00:01
Okay, we're trying to find the work required to stretch a spring an additional 10 centimeters, and the force required to hold the springs, the spring in place in these two positions.
00:14
So the first case is on the top you have a spring, you stretch at a distance x1, and the work, we'll call it work 1, required is going to be equal to 4 joules, and that's for a distance x1 equals 10 centimeters.
00:41
Okay, and in the second case, it requires some work, work w2 to stretch it, and we want to find the extra work required.
00:55
So if we call work to the total work it takes to stretch the spring from its unstretched length to x1 plus x2, then what we're looking for is the difference between w and w1, right? w2 tells us the total work to stretch it 20 centimeters.
01:13
W1 tells us the work required to stretch it 10 centimeters, so the difference in the two tells us the work required to stretch it from 10 to 20 centimeters.
01:22
And then we'll look at the forces too.
01:25
So the work required to stretch a spring, work to stretch a spring, w sub s is 1 half k, which is the constant, spring constant of the spring, times the distance it's stretched from its natural length squared.
01:44
Okay, so w1 is four jewels, which is equal to 1 half k x1 squared.
01:54
We're probably going to need to solve for k here, so let's do that...