Question

A symmetrical beam (mass 68.2 kg, length 57.2 m) is supported by a wire that makes an angle with the wall ofβ = 27.7^o with the wall. The wire is attached to the beam at a point d = 0.881L from the wall. A small box of mass 82.6 kg slides on the beam. Find the value of x, the distance from the wall to the small box in meters, for which the tension in the wire is 23.5 times the weight of the beam.

Answer 1

here,

the mass of beam , m1 = 68.2 kg

length of beam , l = 57.2 m

beta = 27.7 degree

d = 0.881 l

mass of small box , m2 = 82.6 kg

the tension in the cable , T = 2.35 * m1 * g

taking moment of force about the hinge

T * d * sin(beta) - m1 * g * l/2 - m2 * g * x = 0

(2.35 * m1 * g) * (0.881 * l) * sin(beta) - m1 * g * l/2 - m2 * g * x = 0

2.35 * 68.2 * 9.81 * 0.881 * 57.2 * sin(27.7) - 68.2 * 9.81 * 57.2/2 - 82.6 * 9.81 * x = 0

solving for x

x = 21.8 m

the distance of small box from the wall is 21.8 m