A spring of negligible mass has force constant k = 800 N/m. (a) How far must the spring be compressed for 1.20 J of potential energy to be stored in it?

Video transcript

Okay, so we have this problem, we have a spring and it has a force constant or spring constant here given by K. Has negligible mass. And we want to store some amount of energy in it and we're wondering what compression we need to give to that spring reply to that spring in order to get that energy. Okay, so when we're talking about springs and energy, it's important to remember that a compressed spring has potential energy and that potential energy given by you can be written one half K X squared. Ok. K is going to be that spring constant here and X is going to be the compression of the stretch, the displacement of the spring. Alright, so let's go ahead and use the values we know We have 1.5 is the energy and it's written jewel in the question but it's important to remember too that that is also one jewel is equal to one Newton meter. Okay, so the units are okay, they check out here. One half the K we're given is 900. We get X squared. And X again is the compression of that spring that we're trying to find. Just working through the numbers. We'll divide both sides by 450 to get x squared is equal to 0.00333 repeated. Okay, taking the square root of X is equal to plus or minus 0.577. Okay, remember when you're taking a square root, you're gonna get the positive and negative solution. Um And you have to kind of infer from the question which one You should be using. So in this case we're looking at X. We're looking at the displacement of that spring. We just want to know the magnitude of the change. So we'll deal with the positive answer here. So we're gonna use x equals 0.0577 m. And then converting that into centimeters. Just so it's a nicer answer. And to kind of match what the solutions were given, we get 5.77 centimeters, multiplying by 100 and so 5.77 centimeters is the compression that we need to apply to the spring in order to get the amount of energy we want. Okay, great.