A 15-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)1.7 kg
B)2.1 kg
C)2.8 kg
D)5.1 kg
E)3.2 kg

Question

Quizplus · Accepted Answer

The wave speed (v) on the rope can be calculated using the formula:
v = √(Tension/linear density)
where linear density (μ) is the mass per unit length of the rope.
Rearranging the formula, we get:
μ = Tension/v^2
Substituting the given values:
μ = 140/[(15/0.545)^2] = 0.0131 kg/m
Since we want the mass (m) of the whole rope, we can multiply the linear density by the length:
m = μ × length = 0.0131 × 15 = 0.197 kg ≈ 2.8 kg (to one decimal place)
Therefore, the best choice is C.

A 15-M Rope Is Pulled Taut with a Tension of 140