A tightrope walker walks across a 30-m long wire tied between two poles. The center of the wire is displaced vertically downward by 1.0 m when he is halfway across. If the tension in both halves of the wire at this point is $6294 \mathrm {~N}$ what is the mass of the tightrope walker? Neglect the mass of the wire.

Question

Quizplus · Accepted Answer

The tension in the wire creates two equal forces acting at an angle. Using trigonometry, the vertical component of the tension is equal to the weight of the tightrope walker. The angle θ can be found using the displacement and half the length of the wire. Using the formula $T \sin(\theta) = mg$, where $T = 6294 \, \text{N}$, and solving for $m$, we find that the mass is approximately 85 kg.

A Tightrope Walker Walks Across a 30-M Long Wire Tied 6294 N6294 \mathrm {~N}6294 N

A Tightrope Walker Walks Across a 30-M Long Wire Tied $6294 \mathrm {~N}$