What is the total gravitational potential energy of the three masses in FIGURE P13.35?

Video transcript

Hey everyone. So this problem is dealing with gravitational energy. Let's see what it's asking us. We have three masses that are placed at the vertices of an equilateral triangle. And we're asked to determine the total gravitational potential energy of the system. The three masses as shown in this diagram are 25 kg 15 kg and 35 kg. And each side of the collateral triangle is 2 m long are multiple choice answers in are a negative 1.18 times 10 to the negative eight Jews B negative 5.91 times 10 to the negative seven Jews C negative 1.18 times 10 to the negative seven Jews or D negative 5.92 times 10 to the negative eight Jules. OK. So the first step to solving this problem is recognizing that the total gravitational potential energy is equal to the sum of each of the potential energy between each pair of masses. And so we can write that as U equals U between mass one and mass two plus U between mass two and mass three plus U between mass one and mass three. And so I'm just going to title on this um figure that mass one is the kg mass mass two is the 15 kg mass and mass three is the 35 kg mass. We can recall that gravitational potential energy is given by the equation U equals negative G multiplied by M one M two, all divided by R where G is our gravitational constant and one of them two are the masses and R is the distance between them. And so when we substitute that into our U total equation, we get negative GM one M two divided by R minus GM two M three divided by R 23 minus G M one M three divided by R 13. We can recognize that R 12, R 23 and R 13 are all the same. So we can just write that as R or R equals m. And so when we factor out the um similar terms here, we can factor out negative G divided by R and then we simply have M one M two plus M two and three plus M one M three. And from there, we can plug in our values and find our total um potential energy. And I should be writing you total here. I apologize. OK. So U total total potential energy is going to be our gravitational constant. We can recall is negative 6.67 times 10 to the negative 11 Newton meters. Squared per kilogram squared divided by R which is 2 m multiply by. So M one multiplied by M two. It's going to be 25 kg multiplied by 15 kg plus M two M 15 kg multiplied by 35 kg. And then plus M one M three or 25 kg multiplied by kg. We plug all of that into our calculator and we get a total potential energy uh five point sorry, negative 5.92 times 10 to the negative eight jolts. And so that is the final answer for this problem and it aligns with answer choice D that's all we have for this one. We'll see you in the next video.