# If the green box weighs 30 lb. and is 1 ft. from the fulcrum, how much force would need to be applied at the blue arrow to balance the lever if the arrow's distance from the fulcrum is 6 ft.?

5.0 lb.

Explanation

To balance this lever the torques at the green box and the blue arrow must be equal. Torque is weight x distance from the fulcrum so the equation for equilibrium is:

$$R_{r} d_{r}=R_{b} d_{b}$$
where a represents the green box and b the blue arrow, R is resistance (weight/force) and d is the distance from the fulcrum.Solving for Rb, our missing value, and plugging in our variables yields:

$$R_{b}=\frac{R_{d} d_{a}}{d_{b}}=\frac{30 \mathrm{lb} \times \times 1 \mathrm{ft.}}{6 f \mathrm{ft} .}=\frac{30 \mathrm{ft} . \mathrm{lb} .}{6 \mathrm{ft} .}=5.0 \mathrm{lb}$$

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