Question

The beam shown is balanced at its midpoint. The weight of the beam is 40 Newton. Calculate the unknown force Z and the length of the beam.


Please answer it once, I'll mark it as brainliest​

Answer 1

Answer:

Length = 1.5m

Z = 30N

Explanation:

Finding the Length:

Consider torque about an axis through the midpoint, and the midpoint as the origin.

Since, torque is about midpoint, Torque due to weight of beam and Z = 0 as

Torque = perpendicular distance x Force

T = r X F

about the midpoint, perpendicular distance is 0, so

1. Torque due to Z, T₁ = 0
2. Torque due to beam's weight, T₂ = 0

Since, the beam is in equilibrium,

Upward Torque = Downward Torque

Let T₃ and T₄ be torques due to 30N and 40 N respectively.

Then according to Principle of moments

(-0.5)30 + 20y = 0

where 'y' is the distance from midpoint to 20N. 'y' is also half the length of the beam.

(0.5) 30 = 20y

y = 0.75 m

Length of the rod = 1.5m

--------------------------------------

Finding Z:

Now, consider the rotational axis to pass through the 30N force. Again, here torque due to 30N is 0. (See reason above)

Again, using Principle of moments,

T₁ + T₂ = T₃ + T₄

0.5Z + (0.5)40 = 0 + (1.25)20

Z = 30N