A1,000-ti uniform boom at -580. to the horizontal is supported by a cable at an

Question

A1,000-ti uniform boom at -580. to the horizontal is supported by a cable at an angle 0-32.0. to the horrontal as shown in the fare beow. The boom is pivoted at the bottom, and an object of weight w 1.950 N hangs from its top. La (a) Find the tension in the suppert cable. (b) Find the components of the reaction force exerted by the pleot on the boom. (Assume the positive x-direction is to the right and the positive y direction is upward. Include the sign of the value in your answer.) horzontal component vertical component

Explanation / Answer

a) The torque about the pivot

T * (3/4 L) = [1000 * L/2 * cos theta] + [1950 * L cos theta]

L gets cancelled

T = 4/3 * [ (1000 * 0.5 * cos 58) + (1950 * cos 58) ]

T = 1731 N = 1.73 kN

b) horizontal component = T cos theta = 1731 * cos 32

Fx = 1468 N = 1.46 kN

c) Fy = Wboom + W - T sin theta

= 1000 + 1950 - (T * sin 32)

= 2033 N = 2.03 kN

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