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I'm going to show you some examples of how to solve problems involving work imagine a four 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 trashcan slides across the ground for a distance of 10 meters let's try to find the work done by each force on the trashcan 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 zero degrees and since cosine of zero is one 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 a hundred and eighty 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 zero 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 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 zero 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 30 9.2 Newtons so to find the work done by the force that you exert the force is going to be 30 9.2 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 seventy eight point four 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 a hundred and eighty degrees because the displacement points up and the gravitational force points down so the work done by the gravitational force is negative seventy eight point four joules which means the net work done on the trashcan is zero and that makes sense because since the trashcan moved upwards with constant velocity there was no change in the kinetic energy of this object

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