The picture above shows a horizontal 5.5 m long, 40 kg beam of uniform density.

Question

The picture above shows a horizontal 5.5 m long, 40 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 70 kg, and is located 1.65 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. (Watch the sign!... we call clockwise negative and counterclockwise positive.) newton-meters (b) Determine the torque the person exerts about the hinge. (Watch the sign!) newton-meters (c) Determine the torque the cable exerts about the hinge. newton-meters (d) Determine the magnitude of the force the cable exerts on the beam. newtons (e) What is the X component of the force the hinge exerts on the beam? newtons (f) What is the Y component of the force the hinge exerts on the beam? newtons

Explanation / Answer

(a) mass of beam= 40 kg

weight of beam= 40(9.8 )=392 N

length of beam= 5.5 m

weight of beam acts at its center

so torque = 392 (5.5/2)= -1078 N-m (clockwise)

(2) mass of man= 70

weight of person= 70(9.8)= 686 N

torque of person about the hinge= 686 (1.65)= -1131.9 N-m (clockwise)

(3) let the torque due to cable = Tc

sum of all the torques about the hinge=0

Tc -1078-1131.9=0

Tc= +2263.8 N m (anti clockwise)

(d) let force exerted by cable = F

Tc= F r sin 55

2263.8 =F * 5.5 * sin 55

2263.8 = F * 4.5

F= 2263.8/4.5 = 503 N

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