A stunt man whose mass is 70 kg swings from the end of a 4.1 m long rope along t

Question

A stunt man whose mass is 70 kg swings from the end of a 4.1 m long rope along the arc of a vertical circle. Assume he starts from rest when the rope is horizontal. (a) Find the tensions in the rope that are required to make him follow his circular path, at the beginning of his motion. 0 N (b) Find the tensions in the rope that are required to make him follow his circular path, at a height of 1.5 m above the bottom of the circular arc. ___ N (c) Find the tensions in the rope that are required to make him follow his circular path, at the bottom of his arc. ___ N

Explanation / Answer

a)when you plug in F = m * v^2/r, since v is 0, F would also be 0 .

b)by using the conservation of energy. mgh = 0.5mv^2 + mgh,
9.8 * 4.1 = 0.5 * v^2 + 9.8 * 1.5
v = 7.14 m/s.

Plugging in the equation F = ma,
F = m * v^2 / r+mg cos(arccos(2.5/4)=0.68 rad) .

F = 70 * 7.132 / 4.1+686*0.77
F = 1401 N .

c)V= sqrt (2 g R )= sqrt( 2 x 9.8 x 4.1)=
V=8.96 m/s

tension required would be mg+mv2/r =2057 N .

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