A 500-N tightrope walker stands at the center of the rope such that each half of the rope makes an angle of 15.0° with the horizontal.What is the tension in the rope?
A) 1440 N
B) 970 N
C) 480 N
D) 2900 N

Question

Quizplus · Accepted Answer

First, we can draw a free-body diagram of the tightrope walker. The only forces acting on the tightrope walker are the weight force (500 N) acting downward and the tension force in the rope acting upward.

Next, we can break up the tension force into its horizontal and vertical components. Each half of the rope makes an angle of 15.0° with the horizontal, so the angle between the tension force and the horizontal is also 15.0°. Therefore, the vertical component of the tension force is T sin 15° and the horizontal component is T cos 15°.

Since the tightrope walker is in equilibrium, the net force in both the x and y directions must be zero. Therefore, the vertical components of the tension forces on each side of the tightrope walker must balance out the weight force:

T sin 15° + T sin 15° = 500 N
2T sin 15° = 500 N
T = 500 N / (2 sin 15°) ≈ 970 N

Therefore, the tension in the rope is approximately 970 N, which is answer choice B.

A 500-N Tightrope Walker Stands at the Center of the Rope