As test of strength, a diabolical trainer sets up the following apparatus. The trainee must maintain a variable pulling force which is always tangent to a nearly frictionless, semicircular surface . By slowly varying the force, a block with mass 23.0 kg is moved (at a very slow constant speed), and the spring to which it is attached is stretched from position 1 to position 2 (through an angle of 36 degrees). The spring has negligible mass and force constant 450 N/m. The end of the spring moves in an arc of radius a~=~ 49.0 cm.
What is the necessary size of the trainee's variable pulling force at position 2?
The Attempt at a Solution
I found the length of the arc first
36/180 = .2
C = 2(pi)R(1/2)
C = 0.49(pi)
Arc = .2(.49*pi)
Arc = 0.307876 m
then i multiplied that by the spring force constant
F = 0.3079(450)
F = 138.5 N
I think this is wrong cause i am not taking the mass into consideration but i wasnt sure where or how to include the mass of the block.