10. 2/5 points | Previous AnswersSerPSET9 12.P.046. Ask Your Teacher My Notes A

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10.2/5 points |  Previous AnswersSerPSET9 12.P.046.

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My Notes

A 1 175-N uniform boom at = 55.0° to the vertical is supported by a cable at an angle = 35.0° to the horizontal as shown in the figure below. The boom is pivoted at the bottom, and an object of weight m = 1 750 N hangs from its top.

(a) Find the tension in the support cable.
___________kN

(b) Find the components of the reaction force exerted by the floor on the boom.

Horizontal Component. Magnitude _________Kn

Vertical Component. Magnitude__________Kn

Explanation / Answer

a) sum moments about the pivot to resolve tension T,

Assume clockwise is positive moment.
recognize that the boom and its support cable are at 90° to each other

0 = 1175((L/2)cos55) + 1750(Lcos55) - T(¾L)
T = (1175((L/2)cos55) + 1750(Lcos55)) / (¾L)
T = 1787.646 N = 1788 N = 1.7kN

b) sum forces in the horizontal direction. Right is positive

0 = Fh - Tcos35
Fh = 1788cos35
Fh = 1465N = 1.4kN

sum forces in the vertical direction. Up is positive
0 = Fv + Tsin35 - 1175 - 1750
Fv = 1175 + 1750 - 1465sin35
Fv = 2085 N = 2.08kN

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