Work is accomplished when force is applied to an object: W = Fd where F is force in newtons (N) and d is distance in meters (m). Thus, the more force that must be applied to move an object, the more work is done and the farther an object is moved by exerting force, the more work is done. By definition, work is the displacement of an object resulting from applied force.

Kinetic energy is the energy of movement and is a function of the mass of an object and its speed: \(KE = {1 \over 2}mv^2\) where m is mass in kilograms, v is speed in meters per second, and KE is in joules. The most impactful quantity to kinetic energy is velocity as an increase in mass increases KE linearly while an increase in speed increases KE exponentially.

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 10 and the output radius (where the resistance is being applied) is 7 for a mechanical advantage of \( \frac{10}{7} \) = 1.43

W_in = W_out
F_effort x d_effort = F_resistance x d_resistance

In this problem, the effort work is 420 ft⋅lb and the resistance force is 140 lbs. and we need to calculate the resistance distance:

W_in = F_resistance x d_resistance
420 ft⋅lb = 140 lbs. x d_resistance
d_resistance = \( \frac{420ft⋅lb}{140 lbs.} \) = 3 ft.

Static friction is friction between two or more solid objects that are not moving relative to each other. An example is the friction that prevents a box on a sloped surface from sliding farther down the surface.