Answer:
L = 1.5 [m]
Step-by-step explanation:
To find the Force Z we must perform a sum of forces on the Y-axis equal to zero, (it is equal to zero since there is no movement, the beam is in equilibrium).
ΣFy = 0
- 30 - 20 - 40 + Z = 0
Z = 90 [N]
Now to find the length of the beam, we must perform a sum of moments equal to zero at the midpoint of the beam, where the load Z is applied.it is important to clarify that the moment generated by the force of 30[N] tends to rotate the beam counterclockwise (is taken as positive), while the load of 20 [N], tends to rotate the beam Clockwise (is taken as negative).
ΣM = 0
+ (30*0.5) - (20*x) = 0
15 = 20*x
x = 15/20
x = 0.75 [m] (this is the half of the distance)
L = 2*x
L = 2*0.75
L = 1.5 [m]