 Work done by a force can also increase potential energy as well as kinetic energy So the obvious example is when you raise something up So if I have a mass then it's got a force due to gravity going down So the magnitude of that force is going to be that mass times the acceleration due to gravity And if we want to move it up then we're going to have to start it moving Which means you're going to have to apply a force just fractionally over the strength of that And if we want to get it moving we apply just a fraction bit over and we'll start moving And then if we just keep the applied force exactly equal and opposite to the gravitational force Then it will stay moving at a constant speed and it will eventually get up our appropriate distance And supposing we want to move it a total height h Then we look at the work done by that applied force So the work done is going to be equal to the applied force times the distance And for essentially that entire time that's just going to be the mass times the acceleration due to gravity times the distance And we note that this is exactly the gravitational potential energy difference that you get when you raise a particle of mass m by a distance h And it is of course possible to use work to change both your gravitational potential energy and your kinetic energy if you wish For example supposing we want to jump up half a metre in order to spike a ball over a volleyball net And we need to know how much force we need to apply with our legs to do so We'd start in a crouch Then we'd push as hard as we possibly could with our legs to go up Until we got to the point where our legs were straight And at that point we couldn't actually push with our legs anymore So how are we going to get over the net? Well hopefully by that point we have to have some kind of kinetic energy And so we're going to have to have some upward velocity left over from all that pushing And then we wait for some time until the acceleration due to gravity brings us to a stop And hopefully by that point we're high enough to reach over the net and spike that volleyball down So that's the point where we'd have no kinetic energy But we would have a certain amount of gravitational potential energy by the virtue of the fact that we had raised up by a distance h So our legs are providing a force that's going to move our center of mass by a distance d Which is how far we can straighten our legs So we could look at the distance the legs travel, combine it with the force that they apply Use that to calculate the velocity that you reach when your legs get to their full extent And then use the velocity to figure out how high you can go Or you can skip some of those steps Because in this step here your legs are providing some gravitational potential energy and some kinetic energy And then that kinetic energy is turning into more gravitational potential energy So what we could do is just say the legs are directly providing all of this gravitational potential energy So what we can do to calculate how hard you have to jump in order to get that high Is you can say that the work done in the end is going to be equal to the final gravitational potential energy So the work done by the legs on the body is the force that they can reduce Times the distance they can move the center of mass And the gravitational potential energy is just the mass of the human Times the acceleration due to gravity Times the total distance that you've gone And the one possible mistake you could make here is you could forget to include the distance that you moved in each step added together And from there you can rearrange to find the force that you need And now let's do our usual checks We have here a length divided by a length so that cancels And so this is a force we know that's a force so force equals force the units are good Now let's look at the various limits In a limit that we don't have to actually jump up into the air to reach over the volleyball net at all H goes to zero and in that case we're going to have D cancelling with D And so we're going to have the force required is just going to be whatever force we need to overcome gravity To raise our body mass up from a crouch up into standing So that's a good limit And the opposite limit where we have to jump high into the air but we have almost no distance to crouch in Then what's going to happen is that's going to be zero and this is going to get very small So our force is going to go infinite Does that make sense? Well if we can basically not crouch at all then we're going to somehow jump up into the air with a tiny figure of our legs And yes that's going to require an extremely large force So we've seen that conservation laws are very useful for doing certain kinds of calculations on closed systems Where there's no external forces or external interactions acting on the system But actually even when there are external interactions on the system We can often use the work done to include that into our energy calculations And we can still use conservation of energy or energy considerations to calculate things as we've seen here And remember just as external forces can cause work that increases potential and kinetic energy They can also go in the direction such that they decrease kinetic and potential energy And you just got to use your common sense to make sure you're getting the sign right