Formula Card 06-07 - Weeblydensmorephysics.weebly.com/.../2/7/3/2/27327839/formulas.pdf ·...
2
Physics I Formula Card Reminder: Homework is fun to do! Williamsport Area High School Williamsport, PA cosθ= adj hyp tanθ= opp adj tanθ= sinθ cosθ x = - b ± b 2 - 4 ac 2a ∆= final - initial % error = | theoretical – experimental | theoretical y = mx + b m = ∆y ∆x sinθ= opp hyp Do not worry about your problems with mathematics, I assure you mine are far greater. – Albert Einstein R 2 = A 2 + B 2 - 2 AB cosθ Law of Cosines R 2 = A 2 + B 2 Pythagorean Theorem m = h i h o = -d i d o F = Kq A q B d 2 V = IR P = I 2 R = IV E = PT E = hf E = mc 2 Electricity & Magnetism f = 1 T v =λf n i sinθ i = n r sin θ r n = c v 1 f = 1 d i + 1 d o E = P 4π d 2 Waves & Sound Optics P = F A F 1 A 1 = F 2 A 2 ρ= m V P =ρ gh F buoy =ρ Vg W app = mg - F buoy ∆L =αL o ∆T ∆V =β V o ∆T Fluids & Solids ΣE o =ΣE T K = T °C + 273.15 T °F = (T °C ⋅ 1.8) + 32 T °C = T ° F - 32 1.8 Q = mC∆T Q = mH T f = m A C A T Ai + m B C B T Bi m A C A + m B C B C B = m A C A | T Af - T Ai | m B | T Bf - T Bi | Heat & Thermo- dynamics It is much more interesting to live not knowing than to have answers that might be wrong. –Richard Feynman p = mv F∆ t =∆ p F = m ∆v ∆ t p = p o K = 1 2 mv 2 W = Fd W = Fd cosθ P = W t MA = F r F e IMA = d e d r EFF = MA IMA = W o W i = F r d r F e d e W i = W o U g = mgh Momentum, Work, Energy & Machines E mech = K + U g IMA = teeth on rear sprocket teeth on front sprocket × pedal arm length wheel radius K before + U g before = K after + U g after C r = v v 0 = h H W =∆ E v = 2 π r T v = rg v = μrg F ∝ 1 d 2 T A T B 2 = r A r B 3 F = G m A m B d 2 g = G m d 2 v = Gm c r T = 2 π r 3 Gm c g = F m r A = r B T A 2 T B 2 3 T A = T B r A 3 r B 3 Circular & Planetary Motion T 2 = 4 π 2 Gm c r 3 Johannes Kepler Galileo Galilei t up = v o sin θ g t tot = 2v o sin θ g t = 2 y g R = v o 2 sin2 θ g y max = v o 2 sin 2 θ 2g Projectiles “With artillery, war is made” Napoleon Bonaparte F = ma w = F g = mg a c = v 2 r F c = ma c = mv 2 r τ= F ⊥ d T 2245 2 π l g F f =μ F N Dynamics v = ∆ d ∆t a = ∆v ∆t v = v o + at d = 1 2 ( v + v o )t d = v o t + 1 2 at 2 v 2 = v o 2 + 2ad Kinematics Isaac Newton % difference = | difference between values | average of values Degree Mode! Find Time! www.MrFlint.com [email protected] AIM SN: ljflintstone Scientific Notation Values in scientific notation are written as M x 10 n where 1 ≤ M < 10 and n is an integer. A cir =π r 2 C cir = 2 π r V sphere = 4 3 π r 3 A sphere = 4 π r 2 V cyl =π r 2 h A cyl = 2π r(r + h ) Math is Cool 1. Diagram 2. List values with std. units 3. Find & rearrange formula 4. Plug & chug 5. Units & sig. digs. 6. Realistic? Problem Solving
Transcript of Formula Card 06-07 - Weeblydensmorephysics.weebly.com/.../2/7/3/2/27327839/formulas.pdf ·...
Physics I Formula Card
Reminder: Homework is fun to do!
Williamsport Area High School Williamsport, PA
€
cosθ =adj
hyp
€
tanθ =opp
adj
€
tanθ =sinθcosθ
€
x =−b± b2 − 4ac
2a
€
∆ = final− initial
€
% error=|theoretical– experimental|
theoretical
€
y = mx+ b
€
m=∆y
∆x
€
sinθ =opp
hyp
Do not worry about your problemswith mathematics, I assure you mineare far greater. – Albert Einstein
€
R2 = A2 + B2 − 2 ABcosθLaw of Cosines
€
R2 = A2 + B2
Pythagorean Theorem
€
m=hi
ho
=−di
do
€
F =KqAqB
d2
€
V = IR
€
P = I 2R= IV
€
E = PT
€
E = hf
€
E = mc2Electricity &Magnetism
€
f =1
T
€
v = λf
€
ni sinθ i = nr sinθ r
€
n =c
v
€
1
f=
1
di
+1
do
€
E =P
4π d2
Waves &Sound
Optics
€
P =F
A
€
F1
A1
=F2
A2
€
ρ =m
V
€
P = ρgh
€
Fbuoy = ρVg
€
Wapp = mg− Fbuoy
€
∆L =αLo∆T
€
∆V = β Vo∆TFluids &Solids
€
ΣEo = ΣE
€
TK = T°C + 273.15
€
T°F = (T°C ⋅1.8) + 32
€
T°C =T° F − 32
1.8
€
Q = mC∆T
€
Q = mH
€
Tf =mACATAi + mBCBTBi
mACA + mBCB
€
CB =mACA |TAf −TAi |
mB |TBf − TBi |
Heat &Thermo-dynamics
It is much more interesting to live notknowing than to have answers that mightbe wrong. –Richard Feynman
€
p= mv
€
F∆ t = ∆ p
€
F = m∆v
∆t
€
p= po
€
K = 12 mv2
€
W = Fd
€
W = Fdcosθ
€
P =W
t
€
MA =Fr
Fe
€
IMA =de
dr
€
EFF =MA
IMA=
Wo
Wi
=Fr dr
Fede
€
Wi =Wo
€
Ug = mghMomentum,Work,Energy &Machines
€
Emech = K + Ug
€
IMA =teeth on rear sprocket
teeth on front sprocket×
pedal arm length
wheel radius
€
Kbefore+ Ug before = Kafter +U g after
€
Cr =v
v0
=h
H
€
W = ∆ E
€
v =2 π r
T
€
v = rg
€
v = µrg
€
F ∝1
d2
€
TA
TB
2
=rA
rB
3
€
F = GmAmB
d2
€
g= Gm
d2
€
v =Gmc
r
€
T = 2 π r 3
Gmc
€
g=F
m
€
rA = rB TA
2
TB2
3
€
TA = TB rA
3
rB3
Circular &PlanetaryMotion
€
T 2 =4π 2
Gmc
r 3
JohannesKepler
Galileo Galilei
€
tup =vosinθ
g
€
ttot =2vosinθ
g
€
t =2y
g
€
R=vo
2 sin2θg
€
ymax =vo
2sin2θ2g
Projectiles
“With artillery,war is made”NapoleonBonaparte
€
F = ma
€
w = Fg = mg
€
ac =v2
r
€
Fc = mac =mv2
r
€
τ = F⊥ d
€
T ≅ 2 πl
g
€
Ff = µ FNDynamics
€
v =∆d
∆t
€
a =∆v
∆t
€
v = vo + at
€
d = 12 (v + vo)t
€
d = vot + 12 at2
€
v2 = vo2 + 2adKinematics
IsaacNewton
€
% difference=|difference between values|
average of values
DegreeMode!
FindTime!
AIM SN: ljflintstone
Scientific NotationValues in scientific notation are written as
M x 10n
where
€
1≤ M <10 and n is an integer..
€
Acir = π r 2
€
Ccir = 2 π r
€
Vsphere=43 π r 3
€
Asphere= 4π r 2
€
Vcyl = π r 2h
€
Acyl = 2π r(r + h)
Math is Cool
1. Diagram 2. List values with std. units 3. Find & rearrange formula 4. Plug & chug 5. Units & sig. digs. 6. Realistic?ProblemSolving
Switch to SI... The rest ofthe world already has!
1 m = 39.6 in = 1.1 yard1 km = 0.62 mi1 m/s = 2.24 mph1 knot = 1.15 mph9.8 m/s2 = 32 ft/s2
1 kg = 2.20 lb (mass)1 N = 0.224 lb (weight)1 L = 1.06 quarts = 0.265 gal1 hp = 746 W 1 cal = 4.184 J
SI Prefixespenta-tera-giga-mega-kilo-hecto-deka-deci-centi-milli-micro-nano-pico-femto-
PTGMkhdadcmµnpf
1015
1012
109
106
103
102
101
10–1
10–2
10–3
10–6
10–9
10–12
10–15
Tycho Brahe
My goal is simple.It is complete
understanding ofthe universe, why
it is as it is andwhy it exists at all.
Earth–moon distance
Before
“SI changed our lives!It gave us newfoundhope and confidencewithout having to buyall of those expensivediet foods. Thanks SI!”After
Typical Coefficients of Frictionvalues vary with condition and preparation of surfaces
InterfaceRubber on concrete 0.80 0.65Rubber on wet concrete 0.60 0.40Rubber on ice 0.10 0.05Wood on wood 0.50 0.20Steel on steel (dry) 0.78 0.58Steel on steel (oiled) 0.15 0.06Teflon on steel 0.04 0.04
€
µs
€
µk
alphabetagammadeltaepsilonzetaetathetaiotakappalamdamu
nuxiomicronpirhosigmatauupsilonphichipsiomega
α Αβ Βγ Γδ ∆ε Εζ Ζη Ηθ Θι Ικ Κλ Λµ Μ
ν Νξ Ξο Οπ Πρ Ρσ Στ Τυ Υφ Φχ Χψ Ψω Ω
It’s All Greek To Me...
Physical Constantsand Useful Data
€
K = 8.988×109 N⋅m 2
C2
Absolute zero –273.15°C
€
G = 6.673×10−11 Nm2
kg2
€
h = 6.626×10−34J⋅ s
€
ρH2O ≡1000 kg
m 3
g = 9.80 m/s2
c = 2.998 x 108 m/s
€
ρH2O ≡1000 kg
m 3
proportional todefined as
€
F ∝1
d2
change in
€
v =∆d
∆t
Mathematics symbols
*Nonzeroes are always significant*Final zeroes but only after a decimal are significant
*Zeroes between sigificant digits are significant*Placeholding zeroes are not significant
Addition & SubtractionRound your answer to the least precise measurementyou’ re working with. (Usually the least decimal places.)
Multiplication & DivisionRound your answer to the least number of significantdigits among the measurements you’ re working with.
Some Significant Digit Rules Indices of RefractionMedium nvacuum 1.00air 1.0003water 1.33methanol 1.36crown glass 1.52quartz 1.54flint glass 1.61diamond 2.42
Thermodynamics Data C H
f H
vMaterial (J/kg•K) (J/kg) (J/kg)aluminum 903 3.97 x 105 1.09 x 107
brass 376 — —carbon 710 — —copper 385 2.05 x 105 5.07 x 106
glass 664 — —gold 130 6.30 x 104 1.64 x 106
iron 450 2.66 x 105 6.29 x 106
lead 130 2.04 x 104 8.64 x 105
mercury 130 1.15 x 104 2.72 x 105
methanol 2450 1.09 x 105 8.78 x 105
silver 235 1.04 x 105 2.36 x 106
water: liquid 4180 3.34 x 105 2.26 x 106
ice 2060 — —steam 2020 — —
zinc 388 1.12 x 105 1.89 x 106
JamesJoule
Coefficients of Expansion
Material values are (°C –1 or K –1)Solids α βaluminum 25 x 10–6 75 x 10–6
brass 21 x 10–6 63 x 10–6
concrete 12 x 10–6 36 x 10–6
copper 17 x 10–6 51 x 10–6
glass (soft) 9 x 10–6 27 x 10–6
glass (Pyrex) 3 x 10–6 9 x 10–6
iron & steel 12 x 10–6 36 x 10–6
stainless steel (410) 10 x 10–6 30 x 10–6
L iquidsMethanol — 1100 x 10–6
Gasoline — 950 x 10–6
Mercury — 180 x 10–6
Water (H20) — 210 x 10–6
GasesAir (and most other gases) 3400 x 10–6
Solar System Data
SunMercuryVenusEarthMarsJupiterSaturnUranusNeptune1 CeresPluto2003 UB
313
€
3.84×108m
Speeds of Sound
Bell X-1The first supersonic
aircraft
MediaAir (0°C)Air (20°C)Water (25°C)Sea water (25°C)Iron (25°C)Rubber (25°C)
m/s 331 343 1493 1533 5130 1550
–Steven Hawking
values may vary by alloy or mixture
Pierre andMarie Curie
averagev–
Radius(m)
Mass(kg)
OrbitalRadius (m) Eccentricity
OrbitalInclination
OrbitalRadius (AU)
6.96×108
2.44×106
6.05×106
6.38×106
3.40×106
7.15×107
6.03×107
2.56×107
2.48×107
9.42×105
1.15×106
2.86×106
?
1.99×1030
3.30×1023
4.87×1024
5.97×1024
6.42×1023
1.90×1027
5.69×1026
8.66×1025
1.03×1026
9.43×1020
1.5×1022
4.1×1022?
—5.79×1010
1.08×1011
1.50×1011
2.28×1011
7.78×1011
1.43×1012
2.87×1012
4.50×1012
4.15×1011
5.91×1012
1.01×1013
—0.2050.006770.01670.09340.04820.05420.04720.00860.0800.24880.442
—7.00°3.39°0.00°1.85°1.31°2.48°0.77°1.77°9.73°17.1°44.2°
— 0.387 0.723 1.00 1.52 5.20 9.5419.230.1 2.7739.567.3
Comet Halley 2.69×1012 17.9 ? 0.968 162°
![DX260LCA - Doosan · 2018. 6. 1. · 130 X 90 X 1,355 140 X 100 X 1,705 130 X 90 X 1,080 engine Engine Cylinder Horse Power [SAE J1349, net] Displacement Max Torque Tank Capacity](https://static.fdocuments.in/doc/165x107/60c1362522eb9f142b2ce4dd/dx260lca-doosan-2018-6-1-130-x-90-x-1355-140-x-100-x-1705-130-x-90-x-1080.jpg)
![coMMerciAl vehicleS · ZO74059-76B 130 x 130 8004927 TOWING EYE ZO76 VG 74059 WITH FLANGE reference flangelochbild mm] ite no.nr. ZO74053-50D1 100 x 110 8000537 ZO74053-50D2 130 x](https://static.fdocuments.in/doc/165x107/5e5236eb8153c82138628c50/commercial-vehicles-zo74059-76b-130-x-130-8004927-towing-eye-zo76-vg-74059-with.jpg)
