1. The problem statement, all variables and given/known data This isn't actually a homework question (well it is for homework). Basically for one of our projects we had a motor pull a cup through an upside down parabola shape. The motor was located off-axis in comparison to the parabola. The cup started from zero, then as the motor rotated it would wind the string and thus pull the cup. Now I need to calculate the work done on the cup by the motor (neglecting friction and such). 3. The attempt at a solution I'm not sure what to do here. I thought of getting equations for both accelerations (tangential and normal), then combining them into just one acceleration. integrating over all radii (it decreases) to get the total force exerted, but I'm not sure it's additive? Then maybe multiply that total force by the arc length of the parabola? Either way, I'm just looking for suggestions on how to do this.