Question

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?

Answer 1

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:

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

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

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

$T = 250.674\,N$