Determine the magnitude of F 1 for equilibrium of the particle.(Figure 1) Expres

Question

Determine the magnitude of F1 for equilibrium of the particle.(Figure 1)

Express your answer to two significant figures and include the appropriate units.

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Part B

Determine the magnitude of F2 for equilibrium of the particle.

Express your answer to two significant figures and include the appropriate units.

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Part C

Determine the magnitude of F3 for equilibrium of the particle.

Express your answer to two significant figures and include the appropriate units.

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Figure 1 of 1

Explanation / Answer

here,

writing all force in cartesian form

F1 = 0.5(i cos60 + j sin 60)
F2 = -0.8((3/5)i - (4/5)j )
F3 = -0.866(- i cos30 - j sin 30)

Equillibrium Equation of Particles :
for X ,Y and Z axis

Summation(Fx) = 0 = 0.5F1 + 0.6F2 - 0.866F3 ---------------Eqn(1)
Summation(Fy) = 0 = -0.8F2 - 0.5F3 + 800*Sin30--------------Eqn(2)
Summation(Fy) = 0 = 0.866F1 - 800Cos30 --------------Eqn(3)

F1 = (800*0.866)/ 0.866 = 800 N

also,using F1 in Eqn (1)

0.6F2 - 0.866F3 = - 0.5*800 = -400 --------------Eqn(4)

and Rewriting Eqn(2),
0.8F2 + 0.5F3 = -400 --------------Eqn(5)

Soving Eqn(4) and Eqn(5)
we get

F1 = 800N
F2 = 147N
F3 = 564N

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