Torque Balance in Lever System
<p>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.</p>
<p>To find the force \( F \), we use the principle of moments (torque balance) where the clockwise moments equal the anticlockwise moments about the pivot.</p>
<p>The weight of the mass \( W \) acting at a distance \( b \) from the fulcrum is given by:</p>
<p>\( W = m \cdot g \)</p>
<p>\( W = 72 \cdot 9.8 \) (taking \( g = 9.8 \, \text{m/s}^2 \))</p>
<p>\( W = 705.6 \) N</p>
<p>The anticlockwise moment due to \( W \) is \( W \cdot b \).</p>
<p>Let \( a = L - b \). Then \( a = 96 - 12 = 84 \) cm \( = 0.84 \) m.</p>
<p>The clockwise moment due to \( F \) is \( F \cdot a \).</p>
<p>Setting the moments equal for balance:</p>
<p>\( W \cdot b = F \cdot a \)</p>
<p>\( F = \frac{W \cdot b}{a} \)</p>
<p>\( F = \frac{705.6 \cdot 0.12}{0.84} \)</p>
<p>\( F = 100.8 \) N</p>
<p>Now, to find the reaction \( R \) at the fulcrum, we use equilibrium of vertical forces:</p>
<p>\( R = W + F \)</p>
<p>\( R = 705.6 + 100.8 \)</p>
<p>\( R = 806.4 \) N</p>
<p>Since \( F \) is 100.8 N which is approximately 100.9 N, and \( R \) is 806.4 N which is approximately 806.7 N.</p>
