The beauty of the work-energy theorem (assuming only conservative forces act on the system) is that energy is a scalar, so you don't need any vector components in order to solve the problem.
Initial kinetic + initial potential = final kinetic + final potential
final kinetic = Initial kinetic +...
Well, the system is not in equilibrium in the sense that there needs to be a net centripetal force acting on the rotating object in order to enable circular motion.
However, the sum of the forces on the washers will be zero. The tension in the string and the gravitational force acting on the...
As a general rule, you define the direction of motion of any object to be the positive direction. Imagine if you unwound the string from around the pulley and laid the two blocks out on a flat surface. In that case you would clearly see that pulling on one block makes them both move in the same...
Well, you could come to office hours and ask me yourself, or you could do the following...
Rearrange the horizontal equation for range to solve for time. Insert that 't' into the vertical displacement equation and isolate the initial speed. That'll tell you how fast the potato needs to be...
Once you include the effects of friction, then you'll need to evaluate the path integral for the friction force from theta=0 to theta=theta critical, but that'll end up being a lot like the example I did in class last week.
cheers
Hi Amber
I suggest using summation of forces for circular motion as well as conservation of energy.
Since energy conservation and summation of radial forces hold at any point for the cube-sphere system, that should get you there.