Find the magnitude and sense of the forces required along the given lines of action, A...

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Find the magnitude and sense of the forces required along the given lines of action, A and B, for equilibrium. Show the locations of the forces on the diagram. 3. 120# 70# 170# 30#

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Answer 1

Answer #1

3.

120# 70# | 70# 30# 8

F_A = force at A

F_B = force at B

F_a = F_f = 70

F_d = 120

F_b = 30

ab = 2'

bc = 2'

cd = 8'

de = ef = 2'

using equilibrium of torque about "c"

taking clockwise torques as negative

F_a (ac) - F_b (bc) + F_A (0) - F_d (cd) + F_B (ce) - F_f (cf) = 0

(70) (2' + 2') - (30)(2') + 0 - (120) (8') + F_B (8' + 2') - (70) (8' + 2' + 2') = 0

F_B = 158

using equilibrium of force in vertical direction , taking upward force as positive

- F_a + F_b + F_A - F_d + F_B - F_f = 0

- 70 + 30 + F_A - 120 + 158 - 70 = 0

F_A = 72

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Answer 2

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