Week 2 Overview

Physics is defined as the study of energy and its interactions.
Energy is what enables action to occur, thus physics is foundational to our understanding of everything.
Source: Pearson Publishing

Speed Equation:
$ext{distance} = ext{speed} imes ext{time}$
Or in symbols:
$x = v imes t$
Where:
- $v$ = speed (in $m/s$ )
- $x$ = distance (in $m$ )
- $t$ = time (in $s$ )
Speed describes how fast something moves.
Velocity describes the speed and the direction of the motion.
Example: A car traveling at a speed of 30 m/s has a velocity of 30 m/s heading north.

Acceleration represents the change in velocity over time.
Acceleration Equation:
$ext{acceleration} = rac{ ext{change in speed}}{ ext{time}}$
Units for acceleration include $m/s^2$ .
A net Force is necessary to initiate acceleration.
Force Equation:
$F = ext{mass} imes ext{acceleration} = m imes a$
Force has an International System (SI) unit of kilograms (kg) times meters per second squared (m/s²), which corresponds to one Newton (N).
The common unit of force is also recognized as pounds (lb).

The force of gravity on Earth accelerates objects at $9.8 m/s^2$ .
In a hypothetical scenario, Superman weighs approximately 200 pounds, equivalent to a mass of about 91 kg.
To determine the minimum force Superman must exert to ascend:
$F = m imes a$
$F = 91 kg imes 9.8 m/s^2$
$F = 892 N$
Source: Warner Brothers

Pressure is generated by force acting over an area.
Pressure Equation:
$ext{Pressure} = rac{ ext{Force}}{ ext{Area}}$
The SI unit for pressure is Pascals (Pa), while in common usage, pressure is often described in pounds per square inch (psi).
Source: New York Post

For an event to occur, a source of potential energy is essential, such as a battery.
Movement is achieved through the conversion of potential energy into kinetic energy.
In simpler terms, potential energy decreases (e.g., draining a battery), while kinetic energy increases (e.g., speeding up).
Energy cannot be created or destroyed; it can only be transformed from one form to another within the universe.
Source: Wikipedia

Gravitational Potential Energy Equation:
$ext{Gravitational Potential Energy} = ext{mass} imes g imes ext{height} = mg h$
Kinetic Energy Equation:
$ext{Kinetic Energy} = rac{1}{2} ext{mass} imes ext{speed}^2 = rac{1}{2} mv^2$
The total energy when an object falls is described by:
$ext{Potential Energy} + ext{Kinetic Energy} = ext{Total Energy}$
$PE + KE = TE$
Specifically, this can be written as:
$mg h + rac{1}{2} mv^2 = TE$
Where:
- $m$ = mass (kg)
- $h$ = height (m)
- $v$ = speed (m/s)
- $g$ = gravitational acceleration = $9.8 m/s^2$

Consider a 10 kg ball released from a height of 6 meters.
Total energy at release is calculated as follows:
$PE + KE = TE$
$PE + 0 = TE$
$10 kg imes 9.8 m/s^2 imes 6 m = TE$
$TE = 588 J$
During its fall, kinetic energy increases until it reaches the ground while maintaining the total energy at 588 J (ignoring friction).

The potential energy at the height of 4 meters can be calculated:
$PE = mgh = 10 kg imes 9.8 m/s^2 imes 4 m = 392 J$
The kinetic energy at 4 meters is derived from the total energy:
$PE + KE = TE$
$392 J + KE = 588 J$
$KE = 588 J - 392 J = 196 J$

For the falling ball at 6 meters, it has an initial KE of 588 J just before impacting the ground:
To calculate the speed right before impact:
$KE = rac{1}{2} mv^2$
Rearranged as:
$2 imes KE = mv^2$
$v = rac{2 imes KE}{m}$
$v = rac{2 imes 588 J}{10 kg}$
$v = 117.6 rac{J}{kg}$
$v = 10.84 m/s$

Filling a balloon increases the internal pressure.
If punctured, the higher internal air pressure causes air to rush out until equilibrium is reached with external air pressure, resulting in a deflated balloon.
Pressure acts as a source of energy, similar to a battery; stored pressure allows for a flow of fluid (air, water) when released, converting potential energy to kinetic energy.

Boyle's Law Equation:
$P1 V1 = P2 V2$
Under constant temperature, reducing the volume of a gas increases its pressure as the gas is compressed.
Conversely, increasing the volume decreases the pressure as the gas expands.
This concept is also applicable in respiratory physiology, illustrating how pressure changes aid in breathing.
- Source: https://www.criticalcarepractitioner.co.uk/human-physiology/respiratory-system-physiology/

Fluid dynamics demonstrates that fluids move from areas of high pressure to areas of low pressure or from high potential to low potential.

States that increasing the speed of a fluid reduces its pressure.
Pressure builds up behind an obstruction, converting potential energy into kinetic energy within the flowing fluid.
- Real-world analogy: Water flowing from a faucet releases pressure and lowers it compared to the pressure behind the valve.

At junctions, narrower channels facilitate faster flow and have lower pressure compared to wider channels.
Bernoulli vs. Boyle:
- Bernoulli's Principle pertains to moving fluids, while Boyle’s Law concerns gas behavior under varying pressure and volume when static.

Demonstration: Covering the end of a garden hose decreases the cross-sectional area, resulting in higher pressure behind the obstruction, allowing a faster flow of water when released.

Given:
- For Section 1 with a speed of 2 m/s and area of 3 square inches, solve for area of Section 2 with speed of 6 m/s:
 $3 ext{ in}^2 imes 2 ext{ m/s} = A_2 imes 6 ext{ m/s}$
- Solve for $A2$ gives: $A2 = 1 ext{ in}^2$

The glottis opens when air from the lungs is forced through it and closes when the airflow reduces pressure sufficiently to shut it closed.

Observing everyday physical phenomena illustrating Bernoulli's effect, such as flying, which utilizes different pressure distributions over wings to create lift.
- Reference Links:
- NASA Bernoulli Principle