CALC A particle that can move along the x -axis is part of a system with potential energy U(x)= A/x2 − B/x where A and B are positive constants. a. Where are the particle's equilibrium positions?

Video transcript

Welcome back everybody. We are making observations about a particular object that we are told has a potential energy function given by this equation right here where A and B are constants. And we are tasked with finding the equilibrium positions in which the net force on the particle is zero. Let's read through our answer choices here. Answer choice A is four A over three B. Answer choice B is three B over four A answer choice C is three B over two A and answer choice D is two B over three A. Well, if you'll recall the net force is just equal to the negative of the derivative of the potential with respect to X. Let's go ahead and take the derivative of our equation up here. Remember this is gonna be negative uh the derivative of the first term which is going to be using the power rule negative three A over X to the 4th. And then we have plus two B over X cubed is equal to zero. Distributing this negative sign here we have that this is now three A over X to the fourth plus two B over X cubed is equal to zero. Now, let's just go ahead and multiply both sides by X to the fourth. What this is going to give us is 3 a plus or sorry. This should rather be minus, this will be minus and this will be minus minus two B X is equal to zero. Now, I'm gonna add two B XX to both sides. And what we get is two B X is equal to three A dividing both sides by two B. We get that X is equal to three A over two B corresponding to our final answer choice of C. Thank you all so much for watching. I hope this video helped. We will see you all in the next one.