 In this video we are going to be looking at how we can calculate mechanical work due to a force. Just to give you the background again, we will use this when we look at conservation of energy where our final energy is the initial energy plus the work. Remember when I had my water glass, I filled more water in what I have at the end so that I had at the beginning plus the change and the change here comes in form of mechanical work. So let's look at a little card. Let's assume that card is rolling to the right over a distance delta S. So that card has some initial kinetic energy. What do you think how the change in energy is going to be greatest? Force one by pushing forward or force three by pushing backwards? I think we agree force one is going to add energy while force three is going to remove energy. So we have to figure out the way how we can calculate this. So I think it is intuitive to look at the force first. The more force we have, the more energy can be added. So I think we can write down that the work is the force. Then for the more distance the force is acting, the more work or the more the change will be. So the main trick is to come up with the way for the directions. So let's look at my force one first. My force one has an angle of zero degrees in the direction in which the object is traveling. And the already established force one will increase the kinetic energy of the object that already goes in that direction. Therefore the work done by force one is positive. Force two is pushing down on the cart and has an angle of 90 degrees with the direction of travel of the cart. So we have an angle of 90 degrees. And can it change the speed of the cart if we have a flat surface pushing downward? It will not change the speed of the cart. So actually we won't even have any change. Force three is at an angle of 180 degrees from the direction of travel of the cart. And if the cart is traveling this way and you're pulling that way, then you're slowing down the cart. So the change of energy must be negative, so then the science should become negative. And then last but not least, if you're pulling up, you're at an angle of 90 degrees again and you cannot change the energy of the system at all because you're pulling it up but you cannot change the speed at which the cart goes in horizontal direction. So now the main question is what function will for zero degrees produce a positive sign? For 90 degrees gives us zero, for 180 degrees will give us a negative sign and for 90 degrees again will give us zero. Well, that's correct. Cosine, right? Cosine. Cosine of zero is plus one. Cosine of 90 is zero and cosine of 180 is minus one. So all we have to change here is that cosine of the angle and we're good. So we have found how to calculate work. So work in general, you have to look at which way is your displacement, which way is your object traveling. You look at the force and you look at the angle in between. So a force that goes straight forward will add energy, a force that goes in the opposite direction as the movement will remove energy and the force at 90 degree angle will just not do anything. And that's it for the calculation of work.