A particle moving along the y-axis is in a system with potential energy U = 4y^3 J, where y is in m. What is the -component of the force on the particle at y = 0 m, 1 m, and 2 m?

Video transcript

Welcome back everybody. We are given the potential energy function of an object that is moving along the Y axis. And it's given by this equation right here. And we are tasked with finding what the Y component of the force is at these three points along the object's journey. Let's read through our answer. Choices here. For option A at zero m, the Y component will be 10 newtons at two m. The Y component will be negative 20 newtons and at six m, the Y component will be negative 60 newtons or B it reads as zero newtons, then negative 20 newtons, then negative 60 newtons. For answer choice C it's negative 20 newtons, then zero newtons, then negative 60 newtons. And for answer choice D it's zero newtons, then negative 20 newtons, then 40 newtons. Here's what we know. We know that the Y component of force or when you plug in Y to this force, this is just going to be equal to the negative derivative of our potential with respect to Y. So let's go ahead and calculate that. Well, the derivative of five Y squared plus three is going to be 10 Y and then we just make it negative. So now what we're going to do for each of our three points is simply just plug in the point into this equation right here. So negative 10 times zero is going to be equal to zero for our first point. Then let's go ahead and plug in two m which gives us negative 10 times two, which is 20 or negative 20. And then finally plugging in six m. This is gonna be negative 10 times six which is negative 60. So now we have found the Y component of our force at all three points which corresponds to answer choice B Thank you all so much for watching. I hope this video helped. We'll see you all in the next one.