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

m = 42 kg

M = 60 kg

L = 5.5 m

a) the torque the beam exerts about the hinge = -m*g*(L/2)*sin(90)

= -42*9.8*(5.5/2)*1

= -1132 N.m

b) the torque the person exerts about the hinge = -M*g*d*sin(90)

= -60*9.8*1.27*1

= -746.76 N.m

c) the torque the cable exerts about the hinge. = 1132 + 746.76

= + 1878.76 N.m

d) T*L*sin(55) = 1878.76

T = 1878.76/(L*sin(55))

= 1878.76/(5.5*sin(55))

= 417 N

e) Fx = Tx

= 417*cos(55)

= 239.2 N

f) Fnety = 0

Ty - Fy - m*g - M*g = 0

Fy = g*(m+M) - Ty

= 9.8*(42+60) - 417*sin(55)

= 658.1 N

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