Question

A 560-N uniform rectangular sign 4.00 m wide and 3.00 m high is suspended from a horizontal, 6.00-m-long, uniform, 120-N rod as indicated in the figure below. The left end of the rod is supported by a hinge and the right end is supported by a thin cable making a 30.0° angle with the vertical. (Assume the cable is connected to the very end of the 6.00-m-long rod, and that there are 2.00 m separating the wall from the sign.) (a) Find the (magnitude of the) tension T in the cable. N (b) Find the horizontal and vertical components of the force exerted on the left end of the rod by the hinge. (Take up and to the right to be the positive directions. Indicate the direction with the sign of your answer.) horizontal component N vertical component N

Answer 1

You have not attached the diagram with the problem. However, by analyzing the problem I am solving it.

Consider the left end of the rod be A, and the right end of the rod, B.

Now, do a free body diagram on the rod taking clockwise as positive:

(-120)(3) + (-560)(4) + B(vert)(6) = 0

B(vert)(6) = 360 +  2240 = 2600

=> B(vert) = 2600 / 6 = 433.3 N

Again -  
A(vert) = 560 + 120 - 433.33 = 246.7 N exerted on rod by hinge

T = 433.3/cos30 = 500.3 N

A(horz) = 433.3tan30 = 250.2 N exerted on rod by hinge

Therefore -

(a) Tension in the cable, T = 500.3 N

(b) Horizontal component of the force exerted on the left end of the rod = 250.2 N

Vertical component of the force exerted on the left end of the rod = 246.7 N