f_Ad_A = f_Bd_B

For this problem, the equation becomes:

5 lbs. x 9 ft. = 55 lbs. x d_B

d_B = \( \frac{5 \times 9 ft⋅lb}{55 lbs.} \) = \( \frac{45 ft⋅lb}{55 lbs.} \) = 0.82 ft.

Torque measures force applied during rotation: τ = rF.  Torque (τ, the Greek letter tau) = the radius of the lever arm (r) multiplied by the force (F) applied. Radius is measured from the center of rotation or fulcrum to the point at which the perpendicular force is being applied. The resulting unit for torque is newton-meter (N-m) or foot-pound (ft-lb).

Static friction is friction between two or more solid objects that are not moving relative to each other. An example is the friction that prevents a box on a sloped surface from sliding farther down the surface.

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_ad_a = R_bd_b

Solving for R_a, our missing value, and plugging in our variables yields:

R_a = \( \frac{R_bd_b}{d_a} \) = \( \frac{50 lbs. \times 7 ft.}{6 ft.} \) = \( \frac{350 ft⋅lb}{6 ft.} \) = 58.33 lbs.

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_ad_a = R_bd_b

Solving for d_a, our missing value, and plugging in our variables yields:

d_a = \( \frac{R_bd_b}{R_a} \) = \( \frac{20 lbs. \times 5 ft.}{60 lbs.} \) = \( \frac{100 ft⋅lb}{60 lbs.} \) = 1.67 ft.