Question

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 in 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 the arc

Answer 1

Given data:

mass m = 70 kg,

length L =  4 m

Solution :-

a)

the beginning of his motion
    v = 0,

   mv²/L = 0

   T = 0

b) a height of 1.5 m above the bottom of the circular arc
h = 1.5 m

mgL = mgh + mv²/R
T - mgcosθ = mv²/L
cosθ = (L - h)/L
T = mv²/L + mgcosθ

      = 2mg(L - h)/L + mg(L -h)/L

     = 3mg(L - h)/L

     = 3*9.8*70*(4 - 1.5)/4

     = 1286.25 N

c) mgL = mv²/2
T - mg = mv²/L
∴T = mg + mv²/L

       = mg + 2mg

      = 3mg

      = 3*70*9.8

      = 2058 N