Question

speed at the bottom of the swing is 8.15 m/s. The archeologist doesn't know that the vine has a breaking strength of 1,000 N. Does he make it safely across the river without falling in?

Answer 1

Answer:

A stuntman with a mass of 80.5 kg swings across a moat from a rope that is 11.5 m. At the bottom of the swing the stuntman's speed is 8.15 m/s.

The archeologist doesn't know that the vine has a breaking strength of 1,000 N. Does he make it safely across the river without falling in?

= 1253.86 N

This is more than the capacity of the rope, so we do not expect the stuntman to make it across the river

Explanation:

Here, the net force needs to be

$F = \frac{mv^2}{r}$

where

m is the mass being accelerated,

v is the tangential velocity, and

r is the radius.

$F = \frac{(80.5 \times 8.15^2)}{11.5} \\= 464.96N$

Gravity exerts a force on the stuntman

$F = ma$

$F = (80.5 \times 9.8)\\= 788.9N$

The tension required in the vine is

464.96 N+788.9 N

= 1253.86 N

This is more than the capacity of the vine, so we do not expect the stuntman to make it across the river