State the laws of equilibrium - Leaving Cert Physics - Question 12 - 2017

To calculate the clockwise moment, we use the formula:

$m = F imes d$

Where:

• The force from the sign is 400 N and acts at a distance of 1.2 m from point X.
• The weight of the rod (330 N) acts at its midpoint (0.6 m from X).

Calculating the moments:

1. Moment due to the sign: $m_{sign} = 400 imes 1.2 = 480 ext{ Nm}$
2. Moment due to the rod: $m_{rod} = 330 imes 0.6 = 198 ext{ Nm}$

Total clockwise moment about point X:

$m_{total} = 480 + 198 = 678 ext{ Nm}$

To find the tension in the cable, we first equate the total clockwise moment to the tension acting at point X:

Using the formula for moment:

$m = T imes d$

Where:

• The distance (d) from X to where the tension acts is calculated as: d = 1.2 imes rac{1}{ ext{sin}(35^ ext{o})}

Substituting the moments:

$678 = T imes (1.2)$

Solving for T gives us:

T = rac{678}{(1.2)} imes rac{1}{ ext{sin}(35^ ext{o})}

Calculating this yields:

$T ext{ (Tension)} ext{ is approximately } 565 ext{ N}$

A rotating object can be in equilibrium if it maintains a constant angular velocity. This occurs when the net torque acting on the object is zero, which means that all the torque forces are balanced. Thus, the object continues to rotate without accelerating or decelerating, maintaining a steady state despite the rotation.