Question

A uniform rope with length L and mass m is held at one end and whirled in a horizontal circle with angular velocity ω. You can ignore the force of gravity on the rope. (a) At a point on the rope a distance r from the end that is held, what is the tension F? (b) What is the speed of transverse waves at this point? (c) Find the time required for a transverse wave to travel from one end of the rope to the other.

Answer 1

The tension, speed of transverse waves, and time required for a wave to travel are determined by various factors including mass, angular velocity, linear mass density, and length of the rope.

Step-by-step explanation:

(a) At a point on the rope a distance r from the end that is held, the tension F can be calculated using the centripetal force:

F = mω²r

Where m is the mass of the rope and ω is the angular velocity.

(b) The speed of transverse waves at the point can be found using the tension and the linear mass density μ of the rope:

v = √(F/μ)

(c) The time required for a transverse wave to travel from one end of the rope to the other is equal to the length of the rope divided by the wave speed:

t = L/v