A variable force F_vec is maintained tangent to a frictionless, semicircular surface View Figure . By slowly varying the force, a block with weight w is moved through the angla theta, and the spring to which it is attached is stretched from position 1 to position 2. The spring has negligible mass and force constant k. The end of the spring moves in an arc of radius a.
Calculate the work done by the force F_vec.
K_1 + U_1 + Wother = K_2 + U_2
The Attempt at a Solution
I'm not sure if I'm getting this correctly. Besides the elastic force, there's also the varying force correct? So that should Wother?
This is my equations so far:
K_1 = 0
U_1 = 0
K_2 = 1/2mv^2
U_2 = 1/2k(a*theta)^2
But I'm stuck on finding the velocity for K_2 in terms of a and theta. Any help is greatly appreciated, thanks. ... Assuming I'm correct so far (which I sort of doubt).