Question

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 8.45 m/s. The rope's breaking strength is 1,000 N. Will the stuntman make it across the moat 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? m/s

Answer 1

• No
• 5.49 m/s

Step-by-step explanation:

The net force required to accelerate the stuntman in a circular arc of radius 11.5 m will be ...

F = mv²/r . . . . where this m is the mass being accelerated, v is the tangential velocity, and r is the radius.

Here, the net force needs to be ...

F = (80.5 kg)(8.45 m/s)²/(11.5 m) . . . . . where this m is meters

≈ 499.8175 kg·m/s² = 499.8 N

Gravity exerts a force on the stuntman of ...

F = mg = (80.5 kg)(9.8 m/s²) = 788.9 kg·m/s² = 788.9 N

Then the tension required in the rope/vine is ...

499.8 N+788.9 N= 1288.7 N

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

_____

The allowed net force for centripetal acceleration is ...

1000 N -788.9 N = 211.1 N

Then the allowed velocity is ...

211.1 = 80.5v²/11.5

30.16 = v² . . . . multiply by 11.5/80.5

5.49 = v . . . . . . take the square root

The maximum speed the stuntman can have is 5.49 m/s.

_____

Comment on crossing the moat

The kinetic energy at the bottom of the swing translates to potential energy at the end of the swing. At the lower speed, the stuntman cannot rise as high, so will traverse a shorter arc. At 8.45 m/s, the moat could be about 16.8 m wide; at 5.49 m/s, it can only be about 11.5 m wide.

Answer 2

The stuntman does not make it across the moat without falling in

a)

Since the rope's breaking strength is 1,000 N Therefore he cant make it without falling

Correct Option NO

b)

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 is

v=5.58m/s

From the question we are told

• 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 8.45 m/s.

• The rope's breaking strength is 1,000 N. Will the stuntman make it across the moat without falling in.

• 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.

a)

Generally the equation for Tension is mathematically given as

`T=(mv^2)/(r)+(mg)`

Where

`T=(80.5*8.45^2)/(11.5)+(80.5*9.8)\\\\T=1288.72N`

Since the rope's breaking strength is 1,000 N Therefore he cant make it without falling

b)

Generally the equation for Tension is mathematically given as

`T=(mv^2)/(r)+(mg)`

`1000=(80.5 *v^2)/(11.5)+(80.5*9.8)`

v=5.58m/s

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