The mechanical advantage (amount of change in speed or torque) of connected gears is proportional to the number of teeth each gear has. Called gear ratio, it's the ratio of the number of teeth on the larger gear to the number of teeth on the smaller gear.  For example, a gear with 12 teeth connected to a gear with 9 teeth would have a gear ratio of 4:3.

Hydraulics is the transmission of force through the use of liquids. Liquids are especially suited for transferring force in complex machines because they compress very little and can occupy very small spaces. Hydraulic pressure is calculated by dividing force by the area over which it is applied: P = F/A where F is force in pounds, A is area in square inches, and the resulting pressure is in pounds per square inch (psi).

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).

f_Ad_A = f_Bd_B + f_Cd_C

For this problem, this equation becomes:

35 lbs. x 8 ft. = 40 lbs. x 2 ft. + f_C x 4 ft.

280 ft. lbs. = 80 ft. lbs. + f_C x 4 ft.

f_C = \( \frac{280 ft. lbs. - 80 ft. lbs.}{4 ft.} \) = \( \frac{200 ft. lbs.}{4 ft.} \) = 50 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 R_b, our missing value, and plugging in our variables yields:

R_b = \( \frac{R_ad_a}{d_b} \) = \( \frac{45 lbs. \times 4 ft.}{7 ft.} \) = \( \frac{180 ft⋅lb}{7 ft.} \) = 25.71 lbs.