# Work

Work. Work is the amount of energy expended in accomplishing a goal. The simplest equation for work is w equals Fd, which means F times d. And that is where F equals the amount of force exerted and d is the displacement upon which force is exerted. So work is going to equal the force times the displacement, how far the object moved. This equations requires that the force be applied in the same direction as the displacement. If force is exerted in the same direction, the equation will work. If force is applied in a different direction, you might have to alter your formula. So if we had this boulder and force was exerted forward, and the boulder moved forward and was displaced this distance, we could say the work equals the force used to push the boulder times its displacement because its force and displacement went in the same direction. Now if this is not the case, work may be calculated a different way. It can be calculated using the formula w equals F d times cosine theta which means the force exerted times the displacement times the cosine of theta, where theta is the angle between the force and displacement vectors. So the angle between the direction force was going and the direction the displacement actually went. So let’s look at our boulder again. Let’s say we pushed at this angle and the boulder moved forward along the ground. Well this angle between this displacement vector and the force vector would be theta and we would plug that into our formula to figure out the actual work done. Now if force and displacement have the same direction, work is positive. So this would be an example of positive work. If force and displacement have opposite directions, work is negative. So an example of that would be if someone were over here, if we had the same displacement but some person was over here and they had a lever system, like a lever and pulley system and they were able to pull the boulder toward them. So if they were able to pull the boulder toward them, they would be exerting force from over here but they would be still be displacing the boulder this way. So if they were exerting force this way while displacing this way, the work would be negative. So force going to the left, displacement is actually going to the right, that would be negative work. And if force and displacement directions are perpendicular, work is 0. So the work done equals zero. And that means no work is done. An example of that would be the ground pushing up on the boulder. The ground has its only pushing up on the boulder. If the boulder is moved to the right, the ground’s force against the boulder did not effect the displacement and so no work was done by this force. So even though the boulder moved from here to here. the ground remained pushing up against the boulder and no work was actually done this force. Work is measured in jewels and a jewel is the work expended by a force of one newton through a distance of one meter. So if you exerted one newton of force through a distance of one meter while you’re pushing an object one meter, that is equal to one jewel. And work is measured in jewels. So when you’re multiplying these in this formula, force is going to be measured in newtons. Your displacement should be measured in meters. So if you need to translate between different units to get your force to newtons and your displacement to meters, then please do so and then you will get a jewel or number of jewels as your answer for how much work was expended.

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Last updated: 07/25/2017

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