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eimsori [14]
4 years ago
6

A movie stunt performer is filming a scene where he swings across a river on a vine. The safety crew must use a vine with enough

strength so that it doesn't break while swinging. The stunt performer's mass is 82.0 kg, the vine is 12.0 m long, and the speed of the stunt performer at the bottom of the swing has been determined to be 9.00 m/s. What is the minimum tension force (in N) the vine must be able to support without breaking?
Physics
1 answer:
Anuta_ua [19.1K]4 years ago
7 0

Answer:

T = 250.674\,N

Explanation:

The vine experiments a centripetal acceleration while swinging (the stuntsman experiments a centrifugal acceleration), whose most critical point occurs at the bottom and can be described by the Newton's Laws:

\Sigma F = T - m\cdot g = -m\cdot \frac{v^{2}}{R}

The minimum tension force that the vine must be able to support without breaking is:

T = m\cdot g - m\cdot \frac{v^{2}}{R}

T = m\cdot \left(g-\frac{v^{2}}{R} \right)

T = (82\,kg)\cdot \left[9.807\,\frac{m}{s^{2}}-\frac{\left(9\,\frac{m}{s} \right)^{2}}{12\,m}  \right]

T = 250.674\,N

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