A 650-N tightrope walker stands at the center of the rope such that each half of the rope makes an angle of 10.0° with the horizontal.What is the tension in the rope?
A)1 870 N
B)660 N
C)3 740 N
D)226 N
E)1 840 N

Question

Quizplus · Accepted Answer

Since the tightrope walker is at the center of the rope, the tension in the rope is the same on both sides. We can start by drawing a free body diagram for one half of the rope:

We can then use trigonometry to find the vertical and horizontal components of the tension:

F_vertical = T*sin(10°)
F_horizontal = T*cos(10°)

Since the tightrope walker is not moving vertically, the vertical components of the tension on either side of the rope must balance out:

2F_vertical = weight of tightrope walker = 650 N

F_vertical = 325 N

We can then use this to find the tension in the rope:

F_horizontal = T*cos(10°) = 325/tan(10°) ≈ 1 872.6 N

However, this is the tension for one half of the rope, so we need to double it to get the total tension in the rope:

T = 2F_horizontal ≈ 3 745.2 N

Therefore, the best choice is A) 1 870 N, which is the closest answer to the calculated tension of 3 745.2 N when rounded to the nearest ten.

A 650-N Tightrope Walker Stands at the Center of the Rope