The translational equilibrium condition allows finding the response for the cable tension in a horizontal bar is:
T = 4250 N
Newton's second law establishes the relationship between force, mass and the acceleration of bodies, in the special case that the acceleration is zero, the relationship is called the equilibrium relationship.
∑ F = 0
where F is the sum of all external forces, the bold indacate vector
The reference system is a coordinate system with respect to which the forces are decomposed, in this case let's set a system where the x is in the horizontal direction and the y axis is in the vertical direction.
In the adjoint we can see the free body diagram of the system with the decomposition of the forces
x-axis
Rₓ - Tₓ = 0
Tₓ = Rₓ
y-axis
[tex]R_y + T_y - W_r - W =0[/tex]
Where T is the tension of the rope, R the reaction of the wall, [tex]W_r[/tex] the weight of the bar and W the weight of the loaded
Let's use trigonometry to find the component of the tension
cos 15 = [tex]\frac{T_x}{T}[/tex]
sin 15 = [tex]\frac{T_y}{T}[/tex]
Tₓ = T cos 15
T_y = T sin 15
Let's write the system of equations
T cos 15 = Rₓ
T sin 15 = mr g + m g + [tex]R_y[/tex]
It can be seen that there are more equations than unknowns, but there is a lack of data for the application of the rotational equilibrium condition, so we will use the special case of a horizontal bar, the vertical reaction becomes zero ([tex]R_y=0[/tex] ) with which the system can be solved
We look for the tension
T = [tex]\frac{W_r + W}{sin 15}[/tex]
T = [tex]\frac{300 \ +800}{sin \ 15}[/tex]
T = 4250 N
In conclusion using the translational equilibrium condition we can find the response for the cable tension is:
T = 4250 N
Learn more about translational equilibrium condition here:
https://brainly.com/question/7031958
