Question - Torque Balance in Lever System

Given that the mass \( m = 72 \) kg, the distance from the fulcrum to the mass \( b = 12 \) cm, and the total length of the lever \( L = 96 \) cm, we need to find the force \( F \) to balance the lever and the reaction \( R \) at the fulcrum.

To find the force \( F \), we use the principle of moments (torque balance) where the clockwise moments equal the anticlockwise moments about the pivot.

The weight of the mass \( W \) acting at a distance \( b \) from the fulcrum is given by:

\( W = m \cdot g \)

\( W = 72 \cdot 9.8 \) (taking \( g = 9.8 \, \text{m/s}^2 \))

\( W = 705.6 \) N

The anticlockwise moment due to \( W \) is \( W \cdot b \).

Let \( a = L - b \). Then \( a = 96 - 12 = 84 \) cm \( = 0.84 \) m.

The clockwise moment due to \( F \) is \( F \cdot a \).

Setting the moments equal for balance:

\( W \cdot b = F \cdot a \)

\( F = \frac{W \cdot b}{a} \)

\( F = \frac{705.6 \cdot 0.12}{0.84} \)

\( F = 100.8 \) N

Now, to find the reaction \( R \) at the fulcrum, we use equilibrium of vertical forces:

\( R = W + F \)

\( R = 705.6 + 100.8 \)

\( R = 806.4 \) N

Since \( F \) is 100.8 N which is approximately 100.9 N, and \( R \) is 806.4 N which is approximately 806.7 N.