The equilibrium condition allows finding the result for the tensions of the cables that support the block are:
T₁ = 245.1 N and T₂ = 263.1 N
Newton's second law establishes a relationship between the net force, the mass and the acceleration of the bodies, in the special case that the acceleration is zero is called the equilibrium condition.
∑ F = 0
Where F is the force.
A free body diagram is a diagram of the forces without the details of the bodies, in the attachment we can see a free body diagram of the system.
Let's write the equilibrium condition for each axis.
x-axis
T₂ₓ - T₁ₓ = 0
T₂ₓ = T₁ₓ
y-axis
[tex]T_{1y} + T_{2y} - W =0[/tex]
We use trigonometry to find the components of stress.
cos 17 = [tex]\frac{T_{1x}}{T_1}[/tex]
sin17 = [tex]\frac{T_{1y}}{T_1y}[/tex]
T₁ₓ = T₁ cos 17
[tex]T_1_y[/tex] = T₁ sin 17
cos 27 = [tex]\frac{T_2_x}{T_2}[/tex]
sin27 = [tex]\frac{T_2_y}{T_2}[/tex]
T₂ₓ = T₂ cos 27
[tex]T_{2y}[/tex] = T₂ sin 27
We substitute.
T₂ cos 27 = T₁ cos 17
T₂ sin27 + T₁ sin17 = W
We solve the system.
[tex]T_1 \frac{cos 17 \ sin 27}{cos 27} + T_1 sin 17 = m g \\T_1 ( tan 27 cos 17 + sin 17) = 19.5 \ 9.8[/tex]
T₁ (0.7796) = 191.1
T₁ = 245.1 N
We look for the T₂ tension.
T₂ = [tex]T_1 \ \frac{cos 17 }{cos 27}[/tex]
T₂ = 245.1 [tex]\frac{cos 17}{ cos 27}[/tex]
T₂ = 263.1 N
In conclusion, using the equilibrium condition we can find the result for the tensions of the cables that the block supports are:
T₁ = 245.1 N and T₁ = 263.1 N
Learn more here: brainly.com/question/19403002
