A 3.0 m long horizontal pole (negligible weight), hinged at a wall, supports a 1500 N...
A 3.0 m long horizontal pole (negligible weight), hinged at a wall, supports a 1500 N sign. The sign hangs 2.0 m from the hinge and, at the pole's other end, a cable pulls up and back at 53.1 degrees to the pole. (a) What is the Tension in the cable? (b) What is the horizontal part of the reaction force of the hinge on the pole?
Homework Answers
a)
Consider T as the tension in the pole.
Since the whole arrangement is in static equilibrium, the net
torque about any point is zero.
Consider net torque about the hinge,
2 x 1500 - 3 x T sin(53.1) = 0
2.399 T = 3000
T = 1250.49 N
b)
Consider the net horizontal forces on the pole,
Rx - T cos(53.1) = 0
Where Rx is the horizontal component of reaction at the
hinge.
Rx = T cos(53.1)
= 1250.49 x cos(53.1)
= 750.82 N
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