Question

a stuntman with a mass of 84.5 kg swings across a pond from a rope that is 12.0 m. at the bottom of the swing the stuntman's speed is 7.90 m/s. the rope's breaking strength is 1,000 n. will the stuntman make it across the pond without falling in? yes no (b) what if? what is the maximum speed (in m/s) that the stuntman can have at the bottom of the swing on this vine to safely swing across the river?

Answer 1

The stuntman will safely make it across the pond without falling in. The maximum speed that the stuntman can have at the bottom of the swing to safely swing across the river is 5.32 m/s.

To determine if the stuntman will make it across the pond without falling in, we need to calculate the tension in the rope at the bottom of the swing. We can use the centripetal force equation: Tension = (Mass x Velocity²) / Radius. Plugging in the given values, we get Tension = (84.5 kg x (7.90 m/s)²) / 12.0 m = 460.083 N. Since the rope's breaking strength is 1,000 N, the stuntman will safely make it across the pond without falling in.

(b) To calculate the maximum speed that the stuntman can have at the bottom of the swing to safely swing across the river, we need to find the tension in the rope. Equating the tension to the rope's breaking strength, we get Tension = (Mass x Velocity²) / Radius. Solving for Velocity, we get Velocity = √((Tension x Radius) / Mass). Plugging in the given values, we get Velocity = √(1,000 N x 12.0 m) / 84.5 kg) = 5.32 m/s.