Question

The three forces shown in the figure below act on a particle (with F1 = 46.0 N, F2 = 59.0 N, θ1 = 61.0°, and θ2 = 29.0°). If the particle is in translational equilibrium, find F3, the magnitude of force 3 and the angle θ3.

Answer #1

The figure is not shown here. But I will try to explain.

The forces are given as,

F1 = 46.0 N,

F2 = 59.0 N,

θ1 = 61.0°,

and θ2 = 29.0°

I think the the first two are in the same quadrant since the
angles are less than 90^{0}.

F_{3}cosθ_{3} = F_{1}cosθ +
F_{2} cosθ_{1}

=>F_{3}cosθ_{3} = 46cos61^{0} +
59cos29^{0}

=>F_{3}cosθ_{3} = 73.90
----------------(i)

& F_{3}sinθ_{3} =
F_{1}sinθ_{1}- F_{2}sinθ_{2}

=>F_{3}sinθ_{3} = 46sin61^{0} -
59sin29^{0}

=>F3sinθ3 = 11.63 --------------(ii)

=>F3 = [(73.9)^{2}
+ (11.63)^{2}]

=>F3 = 74.8 Newton

& By (ii)/(i):-

=>θ =tan^{-1}( 11.63/73.9 )= 8.92

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