Themed Physics Math Equations

 

Physics of Sports:

motion:
Vave = Dd / Dt                   1 m/s = 2.24 mph    real world: double distance takes 2.2  times longer

Vave = (Vf + Vi ) / 2             1 mile = 1610 m
a = (Vf -Vi ) Dt                  a(vertical free fall only) = -9.8 m/s2               

Vectors & projectiles                horizontal             vertical

sin< = opposite/hypotenuse         Vx = Dx / Dt           Vf  = Vi + a Dt

cos< =  adjacent/hypotenuse                                   Vf2 = Vi2 + 2a Dy

tan< =  opposite/adjacent                                       Dy = Vi Dt + ½ a Dt2

pythagorean theorem:   c2 = a2 + b2   



Physics of the Arts:

speed of sound in air                  v = 331 m/s + 0.6 T (in degrees celsius)

speed of sound in air (average):  v = 343 m/s

wave equation:      v = fl    or     v = Dd / Dt

frequency/period:         f = 1/T

stringed instruments and pipes open at both ends:      fn = nv / (2L)    where n = 1,2,3,….

pipes open at one end and closed at the other:         fn = nv/(4L)   where n = 1,3,5,…

western scale (centered about A4):        A4, B4, C5#, D5,   E5,  F5#,  G5#

frequency ratios:                        1,   9/8, 5/4,  4/3, 3/2,  5/3, 15/8

A4: has a frequency  f = 440 hz

# beats = f2 – f1

Intensity:      I = DE/Dt    =    P    =     P

                                   area          area      4Pr2

 

greatest tolerance of intensity:   I = 1 W/m2

lowest threshold of hearing intensity:    I = 1 x 10-12 W/m2

decibell loudness:   dB = 10*log(amplitude) 2

resolution angle:     Q =70 l / D

light spectrum:  radio>microwaves>infrared>visible>uv>x-rays>gamma rays
primary colors:   red, green, & blue   or cyan, magenta, & yellow

 (Mirrors & lenses)

 

Magnification:  M = hi/ho = -do/di
Snell's law:      n1sinQ1 = n2 sinQ2            or     n1v1 = n2v2     
Lens/mirror equation: 1/do + 1/di = 1/f

Indices of refraction:        glass= 1.5      water = 1.33 air = 1.00      diamond = 2.42

Speed of light in vacuum or air   = 3.00 x 108 m/s

At critical angle:  nsmall* sinQc = nbig
Physics of appliances (Electricity & Magnetism):

Electrostatic Force (Newtons)     =        q1 E

=        k q1 q2  / d2

 

Electric field (N/C)                              =  Force/charge

=  k q2 / d2

 

Potential Energy (Joules)            = work

=  Force * distance

                                                =  (-) q1 E d

 

Potential (voltage)                     =  energy/charge or work/charge

=  k q2 / d

Charge             1C =    6.3 x 1018 electrons

                        1e =  - 1.60 x 10-19 C

Mass                 1 electron =  9.11 x1031 kg

                        1 proton   =  1.67 x 10-27 kg

Coulomb  constant (Nm2/C2):   k  =  8.99 x 109    Nm2/C2

 

Electric Current Formulas to Use:

 

Voltage:   V = I*R   (Voltage = current*resistance  )
Power:      P = I*V    (or V2/R or I2*R )
cost:              cents=  rate (8 cents/kw-hr) * Power (kw) * time (hrs)     
1 horsepower = 746 watts  (watts is energy per second)

Magnet Formulas to Use:

 

Emf = #of turns * area * current change/time
transformer:  primary voltage/# turns =  secondary voltage / # turns