Solving Work with Constant Force and Gravity on Mass in a Vertical Circle

[particlemath]

So I have a constant force F acting tangentially on a mass m in a vertical circle around a loop of radius r. The mass starts from rest at the very top of the loop. The only other force is gravity, that is m*g

Now I did Work=Change in energy with a system that is comprised of both the Earth and mass.

Here work is simply 2*pi*r*F.

When I try to solve this by seperating this into two parts, finding velocity at the bottom of the loop using work energy thm then using that as the initial velocity for another work energy theorem setup, it didn't work.

Why? Work energy theorem is supposed to work all the time. Gravity is conservative, so the results should be the same regardless.

Any help would be appreciated. Thanks.

 

[CWatters]

I think you will have to show your working so someone can see where the error is.

 

[BruceW]

hmm. to start with, if the particle initially has zero velocity, and there is only a tangential force F, plus gravity force, then the particle will not be able to move in a circle.

edit: although, the radial force should not matter for your work energy theorem calculation anyway, since it will be perpendicular to the particle's velocity. So anyway, what is it that you are calculating? (as CWatter says, more information would help). In the work-energy theorem method, I'm guessing you say that when the particle is initially at the top of the loop, it has zero kinetic energy, and the constant tangential force F acts on it as it goes around the loop once, so that work 2*pi*r*F is done on the particle, so when it has done the loop once, it should have kinetic energy equal to 2*pi*r*F, right?