The efficiency of a machine describes how much of the power put into the machine is turned into movement or force. A 100% efficient machine would turn all of the input power into output movement or force. However, no machine is 100% efficient due to friction, heat, wear and other imperfections that consume input power without delivering any output.

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 12 and the output radius (where the resistance is being applied) is 7 for a mechanical advantage of \( \frac{12}{7} \) = 1.71

The modulus of elasticity measures how much a material or structure will deflect under stress. Stretch modulus is longitudinal stretch (like stretching raw bread dough), shear modulus is longitudinal deflection (like the horizontal displacement of a stack of magzines when a heavy object is placed upon them), and bulk modulus is compression of volume (like the compression of a loaf of bread under a heavy can at the bottom of a grocery bag).

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_b, our missing value, and plugging in our variables yields:

R_b = \( \frac{R_ad_a}{d_b} \) = \( \frac{55 lbs. \times 5 ft.}{9 ft.} \) = \( \frac{275 ft⋅lb}{9 ft.} \) = 30.56 lbs.

Mechanical advantage is resistance force divided by effort force:

MA = \( \frac{F_r}{F_e} \) = \( \frac{240 lbs.}{30 lbs.} \) = 8