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_ad_a = R_bd_b

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

R_a = \( \frac{R_bd_b}{d_a} \) = \( \frac{20 lbs. \times 7 ft.}{2 ft.} \) = \( \frac{140 ft⋅lb}{2 ft.} \) = 70 lbs.

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).

Drag is friction that opposes movement through a fluid like liquid or air. The amount of drag depends on the shape and speed of the object with slower objects experiencing less drag than faster objects and more aerodynamic objects experiencing less drag than those with a large leading surface area.

The mechanical advantage (MA) of an inclined plane is the effort distance divided by the resistance distance. In order to increase mechanical advantage, this ratio must increase which means making the effort distance longer and this can be accomplished by lengthening the length of the ramp.

W_in = W_out
F_effort x d_effort = F_resistance x d_resistance

In this problem, the effort work is 350 ft⋅lb and the resistance force is 70 lbs. and we need to calculate the resistance distance:

W_in = F_resistance x d_resistance
350 ft⋅lb = 70 lbs. x d_resistance
d_resistance = \( \frac{350ft⋅lb}{70 lbs.} \) = 5 ft.