Finding Equilibrium Force and Fulcrum Reaction in a Leverage System
Given:
Mass, \( m = 72 \text{ kg} \)
Distance to fulcrum, \( b = 12 \text{ cm} = 0.12 \text{ m} \)
Fulcrum reaction, \( R = 807.2 \text{ N} \)
Gravity, \( g = 9.81 \text{ m/s}^2 \)
Total length of lever, \( L = 96 \text{ cm} = 0.96 \text{ m} \)
Distance \( a = L - b = 0.96 \text{ m} - 0.12 \text{ m} = 0.84 \text{ m} \)
To find the equilibrium force \( F \), we use the principle of moments (torque \( \tau = Fd \)), where \( d \) is the distance from the fulcrum:
<p>\( \tau_{\text{clockwise}} = \tau_{\text{counterclockwise}} \)</p>
<p>\( F \cdot a = m \cdot g \cdot b \)</p>
<p>\( F \cdot 0.84 \text{ m} = 72 \text{ kg} \cdot 9.81 \text{ m/s}^2 \cdot 0.12 \text{ m} \)</p>
<p>\( F = \frac{72 \cdot 9.81 \cdot 0.12}{0.84} \)</p>
<p>\( F = \frac{847.872}{0.84} \)</p>
<p>\( F \approx 1009.61 \text{ N} \)</p>
To confirm that the given \( F = 100.9 \text{ N} \) is not correct, and the correct \( F \) is approximately \( 1009.61 \text{ N} \).
