A system in equilibrium has a moment sum of zero and the sum of upward
forces equal to the sum of the downward forces.
The correct values are;
The x and y component of the reaction at pin B are;
Bₓ = 1471.5 N
[tex]B_y[/tex] = 1103.625 N
The x and y component of the force at pin C are;
Cₓ = 588.6 N
[tex]C_y[/tex] = 220.725 N
Reasons:
The weight of the cylinder, W = 90 kg × 9.81 m/s² = 882.9 N
Considering member AB, gives;
[tex]\sum M_A[/tex] = [tex]B_y[/tex] × 2 - [tex]B_x[/tex] × 1.5 = 0 ⇒ [tex]B_y[/tex] = 0.75·Bₓ
Considering member CB, gives;
[tex]\mathbf{\sum M_C}[/tex] = -[tex]B_y[/tex] × 2 + 882.9 × 2.5 = 0 ⇒ [tex]B_y = \dfrac{882.9 \times 2.5}{2} = 1103.625[/tex]
[tex]B_y[/tex] = 0.75·Bₓ ⇒ [tex]B_x = \dfrac{B_y}{0.75} = \dfrac{1103.625}{0.75} = 1471.5[/tex]
The x and y component of the reaction at pin B are;
Bₓ = 1471.5 N, [tex]B_y[/tex] = 1103.625 N
[tex]\mathbf{\sum F_y}[/tex] = 0 ⇒ -[tex]C_y[/tex] + [tex]B_y[/tex] - 882.9 = 0 ⇒ [tex]-C_y[/tex] + 1103.625 - 882.9 = 0
[tex]C_y[/tex] = 1103.625 - 882.9 = 220.725
[tex]\sum F_x[/tex] = 0 ⇒ -Cₓ + Bₓ - 882.9 = 0 ⇒ -Cₓ + 1471.5 - 882.9 = 0
Cₓ = 588.6
The x and y component of the reaction at pin C are;
Cₓ = 588.6 N, and [tex]C_y[/tex] = 220.725 N
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