# If the green box weighs 5 lb. and a 30 lb. weight is placed 7 ft. from the fulcrum at the blue arrow, how far from the fulcrum would the green box need to be to balance the lever?

42.0 ft.

Explanation

To balance this lever the torques on each side of the fulcrum must be equal. Torque is weight x distance from the fulcrum so the equation for equilibrium is:
$$R_{a} d_{a}=R_{b} d_{b}$$
where a represents the left side of the fulcrum and b the right, R is resistance (weight) and d is the distance from the fulcrum.Solving for da, our missing value, and plugging in our variables yields:
$$d_{a}=\frac{R_{b} d_{b}}{R_{a}}=\frac{30 l b . \times 7 f t .}{5 l b .}=\frac{210 f t . l b .}{5 l b .}=42.0 f t$$