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 = \( \frac{R_bd_b}{d_a} \) = \( \frac{75 lbs. \times 7 ft.}{4 ft.} \) = \( \frac{525 ft⋅lb}{4 ft.} \) = 131.25 lbs.

The efficiency of a machine describes how much of the power put into the machine is turned into movement or force. A 100% efficient machine would turn all of the input power into output movement or force. However, no machine is 100% efficient due to friction, heat, wear and other imperfections that consume input power without delivering any output.

According to the principle of moments, you can maintain equilibrium if the moments (forces) tending to clockwise rotation are equal to the moments tending to counterclockwise rotation. Another name for these moments of force is torque.

This problem describes an inclined plane and, for an inclined plane, the effort force multiplied by the effort distance equals the resistance force multipied by the resistance distance:

F_ed_e = F_rd_r

Plugging in the variables from this problem yields:

F_e x 9 ft. = 270 lbs. x 3 ft.
F_e = \( \frac{810 ft⋅lb}{9 ft.} \) = 90 lbs.

Dead load is the weight of the building and materials, live load is additional weight due to occupancy or use, snow load is the weight of accumulated snow on a structure and wind load is the force of wind pressures against structure surfaces.