AP PHYSICS C MECHANICS: How to Create a Work vs. Position Graph for an Object Moving on an Incline

Interpreting and creating graphs of potential energy vs. position and work vs. position can be a bit of a confusing task.

In this video, we'll cover a practice AP question which involves drawing a graph of work vs. position for a block that first slides up an incline, then slides back down. We'll also talk a little bit about the corresponding potential energy vs. position graph and the relationship between work and the change in potential energy.

As the block-Earth system moves up the incline, the system's gravitational potential energy increases as its kinetic energy decreases. At its maximum height, the system has its greatest amount of potential energy and no kinetic energy. As the block descends the incline, its kinetic energy increases while the gravitational potential energy decreases back to zero. While this process is going on, gravity (a conservative force of constant magnitude) acts within the system.

Making a different system choice of the block alone, we can analyze the system's change in energy by considering work done by the gravitational force. As the block goes up the incline, the force of gravity is exerted in the opposite direction of the block's displacement, meaning negative work is done.

When the block has reached the top of the incline, the total work done from the initial position to that point is a relatively large, negative value. As the block descends the incline, the work done by gravity is positive, BUT the net work done (that is, the work done from the beginning of the situation until now) is still negative until the block has reached its original position at the bottom of the ramp. Because gravity is a conservative force, the net work done by gravity throughout this process is zero. Our work vs. position graph must indicate that the work done at any position reflects the net work done by gravity on the block.