Download Math Basics - Mercy

Math Basics
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•Algebra
•Trigonometry
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Algebra 1st
Show Units
Calculator in degrees!
Right Triangles
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Tools
protractor
metric ruler
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Constant Velocity
Kinematics - Motion!
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Uniform Acceleration
Constant
v=d
t
Forces are unbalanced
Fnet ! 0, a ! 0
not in equilibrium
Newton’s second law
•acceleration
a = ∆v
t
d = vit + 1/2at2
slo
pe
slo
Distance v.
time
vf2 = vi2 + 2ad
pe
=
=
v
a
Forces are balanced
Fnet = 0, a = 0
In equilibrium
Newton’s first law
•constant velocity
Speed v.
time
Acceleration v.
time
Distance v.
time
Speed v.
time
Acceleration v.
time
area under line = displacement
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! Horizontal
! velocity
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vx =! constant
– constant
speed
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Vertical
– constantmotion
acceleration Angle
vy = accelerated
Launch
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Horizontal Launch !
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Components
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v
-g
vy
+g
θ
v0 = vy
a = g = 9.81 m/s2
vx
v0 = vx
v0 = vx + vy
Dynamics - Forces!
• 3 Laws of motion
Free Body Diagrams
Forces at angles
FN = Fg
1. Inertia
2. a = Fnet
m
F
newtons
FA
=
0.
10
Fy =?
θ = 30˚
Ff = μFN
3. Action and Reaction
Fx =?
ax = Fx
m
!
N
Fy = (sin θ)(F)
Fx = (cos θ)(F)
Fg = mg
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Maximum 2
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Minimum 2
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FN
Resultant
Concurrent
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Block on an Incline (at rest)
FA
Equilibrant
5
7
5
Ff
θ
θ
3
Fgy
Fg
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Circular Motion
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v
Ff = μFN
Fc
ac
centripetal = “center seeking”
•
•
centripetal acceleration
ac =
centripetal force
Fc =
v2
r
mv2
r
Momentum
Gravitational Force
F
F
p = mv
Fg = G m1 m2
r2
m2
m1
(kg ⋅ m/s)
J = Δp
Impulse = change in momentum
r
Ft = Δmv
mutual attraction
Conservation of Momentum
m1v1 = m2v2
Fg
Fg
Before
m
v = 10 m/s
r
direct
After
5 kg
2 kg
v = 0 m/s
v = 0 m/s
2 kg
inverse square
•work
elastic collision KE and p conserved Bouncy!
W = Fd
Joule (J)
inelastic collision p conserved KE not conserved Sticky!
work done change in total energy of the system
F
5
=6
N
Fy
55˚
W = Fxdx
Fx
d = 15 m
•power
watt (W)
P = W = Fd = Fv
t t
5 kg
energy
Waves
joules
Gravitational Potential Energy PE = mgΔh
Spring Potential Energy
PEs = 1/2kx2
F = kx
k = spring constant (units: N/m)
Kinetic Energy
KE = 1/2mv2
PEg increases if height increases.
KE increases if speed increases.
PEs increases if spring is stretched or compressed.
types
mechanical (medium required) - sound
electromagnetic (no medium required) - light
energy +
medium
shapes
longitudinal - sound
!
!
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transverse - water
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2m
frequency (Hz)
Period (s) T = 1/f
Amplitude (m)
Wavelength (m) λ
Conservation of Energy
ET = PE + KE + Q
2m
period T = 1/f
ET
wave speed
(J)
depends upon the medium!
v=fλ
h
(J)
inverse relationship between f and λ
energy transformations
f
λ
speed of sound 331 m/s
speed of light 3.00 x 108 m/s
Reflection
Refraction
law of reflection
measure + draw
normal
θ2
Diffraction
In phase
(+ amplitudes)
λ, 360˚
index of refraction
n1 sinθ1 = n2 sinθ2
θ1
Interference
!
Out of phase
(- amplitudes
λ/ , 180˚
2
n1
n2
n2 = v1 = λ1
n1
v2
λ2
beats = f1 - f2
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Doppler Effect: change in the observed frequency due to motion
Polarization
Only transverse waves can be polarized
– light = yes,
sound = no.
lower
frequency
higher
frequency
Electricity and Magnetism
•electrostatics
electric fields
Fe = K q1q2
r2
test charges
!
!
coulomb
!
F
F
q
r
Law of Charges
A neutral object will be attracted (never repelled) by any charged
object. If two objects attract, they could have opposite charges or one
could be neutral. If two objects repel, they must have the same type of
charge.
Elementary Charge
electroscope
electron = proton = 1.6 x 10-19C
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Conservation of Charge
If two or more identical charged spheres touch, the
final charge on each is the average charge (total
charge ⁄ # of spheres). The total charge is conserved.
e+
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Field Strength
uniform electric field
+
E = Fe
q
Potential Difference
-
V= W
q
electron volts
•current electricity
circuit types
series
parallel
power
current
I = Δq
t
amps
watts
P = VI = I2R = V2
R
12 V
= 2.0Ω
= 4.0Ω
Ohm’s Law
R = V
I
Rt = R1 + R2 + R3 +...
ohms
1
1
1
1
Rt = R1 + R2 + R3
It = I1 = I2 = I3 . . .
Vt = V1 = V2 = V3 ...
resistance
R= ρl
A
•magnetism
Kirchoff’s Conservation Rules
law of magnets
Vt = V1 + V2 + V3 ...
“short, fat, cold” = least resistance
N
S
N-S poles
It = I1 + I2 + I3 ...
magnetic fields N to S
compass
slope = resistance
!
V
voltmeters/ammeters
!
I
A in series
V in parallel
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From N to S, density = strength (intensity)
Direction of lines = direction of compass needle
Modern + Nuclear Physics
wave - particle duality
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energy level diagram
Rutherford Model
emit
photon
Bohr Model
n=3
Ephoton = hf
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Ionization
energy
1.51 eV
Cloud Model
n=2
3.40 eV
Standard Model
n=1
13.6 eV
Excited state: higher energy
Ephoton = Ei - Ef
Ground state: lowest energy
absorb
photon
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photon = “particle” of light
Fundamental forces
Fundamental particles
electromagnetic
quarks
gravitational
Baryons Mesons Leptons
weak
proton = uud [+1]
strong
antiproton = uud [-1]
!
Mass Defect: mass of nucleus less than expected
E = mc2 (kg)
____ x 931 MeV (u)
fission
fusion