A wheel and axle uses two different diameter wheels mounted to a connecting axle. Force is applied to the larger wheel and large movements of this wheel result in small movements in the smaller wheel. Because a larger movement distance is being translated to a smaller distance, force is increased with a mechanical advantage equal to the ratio of the diameters of the wheels. An example of a wheel and axle is the steering wheel of a car.

To balance this lever the torques on each side of the fulcrum 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 = \( \frac{R_bd_b}{d_a} \) = \( \frac{70 lbs. \times 1 ft.}{4 ft.} \) = \( \frac{70 ft⋅lb}{4 ft.} \) = 17.5 lbs.

Ceramics are mixtures of metallic and nonmetallic elements that withstand exteme thermal, chemical, and pressure environments. They have a high melting point, low corrosive action, and are chemically stable. Examples include rock, sand, clay, glass, brick, and porcelain.

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).

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 8 and the output radius (where the resistance is being applied) is 3 for a mechanical advantage of \( \frac{8}{3} \) = 2.67

MA = \( \frac{load}{effort} \) so effort = \( \frac{load}{MA} \) = \( \frac{95 lbs.}{2.67} \) = 35.58 lbs.