A small ring of mass is suspended from the ceiling by three light
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Force and Translational Dynamics · Force and Translational Dynamics
Problem
A small ring of mass m is suspended from the ceiling by three light, inextensible strings of equal length. The upper ends of the strings are attached to the ceiling at the vertices of an equilateral triangle of side 2a. The ring hangs directly below the centroid of the triangle so that each string makes the same angle θ with the vertical. The ring remains at rest.
(i) Sketch the free-body diagram of the ring, indicating the weight and the tensions T in the three strings.
(ii) Show that the horizontal components of the three tensions cancel each other by symmetry.
(iii) Derive an expression for the tension T in each string in terms of m, g and θ.
(iv) If a=0.75m, θ=35∘ and m=1kg, calculate the numerical value of T.