Question

A 207.8 kg uniform, a horizontal beam is hinged at one end and at the other is supported by a cable that is at 26 degrees to the left of the vertical. The beam is 2.63 m long. Calculate the direction of the force at the hinge (measured with respect to the horizontal). Answer with a number in degrees

Answer 1

here,

mass of unform beam , m1 = 207.8 kg

theta = 26 degree

l = 2.63 m

let the tension in the cable be T

taking moment of force about the hinge

T * cos(theta) * l - m1 * g * l/2 = 0

T * cos(26) - 207.8 * 9.81 /2 = 0

T = 1134 N

the tension in the cable is 1134 N

equating the force hoirzontally

the horizontal component of force at the hinge , Fx= T * sin(theta)

Fx = 1134 * sin(26) N = 497.1 N

equating the forces vertically

the vertical component of force at the hinge , Fy = m1 * g - T * cos(theta)

Fy = 207.8 * 9.81 - 1134 * cos(26) N

Fy = 1019.2 N

the direction of the force at the hinge , phi = arctan(Fy/Fx)

phi = arctan(1019.2 /497.1)

phi = 64 degree

the direction of the force at the hinge is 64 degree