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A traffic light hangs from a pole as shown in the picture. The uniform aluminum

ID: 1486441 • Letter: A

Question

A traffic light hangs from a pole as shown in the picture. The uniform aluminum pole AB is 7.50 m long and has a mass of 12.0 kg. The mass of the traffic light is 21.5 kg.

1) Determine the torque due to the weight of the aluminum pole using the hinge as the axis.

2) Determine the tension in the horizontal massless cable CD, and the vertical and horizontal components of the force exerted by the pivot A on the aluminum pole.

3) Please give details answer to this problem Dont Skip any step in order to undertand what you did. Thanks a lot in advance.

Explanation / Answer

1) Torque due to pole is T =(7.5/2)*12*9.8)*cos(37) = 352.19 Nm

2) Tension in CD (Tcd) is obtained by balancing torques

Tcd *cos 53*(3.8/sin37) = (21.5*9.8*cos37)*7.5 +(12*9.8*cos37)*3.75

Tcd = 424.8 N

The forces exerted by A will be equal and opposite to the
sums of the vertical and horizontal forces exerted by the pole,
cable and light.

Favertical = (21.5*9.8*cos37)+ (12*9.8*cos37) = 262.19 N direction is upwards
Fahorizontal = 424.8 N , direction is to the right

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