Question

A stuntman with a mass of 82.5 kg swings across a pool of water from a rope that is 12.0 m. At the bottom of the swing the stuntman's speed is 8.65 m/s. The rope's breaking strength is 1,000 N. Will the stuntman make it across the pool without falling in?

Answer 1

Answer:

The stuntman will not make it

Explanation:

At the bottom of the swing, the equation of the forces acting on the stuntman is:

$T-mg = m\frac{v^2}{r}$

where:

T is the tension in the rope (upward)

mg is the weight of the man (downward), where

m = 82.5 kg is his mass

$g=9.8 m/s^2$ is the acceleration due to gravity

$m\frac{v^2}{r}$ is the centripetal force, where

v = 8.65 m/s is the speed of the man

r = 12.0 m is the radius of the circule (the length of the rope)

Solving for T, we find the tension in the rope:

$T=mg+m\frac{v^2}{r}=(82.5)(9.8)+(82.5)\frac{8.65^2}{12.0}=1322 N$

Since the rope's breaking strength is 1000 N, the stuntman will not make it.