Question

A man is going to complete a full vertical loop around a post to which a swing is attached. The swing's rope mass is negligible. If the length of the swing's rope is 3m, what is the minimum speed that the man must have at the top of the swing's circular trajectory such that the rope does not collapse? What is the speed of the man at the bottom of the swing's circular trajectory using the man's speed at the top of the swing's trajectory found previously?

Answer 1

(a) Length of the swing rope, L = 3.0 m

Suppose mass of the man = m and speed of the man at the top of the trajectory = v

So, at the top of the trajectory -

Centrifugal force = Weight of the man

=> m*v^2 / L = m*g

=> v^2 = L*g

=> v = sqrt(L*g) = sqrt(3.0 * 9.8) = 5.42 m/s

(b) Suppose at the bottom of trajectory, speed of the man = v'

Apply conservation of energy -

Total energy at the top = Total energy at the bottom

=> (1/2)*m*v^2 + m*g*(2L) = (1/2)*m*v'^2

=> v'^2 = v^2 + 2*g*(2L)

=> v'^2 = 5.42^2 + 2*9.8*(2*3.0) = 29.4 + 117.6 = 147

=> v' = 12.12 m/s (Answer)