A stuntman whose mass is 70 kg swings from the end of a 4.0-m-long rope along the arc of a vertical circle. Assuming he starts from rest when the rope is horizontal, find the tensions on the rope that are required to make him follow his circular path,(a) at the beginning of his motion, (b) at a height of 1.5 m above the bottom of the circular arc, and (c) at the bottom of his arc.
F = ma
F = m * v^2/r
The Attempt at a Solution
a) Using the equation F = m*v^2/r, F is 0 because v is 0
b) First, I used the energy approach attempting to solve the problem:
mgh = 0.5mv^2 + mgh,
9.8 * 4 = 0.5 * v^2 + 9.8 * 1.5
v = 7m/s.
As I get velocity, I plugged the value into
F = m * v^2 / r
F = 70kg * 7^2 / 4
F = 857N
I do not think this is right, since the value is too large. Also, I found out that I can calculate the angle of the distance he travelled: arccos(2.5/4) = 0.89rad --> pi/2 - 0.89 rad = 0.68 rad, this is the angle which he travelled. But I do not know where to plug this in anywhere.