I had a lab that tested the dependence of gravitational potential energy on its position and the goal out of each exercise was to see if kinetic energy equaled potential energy. A cart was on a flat frictionless track, with a string attached to it and a hanging 20-g mass on the opposite end of the string hanging down by a pulley. We saw that the kinetic energy was inversely proportional to the PE in this exercise and that in this case there were multiple kinetic energy forms and a single potential energy term.
My confusion lied in the exercise that followed, where the track was now raised at an angle, the front of the cart pointing down the ramp. The difference aside from the elevated track was now we had multiple potential and kinetic energy forms. Our lab instructor mentioned that the carts height will change as it moves along the ramp but NOT by the same amount as the hanging mass. I don't understand that statement because when I plotted the potential and kinetic energy vs time graphs for both exercises they were basically identical, showing that both KE and PE were inversely proportional. Am I not understanding the question correctly when I relate it to the the kinetic energy and potential energy graphs?
Disclaimer: I know the colors suck and are distracting but the software I use in class to collect data doesn't have an easy way of making the graphs appealing to the eye.
For both exercises I used the equation to plot the graphs where kinetic energy was:
and potential energy was:
$PE = mgh_i+mgh_f$
Flat Surface Exercise
Surface Raised At Angle Exercise