![]() And say, this might be x isĮqual to 10 because we've compressed it by 10 meters. To the left in my example, right? This is where x is equal Other way, but I think you understand that x is increasing Plot the force of compression with respect to x. And when the spring isĬompressed and not accelerating in eitherĭirection, the force of compression is going If I'm moving the spring, if I'mĬompressing the spring to the left, then the force I'mĪpplying is also to the left. The same thing, but it's going in the same directionĪs the x. So that's the force that the spring applies to whoever's The spring constant, times the displacement, right? That's the restorative force, Law told us that the restorative force- I'll writeĪ little r down here- is equal to negative K, where K is State, right? And we know from- well, Hooke's So when the spring was initiallyĪll the way out here, to compress it a littleīit, how much force do I have to apply? Well, this was its natural So this axis is how much I'veĬompressed it, x, and then this axis, the y-axis, is how Right, so that you can- well, we're just worrying about the So let's look at- I know I'mĬompressing to the left. Graph to maybe figure out how much work we did in compressing I've applied at different points as I compress So what I want to do is thinkĪ little bit- well, first I want to graph how much force Magnitude, so we won't worry too much about direction. Spring, it would stretch all the way out here. ![]() Here, and let's see, there's a wall here. I'm sorry if this was too long of a response, I have had so much trouble with this topic and I still do. To make it a little easier, we can revert to integration (which is a b word), because when we integrate a function (say, a function for a force), then we are able to account for the differing Y. Because F is changing, there will be different y values for different x's. When we are given an equation for the force, that means the force is changing and we cannot straight up do W=Fd because F is changing. The force needed CHANGES this is why we are given an EQUATION for the force: F = kx, yes? If the F = a constant, we would, indeed, have a rectangle. Why is it not the whole rectangle in the case of a spring? In the case of a spring, the force that one must exert to compress a spring 1m is LESS than the force needed to compress it 2m or 3m, etc. If you apply a CONSTANT force of 13N, then the graph of work (which would be a graph of force on the y axis and displacement on the x axis) would be a rectangle the vertical component (the force) would be all the way up to 13N (again, on the y axis), while the x component would just be all the way up to 5m. Basically, we would only have a rectangle graph if our force was constant! Unfortunately, the force changes with a spring. We only have a rectangle-like graph when the force is constant. We are looking for the area under the force curve.
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