OpenStax College Physics for AP® Courses, Chapter 7, Problem 2 (Test Prep for AP® Courses)

This is College Physics Answers with Shaun Dychko. We have a cart track, we have a cart, some masses and a position-sensing pulley so this is a high-tech pulley that can tell how many times it's been turned and we can figure out what the position of the hanging mass is in other words with respect to time. So our job is to figure out a relation between the force exerted on the cart, which is the tension created by the force of gravity on this hanging mass and the work that's done through a distance. So the work done will be this force of gravity multiplied by the distance Δx that this mass two falls. So that's one way to express the net work done: force of gravity times change in position. So that's m 2 times gravitational field strength g times Δx and then we can also talk about what the change in kinetic energy of the system is and that also is the net work done; this is the work-energy theorem and the net work done is the change in kinetic energy. So that's the final kinetic energy minus the initial so one-half times total mass times final speed squared minus one-half total mass times initial speed squared. It starts at rest though so this term is zero and the total mass is m 1 plus m 2 and we could fill out this data table— here's time in this column and then the position is being told to us by you know, the computer readout that's attached to this pulley— and then the speed can be figured out based on how much the position changes divided by the change in time between those positions and we can figure out what the final speed is then and compare the work done based on knowing the force and the change in position and compare that to the work done based on the final kinetic energy and they should be the same.