A 520-N uniform rectangular sign 4.00 m wide and 3.00 m high is suspended from a horizontal, 6.00-m-long, uniform, 140-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 rectangular sign hangs along the bottom of a rod connected to a hinge on a wall on its left. A cable with tension T at the right end of the rod connects to the wall above the hinge and makes a 30.0° angle with the vertical. The right end of the sign is at the right end of the rod. (a) Find the (magnitude of the) tension T in the cable.

Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
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Chapter10: Rotational Motion
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Problem 28P: A uniform beam resting on two pivots has a length L = 6.00 m and mass M = 90.0 kg. The pivot under...
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A 520-N uniform rectangular sign 4.00 m wide and 3.00 m high is suspended from a horizontal, 6.00-m-long, uniform, 140-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 rectangular sign hangs along the bottom of a rod connected to a hinge on a wall on its left. A cable with tension T at the right end of the rod connects to the wall above the hinge and makes a 30.0° angle with the vertical. The right end of the sign is at the right end of the rod.
(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
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