Physics Final Exam Study Notes: Energy, Electricity, Waves, and Circular Motion

Unit 6: Energy

Module 1: Passenger Safety in a Car Crash

• Energy Transformation in Crashes: When a moving car crashes into a wall and crumples, most of the car's kinetic energy is dispersed. This energy is specifically used to break the chemical and physical bonds in the metal and plastic components of the vehicle.

• Role of Airbags: During a car crash, an inflating airbag stops a passenger moving forward. The airbag works by slowing the transfer of energy and helping to absorb some of that energy, which reduces the force of impact on the passenger.

• Factors Affecting Kinetic Energy: In a car crash, speed has a greater effect on the amount of kinetic energy involved compared to mass. This was discovered through various laboratory experiments.

• Breaking vs. Bouncing Bumpers: It is critical for a bumper to be designed to break rather than bounce upon impact. Breaking helps disperse the energy so that it does not reflect back entirely into the passengers.

Energy Transfer Diagrams

• Bumper Breaking on Impact:     * Car: Slows down and eventually stops.     * Bumper: Becomes crushed and crumples.     * Observation: The physical deformation of the bumper indicates where the energy was transferred.

• Semi Truck in Sand:     * Truck: Comes to a complete stop.     * Sand: The sand is displaced.     * Observation: The movement of the sand confirms energy transfer from the truck.

• Free Falling Object:     * Gravitational Field: Objects move closer to the Earth.     * Object: Speeds up as it falls.     * Surroundings: Some energy is transferred to the surroundings as heat and noise.

Kinematics and Energy Calculations

• Kinetic Energy (KE) Formulas and Variables:     * $KE = \frac{1}{2}mv^2$     * $E_g = mgh$     * $E_{el} = \frac{1}{2}kx^2$

• Car Kinetic Energy Example:     * Mass ($m$) = $1200\,kg$     * Velocity ($v$) = $10\,m/s$     * $KE = \frac{1}{2} \times 1200 \times (10^2) = 60,000\,J$     * If speed increases to $20\,m/s$: $KE = \frac{1}{2} \times 1200 \times (20^2) = 240,000\,J$     * Comparison: The energy becomes $4\times$ larger when the speed doubles.

• Crash-Test Sled and Spring Compression:     * Mass ($m$) = $900\,kg$, Velocity ($v$) = $5\,m/s$, Spring constant ($k$) = $25,000\,N/m$.     * $KE = \frac{1}{2} \times 900 \times (5^2) = 11,250\,J$     * Assuming all KE transfers to Elastic Energy ($E_{el}$):     * $11,250 = \frac{1}{2} \times 25,000 \times x^2$     * $11,250 = 12,500x^2$     * $0.9 = x^2$     * $x = \sqrt{0.9} \approx 0.95\,m$

• Vertical Spring Egg Launcher:     * $k = 800\,N/m$, Compression ($x$) = $0.25\,m$, Mass ($m$) = $0.20\,kg$.     * Energy transfer equation: $E_{el} = E_g$     * $E_{el} = \frac{1}{2} \times 800 \times (0.25^2) = 25\,J$     * $E_g = mgh \rightarrow 25 = 0.20 \times 9.8 \times h$     * $25 = 1.96h$     * Maximum height ($h$) = $12.76\,m$

Module 2: Electricity and Energy Production

• Key Definitions:     * Voltage: The pressure that causes electrons to flow; it refers to the total quantity of electricity transported.     * Current ($I$): Measured in amperes; the rate at which electrons flow past a specific point in a conductor.     * Battery: Does not provide electrons itself; rather, it creates the "pressure difference" required to get electrons moving collectively.     * Resistance ($R$): The degree to which electrons are hindered in their motion in a conductor; flows negative to positive in one direction.     * Power ($P$): The rate at which electrical energy is transferred or converted into another form.

• Electrical Formulas:     * $P = IV$     * $P = I^2R$     * $P = \frac{V^2}{R}$     * $V = IR$

• Circuit Calculations:     * LED Lights: $V = 12\,V$, $R = 24\,\Omega$.         * Current: $12 = I \times 24 \rightarrow I = 0.5\,A$         * Power: $P = 0.5 \times 12 = 6\,W$     * Phone Charger: $V = 120\,V$, $R = 60\,\Omega$.         * Current: $120 = I \times 60 \rightarrow I = 2\,A$         * Power: $P = 2 \times 120 = 240\,W$     * Laptop Charger: $V = 20\,V$, $P = 40\,W$.         * Current: $40 = I \times 20 \rightarrow I = 2\,A$         * Resistance: $20 = 2 \times R \rightarrow R = 10\,\Omega$     * LED Strip: $R = 48\,\Omega$, $I = 1.5\,A$.         * Voltage: $V = 1.5 \times 48 = 72\,V$         * Power: $P = (1.5^2) \times 48 = 108\,W$     * Voltage Source (Tyler): $P = 1874.4\,W$, $V = 154.4\,V$.         * Current: $1874.4 = I \times 154.4 \rightarrow I = 12.13\,A$     * Circuit (Ursula): $V = 975.4\,V$, $P = 1426.4\,W$.         * Current: $1426.4 = I \times 975.4 \rightarrow I = 1.46\,A$     * Circuit (Wendy): $I = 4.61\,A$, $V = 86.7\,V$.         * Power: $P = 4.61 \times 86.7 = 399.69\,W$

• VR System Power Draw:     * Headset: $90\,W$     * Console ($R = 30\,\Omega$, $V = 120\,V$): $P = \frac{120^2}{30} = 480\,W$     * Cooling Fan ($I = 2\,A$, $V = 120\,V$): $P = 2 \times 120 = 240\,W$     * Total Power: $90 + 480 + 240 = 810\,W$

Energy Generation and Measurement

• Generators: The primary function of a generator in a power plant is to spin a magnet around a copper coil of wire.

• Molecular Mechanism: As a magnet passes through a coil, the magnetic field causes electrons to separate from their atoms and move to the next atom in the same direction.

• Clean Energy: Described as energy that is as close to $100\%$ efficient as possible, meaning no $CO_2$ production and nothing wasted.

• Hydroelectric Power: A higher height difference in water increases Gravitational Potential Energy ($GPE$), which leading to a higher flow rate for energy production.

• Voltmeters: A voltmeter reads positive or negative based on the direction of electron flow.

• Efficiency: Measured as $(\text{output} / \text{input}) \times 100$. It describes how effectively energy is transferred between systems.

• Flow Rate: Measured by determining how much water volume is output per second ($L/s$).

Module 3: Electromagnetic (EM) Waves

• Wave Properties: As frequency increases, wavelength decreases.

• Wave Propagation: EM waves propagate through alternating electric and magnetic fields in an up-and-down manner, similar to people performing "the wave" in a stadium.

• Universal Constant: Every wave on the EM spectrum travels at the same speed (the speed of light), which is $3 \times 10^8\,m/s$.

• Photons: The smallest part of an EM wave is a photon.

• Wave-Matter Interactions: A wave can undergo Transmission, Absorption, or Reflection.

• UV Radiation and Heat: When UV rays reach our skin, they penetrate and cause molecules to move, which generates heat.

• X-Rays: X-ray waves are small enough to penetrate skin and soft tissues but are not small enough to penetrate dense bone, allowing for skeletal imaging.

• Global Warming: $CO_2$ molecules in the air reflect infrared (IR) waves back to Earth. Increased levels of $CO_2$ lead to more IR reflection, raising the Earth's temperature.

• Harmful vs. Non-harmful Waves:     * Non-harmful: Radio waves through Visible light.     * Harmful: Ultraviolet (UV), X-rays, and Gamma rays.

• Microwave Safety: Phones do not work inside foil-covered boxes or microwaves because microwaves (the waves used for communication) are too large to fit through the small holes in a microwave door or the gaps in the foil.

• Wave Intensity and Proximity: Holding a cellphone next to your head is more dangerous than standing $25\,m$ from a cell tower because the intensity of waves decreases significantly as one moves further away.

• 2D vs. 3D Waves: 2D waves are circular; 3D waves are spherical and fade faster than 2D waves.

Unit 7: Circular Motion

Circular Motion Principles

• Terminology: "Centripetal" means center-seeking.

• Fictitious Force: Centrifugal force is considered a fictitious force.

• Acceleration and Radius: There is an inverse relationship between acceleration and radius ($A_c = \frac{v^2}{r}$. As radius decreases, acceleration increases.

• Directional Change: Even if an object's speed is constant, it is accelerating in a circular path because it is constantly changing direction to remain on that path.

• Net Force: For an object in circular motion, the net force is always directed toward the center.

• Release Path: If an object being swung in a circle is released, it will follow a path tangential to the circle (perpendicular to the radius).

Circular Motion Formulas

• $F_c = \frac{mv^2}{R}$

• $A_c = \frac{v^2}{R}$

• $V = \frac{2\pi R}{T}$

• $A_c = \frac{4\pi^2 R}{T^2}$

• $f = \frac{1}{T}$

• $F_{net} = ma$

Calculations and Applied Problems

• Rotating Rod with Beads:     * Bead B has a greater linear speed because linear speed is directly related to radius ($v = \frac{2\pi r}{T}$, so greater $r =$ greater $v$).     * Bead A has a greater centripetal acceleration ($A_c$) because velocity and radius are inversely related in that context ($A_c = \frac{v^2}{r}$).

• Race Car Application:     * $m = 615\,kg$, $T = 14.3\,s$, $r = 50\,m$.     * Velocity: $v = \frac{2\pi(50)}{14.3} = 21.96\,m/s$     * Acceleration: $A_c = \frac{21.96^2}{50} = 9.64\,m/s^2$

• Period vs. Frequency:     * Period ($T$): The time required for one full rotation.     * Frequency ($f$): How many rotations occur per second.

• Roller Coaster Physics:     * $r = 15\,m$, $v = 8\,m/s$, $m = 1200\,kg$.     * Centripetal Acceleration: $A_c = \frac{8^2}{15} = 4.27\,m/s^2$     * Net Force: $F_c = 1200 \times 4.27 = 5120\,N$     * Gravity Force: $F_g = 1200 \times 9.8 = 11760\,N$     * Normal Force: $F_n = F_g - F_c = 11760 - 5120 = 6640\,N$

• Ceiling Fan:     * $75$ rotations in $60$ seconds.     * Period: $60 / 75 = 0.8\,s$     * Frequency: $75 / 60 = 1.25\,Hz$

• Merry-Go-Round:     * $r = 5.0\,m$, $m = 30\,kg$, $F_c = 120\,N$.     * $120 = \frac{30v^2}{5} \rightarrow 600 = 30v^2 \rightarrow 20 = v^2$     * Speed: $v \approx 4.47\,m/s$

Unit 8: Projectile Motion

• Independence of Components: The horizontal components of projectiles are totally independent of the vertical components.

• Initial Vertical Velocity: For an object launched horizontally (e.g., off a cliff, diving board, or desk), the initial vertical velocity is always $0\,m/s$.

• Optimal Launch Angle: A launch angle of $45^\circ$ achieves the maximum distance (farthest range).

• Trajectory Characteristics:     * At the highest point of travel, the vertical velocity is $0\,m/s$.     * The horizontal velocity remains constant and does not change throughout the entire flight path (Initial horizontal velocity = Final horizontal velocity).

• Factors Affecting Distance:     * Speed: Faster launch speed results in further distance traveled.     * Height: A higher launch point results in further distance traveled.