A 500-N tightrope walker stands at the center of the rope.If the rope can withstand a tension of 1400 N without breaking,what is the minimum angle the rope can make with the horizontal?

Question

Quizplus · Accepted Answer

The tension in the rope must be equal to the weight of the tightrope walker in order to maintain equilibrium. Therefore:

Tension = Weight = 500 N

The maximum tension the rope can withstand without breaking is 1400 N. We can use this information to find the minimum angle the rope can make with the horizontal as follows:

Tension = Weight / sinθ

1400 N = 500 N / sinθ

sinθ = 500 N / 1400 N

θ = sin^-1(500 N / 1400 N)

θ ≈ 10°

Therefore, the minimum angle the rope can make with the horizontal is approximately 10°, which corresponds to choice (C).

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