displacement is 0 degrees. And since cosine of 0 is 1, the
work done by the tension force is 500 joules. To find the work
done by friction, we'll plug in the size
of the force of friction, which is 30 newtons. The displacement
is still 10 meters. And since the force
of friction points in the opposite direction
as the displacement, the angle between the force of
friction and the displacement is 180 degrees. Since cosine of
180 is negative 1, the work done by the
force of friction is negative 300 joules. Now let's figure
out the work done by the gravitational force. The force of gravity is mg. So the force of
gravity is 4 kilograms times 9.8 meters per second
squared, which is 39.2 newtons. The displacement
is again 10 meters. But the angle between
the gravitational force and the direction
of the displacement is 90 degrees in this case. And since cosine of 90 is
0, the gravitational force does no work on this trashcan. Similarly, if we were
to find the work done by the normal force, the
angle between the direction of the displacement and the
normal force is 90 degrees. So the normal force also
does no work on the trashcan. This makes sense
because forces that are perpendicular to
the motion can never do any work on that object. So that's how you can find the
work done by individual forces. And if we wanted to know the
net work done on this trashcan, we could just add up the work
done by each individual force. So the net work is
going to be 200 joules. Now that we know the net
work done on the trashcan, we can use the
work-energy principle to figure out the
speed of the trashcan after it's slid the 10 meters. The work-energy principle
says that the net work done on an object is
equal to the change in kinetic energy
of that object. So 200 joules is going
to equal the difference in kinetic energy. If we assume the
trashcan started at rest, which seems reasonable,
the initial velocity is 0. So we can solve for the final
speed of the trashcan, which comes out to be 10
meters per second. This time, let's say
you take the trashcan and lift it upwards
with a constant velocity for a distance of 2 meters. In order to lift the trashcan
up with a constant velocity, you need to push with a
force equal to the weight of the trashcan, which means
you have to push upwards with a force of 39.2 newtons. So to find the work done by
the force that you exert, the force is going
to be 39.2 newtons. The displacement is
going to be 2 meters. And the angle between the
force and the displacement is going to be 0 degrees because
the direction of the force that you exert is in the same
direction as the displacement of the trashcan. So the work that you've done
in lifting up this 4 kilogram trashcan is 78.4 joules. To find the work done
by the force of gravity, we can use the force of gravity,
which is again 39.2 newtons. The displacement
is again 2 meters. But the angle
between the direction of the displacement and
the gravitational force is 180 degrees because
the displacement points up and the gravitational
force points down. So the work done by
the gravitational force is negative 78.4
joules, which means the net work done on
the trashcan is 0. And that makes sense. Because since the trashcan moved
upwards with constant velocity, there was no change in the
kinetic energy of this object.