f_Ad_A = f_Bd_B + f_Cd_C

For this problem, this equation becomes:

30 lbs. x 12 ft. = 50 lbs. x 2 ft. + f_C x 8 ft.

360 ft. lbs. = 100 ft. lbs. + f_C x 8 ft.

f_C = \( \frac{360 ft. lbs. - 100 ft. lbs.}{8 ft.} \) = \( \frac{260 ft. lbs.}{8 ft.} \) = 32.5 lbs.

Tension is a force that stretches or elongates something. When a cable or rope is used to pull an object, for example, it stretches internally as it accepts the weight that it's moving. Although tension is often treated as applying equally to all parts of a material, it's greater at the places where the material is under the most stress.

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.

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.

Coefficient of friction (μ) represents how much two materials resist sliding across each other.  Smooth surfaces like ice have low coefficients of friction while rough surfaces like concrete have high μ.