MCAT Physics: Circuits, Magnetism, Waves, and Sound

Junction Rule

the sum of all currents entering a junction must equal the sum of the currents leaving (conservation of charge)

Elements in Series have equal

current

loop rule

The sum of the potential differences (voltages) across all the elements around any closed circuit loop must be zero

elements in parallel have equal

voltage

Power output by a battery

P=IV

Power dissipated across resistors due to thermal energy

P=I^2R=V^2/R

magnitude of force by a magnetic field

F=qvBsin(theta) (theta= angle between v and B)

right hand rule for the force by a magnetic wave

1. point your hand in the direction of velocity of the particle

2. curl fingers toward B

3. thumb will be in the direction of the force for a positive particle. MUST FLIP DIRECTION FOR A NEGATIVE CHARGE

The Force of the magnetic field is always perpendicular to

both the velocity and magnetic field

In a uniform magnetic field, an accelerated particle will exhibit

uniform circular motion; direction depends on the charge of the particle

Work done by a magnetic field

0

magnetic fields are created by

moving electric charges, like a current

the direction of a magnetic field for a current in a long wire

point your thumb in the direction of the current and curl your fingers around the wire. Your fingers represent the direction of the magnetic field around the wire.

the magnetic field at a point in space is __ compared to the field line

tangent

simple harmonic motion

back and forth motion with a restoring force proportional to displacement

Hooke's Law

F=-kx; restoring force is opposite the displacement from equilibrium and proportional to that displacement and the spring constant

amplitude

+/-A: the greatest displacement from equilibrium during oscillation

energy stored in a spring as it stretches/compresses

PE=1/2 kx^2

work done by the spring

= - delta PE

conservation of mechanical energy

KE₁ + PE₁ = KE₂ + PE₂; where there is no friction or air resistance (or other non-conservative forces)

period

time it takes to complete one cycle (returning to the same position and velocity); independent of amplitude

frequency

number of cycles that occur in one second (Hz)

relationship between frequency and period

f = 1/T

frequency of a spring

f = (1/2π)√(k/m)

propagating oscillations that transfer energy

the medium is not propagated with the energy and oscillates with a series of identical oscillations, slightly out of phase

wavelength

length of one cycle

wave speed

the speed at which a wave travels through a medium. proportional to the wavelength times the frequency

transverse waves

medium oscillate perpendicular to the direction of wave propagation. Ex: ocean waves, waves on a string, electromagnetic waves

longitudinal waves

medium oscillates parallel to the direction of wave propagation. Ex: sound

the speed of a wave in a medium depends on the type of wave and physical properties of the medium

this means that v is constant in a medium regardless of the frequency or the wavelength

a wave moving from one medium to another will maintain the same frequency

the speed can change but the frequency of the wave doesn't change in relation to a change in medium

speed of sound waves in medium

slowest in gases, faster and liquids, and fastest in solids

standing waves

waves that are trapped where the endpoints determine which wavelengths can be trapped

node

point of zero oscillation on a standing wave

antinode

point of maximum oscillation on a standing wave

Standing waves in strings

displacement node at each end

frequency of a standing wave

f = nf1 (f1=frequency of the first harmonic) (n=harmonic integer)

first harmonic

fundamental frequency; longest wavelength standing wave that can exist on the string

wavelength of a standing wave

λ = 2L/n

Intensity

I=power/area

intensity of a spherical wave

I is proportional to 1/r^2

Intensity and amplitude

intensity is proportional to the amplitude squared

sound level

beta = 10 (log intensity +12)

For every increase in the intensity by a factor of 10

add 10 to the sound level

for every decrease in the intensity by a factor of 10

subtract 10 from the sound level

doppler shift

shift in the detected frequency of a wave due to the relative motion between the detector and the sound source.

In general:

as they get closer: higher frequency is detected

as they get further: lower frequency is detected

doppler shift equation (frequency detected)

fd=fs ((350+/-vd)/(350-/+vs))

- "top" sign is towards

- bottom sign is away