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.

Mass is a measure of the amount of matter in an object.  In general, larger objects have larger mass than smaller objects but mass ultimately depends on how compact (dense) a substance is.

Newton's Law of Univeral Gravitation defines the general formula for the attraction of gravity between two objects:  \(\vec{F_{g}} = { Gm_{1}m_{2} \over r^2}\) . In the specific case of an object falling toward Earth, the acceleration due to gravity (g) is approximately 9.8 m/s². 

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 = \( \frac{R_bd_b}{d_a} \) = \( \frac{70 lbs. \times 6 ft.}{3 ft.} \) = \( \frac{420 ft⋅lb}{3 ft.} \) = 140 lbs.

The gear ratio (V_r) of a gear train is the product of the gear ratios between the pairs of meshed gears. Let N represent the number of teeth for each gear:

V_r = \( \frac{N_1}{N_2} \) \( \frac{N_2}{N_3} \) \( \frac{N_3}{N_4} \) ... \( \frac{N_n}{N_{n+1}} \)

V_r = \( \frac{N_1}{N_2} \) = \( \frac{32}{4} \) = 8