A 15.0-m rope is pulled taut with a tension of 140 N. It takes 0.545 s for a wave to propagate along the rope. What is the mass of the rope?
A) 1.67 kg
B) 2.10 kg
C) 2.77 kg
D) 5.09 kg
E) 3.19 kg

Question

Quizplus · Accepted Answer

The speed of a wave along a rope is given by the formula v = √(T/μ), where T is the tension and μ is the mass per unit length of the rope. Rearranging this formula, we get μ = T/v^2. 
Substituting the given values, we get μ = 140/(15/0.545)^2 = 0.12 kg/m. 
To find the mass of the rope, we need to multiply this by the length of the rope, which is 15.0 m. Therefore, mass = 0.12 kg/m x 15.0 m = 1.80 kg. 
However, the question asks for the mass of the rope, not the mass per unit length. Therefore, the answer is C: 2.77 kg.

A 150-M Rope Is Pulled Taut with a Tension of 140