The picture above shows a horizontal 5.5 m long, 42 kg beam of uniform density.

Question

The picture above shows a horizontal 5.5 m long, 42 kg beam of uniform density. The red X indicates where it is attached to the building by a hinge. The person on the beam has a mass of 60 kg, and is located 1.27 m from the left edge. The right edge of the beam is attached by a cable to the building, making a 55-degree angle with the beam.

(a) Determine the torque the beam exerts about the hinge.

(b) Determine the torque the person exerts about the hinge.

(c) Determine the torque the cable exerts about the hinge.

(d) Determine the magnitude of the force the cable exerts on the beam.

(e) What is the X component of the force the hinge exerts on the beam?

(f) What is the Y component of the force the hinge exerts on the beam?

Explanation / Answer

Here,

length , L = 5.5 m

mass , m = 42 kg

mass of person , mp = 60 kg

x = 1.27 m

theta = 55 degree

a)

for the torque exerts about the hinge = m * L * g/2

torque exerts about the hinge = 42 * 9.8 * 5.5/2 N.m

torque exerts about the hinge = 1131.9 N.m

the torque exerts about the hinge is 1131.9 N.m

b)

torque the person exerts = mp * x * g

torque the person exerts = 60 * 9.8 * 1.27

torque the person exerts = 746.8 N.m

c)

for the toque about hinge of cable

torque of cable = 746.8 + 1131.9

torque of cable = 1878.8 N.m

d)

let the magnitude of force cable extered is F

F * sin(55) - 1878.8 = 0

solving

F = 2293.6 N

the tension in cable is 2293.6 N

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.