Cards | 10 |

Topics | Boyle's Law, Force Lines of Action, Gear Ratio, Gear Trains, Kinetic Energy, Mechanics, Modulus of Elasticity, Structural Loads, Types of Simple Machines, Wheel and Axle |

Boyle's law states that "for a fixed amount of an ideal gas kept at a fixed temperature, pressure and volume are inversely proportional". Expressed as a formula, that's \(\frac{P_1}{P_2} = \frac{V_2}{V_1}\)

**Collinear** forces act along the same line of action, **concurrent** forces pass through a common point and **coplanar** forces act in a common plane.

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.

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.

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**.

Mechanics deals with **motion** and the forces that produce motion.

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).

A **concentrated** **load** acts on a relatively small area of a structure, a **static uniformly distributed load** doesn't create specific stress points or vary with time, a **dynamic load** varies with time or affects a structure that experiences a high degree of movement, an **impact load** is sudden and for a relatively short duration and a **non-uniformly distributed load** creates different stresses at different locations on a structure.

The six types of simple machines are the lever, wheel and axle, pulley, inclined plane, wedge, and screw.

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.