A uniform horizontal beam of length 2.5 m and mass 12 kg is fastened to a vertical…
PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion
Problem
A uniform horizontal beam of length 2.5 m and mass 12 kg is fastened to a vertical wall by a frictionless hinge at its left end. At its right end, the beam supports a 25 kg sign that hangs vertically downward from a short hook. A cable is attached to the right end of the beam and makes a 30∘ angle above the beam as it is anchored to the wall directly above the hinge. The system is stationary and the beam remains exactly horizontal. Air resistance is negligible.
(a) Draw a clear free-body diagram of the beam, labeling all forces that act on it.
(b) Derive an algebraic expression for the tension T in the cable in terms of given quantities and fundamental constants.
(c) Calculate the numerical value of the tension T in the cable.
(d) Determine the horizontal and vertical components of the force exerted by the hinge on the beam.