The formula for force of friction (F_f) is the same whether kinetic or static friction applies: F_{f =} μF_N. To distinguish between kinetic and static friction, μ_k and μ_s are often used in place of μ.

Connected gears of different numbers of teeth are used together to change the rotational speed and torque of the input force. If the smaller gear drives the larger gear, the speed of rotation will be reduced and the torque will increase. If the larger gear drives the smaller gear, the speed of rotation will increase and the torque will be reduced.

The mechanical advantage of a wheel and axle lies in the difference in radius between the inner (axle) wheel and the outer wheel. But, this mechanical advantage is only realized when the input effort and load are applied to different wheels. Applying both input effort and load to the same wheel results in a mechanical advantage of 1.

The mechanical advantage of a wheel and axle is the input radius divided by the output radius:

MA = \( \frac{r_i}{r_o} \)

In this case, the input radius (where the effort force is being applied) is 3 and the output radius (where the resistance is being applied) is 8 for a mechanical advantage of \( \frac{3}{8} \) = 0.38

W_in = W_out
F_effort x d_effort = F_resistance x d_resistance

In this problem, the effort work is 920 ft⋅lb and the resistance force is 230 lbs. and we need to calculate the resistance distance:

W_in = F_resistance x d_resistance
920 ft⋅lb = 230 lbs. x d_resistance
d_resistance = \( \frac{920ft⋅lb}{230 lbs.} \) = 4 ft.