Quicksheet: Physics and Math

vectors

physical quantities with both magnitude and direction (ex: force, velocity)

scalar

physical quantities that have magnitude, but no direction (ex: mass, speed)

displacement

the change in position that goes in a straight-line path from the initial position to the final position; independent from the path take (m)

average velocity

v = △ x/ △ t (m/s)

• v = d/t

acceleration

the rate of change of an object’s velocity; it is a vector quantity: a = △ v/ △ t (m/s²)

linear motion

v = v₀+at

x = v₀t + (1/2)at²

v² = v₀² + 2ax

v = (v₀ + v)/2

x = vt = ((v₀+v)/2) t

projectile motion

-vertical component of velocity = vsin(theta)

-horizontal component of velocity = vcos (theta)

fractional forces

static friction, kinetic friction

static friction (f_s)

the force that must be overcome to set an object in motion. It has the formula: 0 < f_s< u_sN

kinetic friction (f_k)

opposes the motion of objects moving relative to each other. It has the formula: f_k = u_kN

Newton’s first law (law of intertia)

a body is a state of motion or at rest will remain in that state until acted upon by a net force

Newton’s second law

when a net force is applied to a body of mass m, the body will be accelerated in the same direction as the force applied to the mass. This is expressed by the formula F = ma (N = kg

relationship btwn Fg and F_drag

-F_g > F_drag: person accelerates downward

-F_g = F_drag: terminal velocity is reached (person travels at constant velocity)

work

for a constant force F acting on an object that moves a displacement of d, the work is W = Fd cos (theta) (joule = N*m)

when the piston expands,

work is done by the system (W>0)

when the piston compresses the gas,

work is done on the system (W<0)

the area under a P vs V curve

amount of work done in a systempo

power

rate at which work is performed; it is given by P = W/△ t

(watt = J/s)

Kinetic energy

energy associated with moving objects: K = ½ mv²

• energy is a scalar quantity (joule)

newton’s third law

if a body A exerts a force on body B, then B will exert a force back onto A that is equal in magnitude, but opposite in direction: F_{A on B} = -F_{B on A}

newton’s law of gravitation

all forms of matter experience an attractive force to other forms of matter in the universe: F = G(m₁m₂) / r²

mass (m)

a scalar quantity that measures a body’s inertia

weight (Fg)

a vector quantity that measures a body’s gravitational attraction to the earth (Fg = mg)

uniform circular motion

a_c = v²/r

F_c = mv²/r

first condition of equilibrium

an object is in translational equilibrium when the sum of forces pushing it one direction is counterbalanced by the sum of forces acting in the opposite direction: sum of F = 0

potential energy

the energy associated with a body’s position. Gravitational potential energy of an object is due to the force of gravity acting on it: U = mgh

total mechanical energy

E = U + K

• is conserved when the sum of kinetic and potential energies remains constant

work-energy theorem

relates the work performed by all forces acting on a body in a particular time interval to the change in energy at the time: W = △E

conservation of energy

when there are no conservative forces (such as friction) acting on a system, the total mechanical energy remains constant: delt

torque

Fdsin(theta)

linear expansion

increase in length by most solid when heated: △L = aL△T

(“a Lot”)

volume expansion

increase in volume of fluids when heated

• △V = BV△T

conduction

the direct transfer of energy via molecular collisions

convection

transfer of heat by the physical motion of a fluidra

radiation

the transfer of energy by electromagnetic waves

specific heat

mc△T (“MCAT”)

• can only be used to find Q when object does not change phase

Q>0

Q<0

heat is gained

heat is lost

heat of transformation

the quantity of heat required to change the phase of 1 g of a substance

• Q = mL (phase changes are isothermal process)

first law of thermodynamics

△U = Q - W

adiabatic (Q = 0)

isometric (W = 0)

isothermal (△U = 0)

△U = -W; without heat flow

△U = Q; same volume

Q = W; same heat

second law of thermodynaics

in any thermodynamic process that moves from one state of equilibrium to another, the entropy of the system and environment together will either increase or remain unchanged

density (p)

p = m/V (kg/m³)

specific gravity

density_substance/ density_water

p_water

=10³ kg/m³

Weight in fluid=

p_{surrounding fluid}gV_fluid

pressure:

scalar quantity defined as force per unit area: P = F/A (N/m²)

• for static fluids of uniform density in a sealed vessel, pressure: P = pgz

Absolute pressure

in a fluid due to gravity somewhere below the surface is given by the equation P = P_o + pgz

Gauge pressure:

P_g = P_absolute - P_atmosphere; P_g = (density)*g*h

continuity equation

for fluids in motion, the mass flow rate must remain constant (conservation of mass)

• A₁v₁ = A₂v₂

bernoulli’s equation:

P + 1/2pv² + pgh = constant

Archimedes’ Principle

F_buoy = p_fluid gV_submerged

• buoyant force = weight of the displaced fluid

  • weight of fluid displaced < obj weight = obj sink

  • weight of fluid displaced > obj weight, obj float

Pascal’s principle

a change in the pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and to the walls of the containing vessel

Coulomb’s Law

the electrostatic force btwn two charged objects

• F = kq₁q₂ / r² (newton)

Electric Field

a positive point charge will move in the same direction as the electric field vector; a negative charge will move in the opposite direction

• E = F_e/q = kQ/r² (N/C or V/m)

Electrical Potential Energy (U)

the electrical potential energy of a charge q at a point in space is the amount of work required to move it from infinity to that point

• U = qdeltaV = qEd = kQq/r (J)

Electric dipoles

-p is the dipole moment (p = qd)

-dipole feels no net translation force, but experiences a torque

Electrical potentioal

-amnt of work required to move a positive test charge q from infinity to a particular point divided by the test charge

• V = U/q (J/C)

potential difference (voltage)

(△V) = W/q = k*Q/r (J/C)

V = Ed

when two oppositely charged parallel plates are separated by a distance d, an electric field is created, and a potential difference exists between the plate

current

the flow of electric charge; direction of current is the direction positive charge would flow, or from high to low potetntial

• I = Q/△t (A = C/s)

ohm’s law

V=IR (can be applied to entire circuit or individual resistors)

Resistance

-opposition to the flow of charge (increases with increase temps for most materials)

• R= pL/A (ohms)

Kirchoff’s laws

1. At any junction within a circuit, the sum of current flow into that point = sum of current leaving

   1. the sum of voltage sources = sum of voltage drops around a closed-circuit loop

Series circuits

Req = R1 + R2 + R3+…

Parallel Circuits

1/Req = 1/R1 + 1/R2 + 1/R3…

Power Dissipated by Resistors

P = IV = V²/R = I²R

capacitance

ability to store charge per unit voltage

• C = Q/V

Capacitors in series vs. parallel

1/Ceq = 1/C1 + 1/C2 + 1/C3…

Ceq = C1 + C2 + C3…

energy stored by capacitors

U = 1/2(QV) = 1/2(CV²) = 1/2(Q²/C)

• electrical potential energy held in electric field btwn its plates

longitudinal wave vs transverse wave

wave formulas

f = 1/T

v = f * wavelength

strings/ open pipes

wavelength = 2L/n

f = nv/2L

• open pipe ends - antinodes (max amplitude)

closed pipes

wavelength = 4L/n

f = nv/4L

• closed end - node

• open end - antinode

sound

propagates through a deformable medium by the oscillation of particles parallel to the direction of the wave’s propagation

intensity

I = P/A (W/m2)

Sound level (B)

= 10log (I/I0) (decibel dB)

Doppler effect

when a source and a detector move relative to one another, the perceived frequency of the sound received differs from the actual frequency emitted

doppler effect equation; stationary source; stationary detector

f’  = f ((v ± v_D)/ (v -/+ v_s)); v_s = 0; v_d = 0

snell’s law

n₁ sin(theta)₁ = n₂ sin(theta)₂

• n₂>n₁: light bends toward the normal

• n₂<n₁: light bends away from normal

n = c/v (c = 3×10⁸ m/s)

photoelectric effect

ejection of an electron from the surface of metal in response to light

• E = hf = hc/wavelength; K = hf - W

• K = max KE to eject electron; W = min energy to eject electron

mass defect

difference btwn the sum of the masses of nucleons in the nucleus and the mass of the nucleus. results from the conversion of matter energy

• E = mc²

Binding energy - hold nucleons within nucleus

exponential decay

half-life

alpha decay

alpha decay - emission of He nucl. (2 prot, 2 neut)

beta minus decay

neutron to proton; emit B-

benta plus decay

proton to neutron; emit B+

gamma decay

not changes; gamma ray emitted