A 75-kg man is attempting a dangerous stunt in which he swings on a single cable

Question

A 75-kg man is attempting a dangerous stunt in which he swings on a single cable of 25
m in length attached to the Skyway Bridge over Tampa Bay. The man swings along the
arc of a vertical circle. If at the lowest point of the swing, he is moving at a speed of 12m/s, what is the magnitude of the centripetal force acting on him at this point, and what is the tension in the cable?

a) Fc = 735 N, T = 1167 N
b) Fc = 735 N, T = 432 N
c) Fc = 432 N, T = 120 N
d) Fc = 432 N, T = 1167 N
e) Fc = 432 N, T = 735 N

Explanation / Answer

Mass   m = 75 kg g = accelaration due to gtavity    = 9.8 m/s^2 centripetal   force   Fc   =   mv^2 / r Here   r = radius   of the circle = 25m velocity v =   12 m/s Fc   = ( 75kg)( 12 m/s)^2 / (25m)   = 432 N ---------------------------- at the lowest point   tenton in the wire is in upward direction gravity mg is in down ward directiom Hence   T   - mg = mv^2 / r     = 432 N Tension in the string T   =   mg + 432N   = (75kg)( 9.8 m/s^2) + 432 N = 1167 N Answer ( d)

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