Question

Static Equilibrium of a Particle

A particle is subjected to three forces, F_1, F_2 and F_3. Forces and F_1 F_2 are defined with respect to the x and y axes as: Magnitude of F_1 = 9N Magnitude of F_2 = 10N Alpha = 57 degree beta = 59 degree Matlab input: Fl_mag = 9; F2_mag = 10; alpha = 57; beta = 59; Determine the magnitude and direction (angle 7) of F3 to maintain static equilibrium of the particle: Magnitude of F_3 = N

Answer 1

F1 = 9 N
F2 = 10 N
α = 57
β = 59

To Maintain Static Equilibrium,
F1 * cos(α) + F3 * cos(γ) = F2 * sin(β)
9 * cos(57) + F3 * cos(γ) = 10 * sin(59)
F3 * cos(γ) = 3.67 -------------1

F1 * sin(α) + F3 * sin(γ) = F2 * cos(β)
9 * sin(57) + F3 * sin(γ) = 10 * cos(59)
F3 * sin(γ) = - 2.397 -------------2

Dividing eq 2/1
tan(γ) = - 2.397/3.67
γ = tan^-1(- 2.397/3.67)
γ = - 33.15^o

F3 * cos(-33.15) = 3.67
F3 = 4.4 N