Question

A 110 kg uniform beam is attached to a vertical wall at one end and is supported by a cable at the other end. Calculate the magnitude of the vertical component of the force that the wall exerts on the left end of the beam if the angle between the cable and horizontal is θ = 39°.

Answer 1

here,

the mass of uniform beam , m = 110 kg

theta = 39 degree

let the tension in the string be T and the length of beam be L

taking moment of force about the left end

T * sin(theta) * L - m* g * ( L/2) = 0

T * sin(39) = 110 * 9.81 /2

T = 857.35 N

equating the forces vertically

T * sin(theta) = m * g - Fy

857.35 * sin(39) = 110 * 9.81 - Fy

Fy = 539.55 N

the magnitude of the vertical component of the force that the wall exerts on the left end of the beam is 539.55 N