00:01
All right, so we have a spring that has an unstretched length or a natural length, we'll call l0 of 10 centimeters.
00:06
So write that a 0 .1 meters.
00:09
And it is stretched to a distance of 30 centimeters upon the application of a 30 -newton force.
00:21
And so we want to, given this information, sorry, this should say 30 -newts, given this information, how much work is done to go from a distance of, we'll say, 0 .0 .0 .1.
00:32
0 .25 meters to 0 .3 meters.
00:38
All right.
00:39
So first off, let's figure out the spring constant in the spring, because we have hooks law which says f equals, you know, negative k delta x, right? so the spring constant is going to be like how far we have to stretch the spring.
00:51
I'm sorry, the force we need to stretch the string divided by how far we need to stretch it.
00:57
So in this case, we had 30 newtons, and we stretched it by distance of 0 .2 meters so k then is 150 newtons per meter all right so the work done is going to be the integral of the force over some displacement vector and the force is negative kx the displacement vector so what we have is the integral of k x d x from the initial point to the final point so like the point is 0 .25 meters the final point is 0 .3 so those are understood to be in meters so this is course is negative 1 half k x squared and we're evaluating this from 0 .25 to 0 .3 using the same spring counts we have before and when we do that we should get about negative 2 .0 063 jules.
01:58
It's negative because you're having to pull against the spring to go from this.
02:04
So you're fighting the spring every bit of the way...