AP Physics 2 Flashcards - Equations

Based on the KcoolScience video ("AP Physics 2 Crash Course") - https://www.youtube.com/watch?v=AB2qIsZEveY

Ideal gas law

PV = nRT = Nk_BT
Where N is the number of particles and we usually take

R = \text{gas constant} = 8.314 \frac{J}{mol*K}
k_B = \text{Boltzmann’s constant} = 1.381 × 10^-23 \frac{J}{K}

Internal Energy of Ideal Monatomic Gas

U=\frac{3}{2}Nk_BT = \frac{3}{2}nRT

Thermal Transfer of Energy Per Time (Conduction)

Q/\Delta t=kA\frac{T_1 - T_2}{L}
Where L is the thickness of the material that is parallel to the direction of heat travels and where T_1 is hot and T_2 is cold and k is thermal conductivity (or R = \frac{1}{k} is thermal resistivity)

\Delta U = Q + W and how manipulating each variable changes

If temperature increases, internal energy increases

If temperature decreases, internal energy decreases

If surroundings put heat into system, Q increases

If system put heat into surrounds, Q decreases

If work is done on a gas, volume of gas decreases, W increases

If work is done by the gas, volume of the gas increases, W decreases

How Charge is Collected (3 Ways)

1. Conducting Negative Charges - one negatively charged object passes its negative charge to another (conductor) object by contacting

2. Conducting Positive Charges - one positively charged object absorbs electrons from another object by contacting thus leaving the other object positively charged

3. Lightning - Electrons burst through the space between two objects

Coulomb’s Law

F = k \frac{q_1q_2}{r²}

Voltage (Electric Potential) Definition

Electrical Isolines (Equipotential Lines)

Where do Positive and Negative Charges go to in an Electrical Field?

Electrical Potential Energy (J) per unit charge (C) so EPE has units (1 V = 1 \frac{J}{C})
Lines of equal potential (no work needed to move particles along those lines, but there will be energy produced or required to move particles perpendicular to those lines)

Negative charges move from low potential (voltage) to high potential (voltage)

Positive charges move from high potential (voltage) to low potential (voltage)

Electrical Potential Energy

E = k\frac{Q}{r²} (where k = 9.0×10^9 N*m²/C²)

E=\frac{1}{4\pi\epsilon_0}\frac{Q}{r^2}\text{ where} \epsilon_0 = 8.85 × 10^-12 c²/Nm²

\Delta PE = q \Delta V where q is the charge of the point charge

Electrical Field

E = F/q the field applies an equal force to identical point charges, regardless of where in the field they are

Electromotive Force is caused by…

Difference in electric potential (\Delta V)

Resistivity - intrinsic property

R = \frac{\rho L}{A} where L is length of material and A is area of cross section (more A means more lanes open for charge to flow) (more L means more matter to flow through)

Ohm’s Law Equation

Electric Power Equations

V = IR

I = \frac{V}{R}

P=\frac{E}{t}=IV=IR^{2}

Ammeter vs Voltmeters

1. Ammeter measures current, Voltmeter measures voltage

   1. Ammeters must be connected directly into DC circuits in series, voltmeters must measure the potential difference between two points and must be connected in parallel

2. Ammeters should have low internal resistance, voltmeters should have high internal resistance

Kirchhoff’s Voltage Law and Current Laws

1. Sum of all changes in potential across any closed path of a circuit must be zero

2. At any junction point, sum of all currents entering equals sum of all current leaving (useful for two batteries)

Capacitor (two plates that are charged by being connected to a battery and then discharged by being connected to a circuit)

Two metal plates with an insulating material (air or dielectric)

C = k \epsilon_0 \frac{A}{d} where k is the dielectric constant and usually k = 1.0 which means C = \epsilon \frac{A}{d} (if A is bigger, can store more charge, so more Q so more C since C = \frac{Q}{V} and if d is larger, then Coloumbic attraction will be weaker meaning the field will be weaker and since V is fixed due to the emf provided by the battery, that means that Q will go down so C will go down)

Energy Stored in Capacitor (stored in E fields)

U_C = \frac{1}{2} Q \Delta V

Capacitance in Circuits

For series, capacitors do not stack capacitance so we use \frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2}

But for parallel, capacitors will stack capacitance independently so we use C_{eq} = C_1 + C_2

RC

RC Circuit (Resistor Capacitor) - Describe what happens when you start charging it and after it’s finished charging.

If switch is closed, then current through R jumps up, and as charge builds on C, the current slows down and then we will see current decrease in R and C until the potential difference across the C will equal the potential of the battery

• Less R means that the battery gets charged quicker

Magnetic Field

B=\frac{\mu_0}{2\pi} *\frac{I}{r}

Where \mu=4\pi * 10^{-7} T m / A

Magnetic Force on Single (positive) Charges (Equation)

F=qvB\sin(\theta)

Use right hand rule to find direction of F

Magnetic Force on Current (Equation)

F = Il \times \vec{B} Where x is the cross product

\vec{F}_M = Il \sin \theta \vec{B}

Where l is length of the wire in the field and theta is the angle between the wire and B and B is the strength of the magnetic field

Two wires that flow together…

Two wires that flow apart…

…go together

…go apart

When a wire moves (v) through a magnetic field (B), current is induced

\varepsilon=Blv=V where l is the length of the wire

Magnetic Flux (scalar measure of total magnetic field passing through an area)

\Phi_B = \vec{B} \cdot \vec{A}

\Phi_B = \| \vec{B} \| \cos \theta \| \vec{A} \|

with units of Weber (Wb)

When a magnetic field (B) changes (\Phi_B changes) while the field is passing through a loop of wire, current is induced

How to increase magnetic flux

\varepsilon = \frac{\Delta \Phi_B}{\Delta t}

1. Rotate coil so that it is \perp to field

2. Increase area of coil (\Phi_B = \vec{B} \cdot \vec{A} )

3. Increase strength of magnetic field (\Phi_B = \vec{B} \cdot \vec{A} )

Len’s Law

Direction of induced current opposes the increase in flux (“Nature abhors a change in flux”)

Wavelength, frequency, speed, period

\lambda = \frac{v}{f} and T = \frac{1}{f}

Transverse vs Longitudinal Waves

Oscillations are perpendicular vs parallel to direction of wave velocity

Waves in graph equation

x = A \cos (2\pi f t)

Law of Reflection

\theta_i = \theta_r

Index of Refraction

n = c/v where v is the speed of light in the medium

Snell’s Law

n_1sin\theta_1 = n_2\sin\theta_2

Concave mirrors:

• Focal length

• Rays div or conv

• Image real/virtual/inverted/upright

Concave mirrors have positive focal lengths and rays converge:

1. If object behind focal length, image will be inverted and real (light converges at that actual point)

2. If object beyond the focal length, image will be upright and virtual

Convex mirrors:

• Focal length

• Rays div or conv

• Image real/virtual/inverted/upright

Convex mirrors have negative focal lengths and rays diverge. The image will always be upright and virtual and smaller than the object

Converging Lens

• Thick in the middle

• Converge rays on the other side of the lens (positive distance)

• Image is virtual and inverted unless the object is closer to the lens than the focus, created taller image that is upright and virtual

Diverging Lens

• Thin in the middle

• Rays diverge on the other side of the lens (the image is now negative distance)

• Image is always virtual and upright (like with convex mirrors)

Mirror/Lens Equation

\frac{1}{d_O} + \frac{1}{d_I} = f where f is the focal length

m = - d_i/d_0=h_i/h_O

Diffraction Pattern (Dark / Light Fringes)

d sin\theta = m\lambda

\Delta L = m \lambda where M = 0,1,2,3,… for light fringes and M=1/2,3/2,5/2,… are the dark fringes

Distance between diffraction patterns

x = \frac{m\lambda L}{d} where L is the distance the light has to travel and we can assume that \tan \theta = \sin \theta since \theta is so small meaning the hypotenuse is approximately equal to L

Thin film interference

Happens when:

• Wave travels through the film, hits the second layer and bounces back (wave travels distance of 2t where t is the height of the film)

• Equation is 2t = m ( \lambda / n ) where \lambda is the wavelength in the thin film and m = 0,1,2,3,… is the interference pattern

Photon Energy

E = hf

Photoelectric Effect (Work Function)

KE_{max} = hf - W_0 where W_0 is the minimum amount of energy needed to remove an electron from the metal atom. Meaning there is some f_0 such that hf_0 = W_0

This finding proved that light has properties of particles. Since wave theory of light predicts that changing intensity should produce more energy, but particle theory says that light is a particle and that it’s frequency is what causes the energy to change (particle theory was correct)

Momentum of a photon (de Broglie wavelength)

p = \frac{E}{c} = \frac{h}{\lambda} since the photon has no mass

Bohr model of a hydrogen atom and its energy levels

1/\lambda = R_H(\frac{1}{n_f²} - \frac{1}{n_i²}) where \lambda is the wavelength of light incident on the H atom

Standard Model

All matter is made of quarks and leptons (electron is leptons, protons and neutrons made of up and down quarks)

All force is made of force carriers:

• nuclear weak force is composed of (W & Z bosons)

• gravity force is composed of (Higgs boson)

Schödinger’s Wave Equation

E\Psi = H\Psi

Nuclear Decays: Alpha, Beta, Positron, Electron Capture, Gamma Decay

1. Alpha - 4/2 He atom produced

2. Beta - 0/-1 electron released by nucleus caused by a neutron turning into electron and proton

3. Positron - 0/+1 proton released by nucleus caused by a proton kicking it’s positive charge out to become a neutron

4. Electron capture - 0/-1 electron captured by nucleus causing a proton and that electron captured to fuse and become a neutron

5. Gamma - Nucleus is excited and releases high energy gamma radiation

Time Dilation Equation

\Delta t = \frac{\Delta t_0}{\sqrt{1-v²/c²}} where \Delta t > \Delta t_0 where the observer is moving at a speed of v (as a clock moves faster, the time it measures is running slower compared to a clock at rest)

Length Contraction Equation

L = L_0 \sqrt{1 - v²/c²} where L = \frac{L_0}{\gamma} where L0 is the distance as measured by the observers at rest and L is the distance measured by observers on the spaceship ( \gamma > 1 so L < L_0 )