A traffic light hangs from a pole as shown in the figure ( Figure 1 ) . The unif

Question

A traffic light hangs from a pole as shown in the figure(Figure 1) . The uniform aluminum pole AB is 7.30m  long and has a mass of 13.0kg . The mass of thetraffic light is 22.0kg .

A)Determine the tension in the horizontal massless cable CD.

B)Determine the vertical and horizontal components of the force exerted by the pivot A on the aluminum pole.

A traffic light hangs from a pole as shown in the figure(Figure 1) . The uniform aluminum pole AB is 7.30m long and has a mass of 13.0kg . The mass of the traffic light is 22.0kg . Determine the tension in the horizontal massless cable CD. Determine the vertical and horizontal components of the force exerted by the pivot A on the aluminum pole.

Explanation / Answer

I started by summing the torques at the hinge. There are three:
T(light)=5*9.8*7.5*cos(37)
T(cable)=-tension*6.31*sin(37)
T(pole)=8*97.5/2)*cos(37)

These all sum to zero.

I computed tension=140.5

The sum of the horizontal forces must be zero.
These are the tension in the cable and the horizontal reaction force at the hing. So the horizontal component is 140.5
The vertical forces are the weights of the pole and the light offset by the vertical reaction force at the hinge
the vertical component is (8+5)*9.8
=127.4

I checked the answer by computing the magnitude of the reaction force two ways. Using Pythagorean theorem
sqrt(140.5^2+127.4^2)
=189

I then summed the forces parallel to the pole:
5*9.8*sin(37)
8*9.8*sin(37)
140.5*cos(37)
=189

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