PHYSICS REVIEWER Velocity
-speed and direction Scalar quantity -physical quantity Vector Quantity
-has both a direction and magnitude Displacement
-change of position; from one from point to another
Vectors may be:
1. Parallel – same Direction
2. Anti-parallel – opposite direction Vector Addition
C = B + A ; where c = a+b
Components of Vectors A = Ax + Ay
If is measured from the (+) x-axis,ѳ rotating towards the (+) y axis
Ax = Acos ; Aѳ y = Asinѳ
If we know vector A A = √ Ax2 + Ay2
So, tan = Aѳ y / Ax; = arctan Aѳ y / Ax
Unit Vector
-vector that has a magnitude of 1 Î = points to the direction of x - axis
= points to the direction of y - axis Ĵ
= xî + y
Ā Ā Ā ĵ
B = Bxî + Byĵ
MOTION ALONG A STRAIGHT LINE vave = x2 – x1 / t2 – t1 = x / tΔ Δ
where:
vave - average velocity
x – Displacement t – time
aave = v2 – v1 / t2 – t1 = v / tΔ Δ
where:
aave = average acceleration
v – Velocity t – time
MOTION WITH CONSTANT
ACCELERATION v = vo + at x = xo +vot + (1/2) at2 v2 = v o2 + 2a(x-xo) x-xo = (vo +v/2)t
Free Falling Bodies
-bodies moving at a constant acceleration
Acceleration due to Gravity g = 9.8 m/s2
MOTION IN TWO OR THREE DIMENTIONS
Projectile
-anybody that is given an initial velocity and then follows a path determined entirely by the effects of gravitational acceleration and air resistance.
Trajectory
-path followed by a projectile is 2-dim because it involves xy-coordinate plane.
Projectile Motion(PM)
-combination of horizontal motion w/ constant velocity & vertical motion w/ constant acceleration Ax = 0; Ay = -g Eq. involve in PM x = (vocosѳo)t y = (vosinѳo) – ½(gt2) vx = vocosѳo vy = vosinѳo – gt
For Finding the projectile speed at any given time:
V = √ Vx2 + Vy2 – magnitude
Tan = Vѳ y / Vx
Things to remember:
At initial position t=0 with the x-axis horizontal & y-axis upward then:
xo = 0; yo = 0; ax = 0; ay = -g
At the highest point of trajectory vy = 0
MOTION IN A CIRCLE
Velocity at one complete revolution (period (T)) v = 2πR/T where: R – Radius T – Time Radial Acceleration
arad = v2 /R – by substitution - arad =
NEWTON’S LAW OF MOTION Newton’s 1st Law:
-a body acted on by no net force moves w/ constant velocity & zero acceleration.
For a body in equilibrium: F = 0; where F – Force Σ Each Component: F Σ x = 0; FΣ y = 0 Newton’s 2nd Law:
-if a net external force acts on a body, the body accelerates. The direction of acceleration is the same as the direction of the net forces.
F = ma; where m = mass, a = Σ acceleration Each component: F Σ x = max; FΣ y = may; FΣ z = maz Mass
-characterizes the initial properties of a body
Weight
-a force exerted on a body by the pull of the earth or some other large body. w = mg ; where w- weight, m-mass,
g - acc. Due to gravity Newton’s 3rd Law:
-If a body A exerts a force on body B (an action), then body B exerts a force on body A (a reaction). These two forces have the same magnitude but are opposite in direction.
Forces acted on different bodies: FA on B = -F B on A
In solving forces, use the free body diagram
Work
W=Fs; where F – Force, s – displacement
Unit for work: Joules = 1 N.m
When force & displacement are on different directions
W = Fscosѳ
WTOTAL > 0 – speeds up
WTOTAL < 0 – slows
WTOTAL = 0 maintains same Speed
KE = ½(mv2)
**the work done by the net force on a particle equals the change in the particles KE WTOTAL = K2 – K1 = K (work-energyΔ theorem) SPRING F = kx – force of a spring Where: k – Spring constant
x – diff. of the stretch and outstretch spring.
W = ½(kX2) – work done on a
spring
If already initially stretch: W = ½(kX22) - ½(kX12)
Power
-the time rate at w/c work is done PAVERAGE = W / t; unit = wattΔ Δ
Momentum
-the product of particles mass times velocity p = mv Law of Gravitation FG = Gm1m2/r2 Where: G-Gravitational constant m – mass of the object
r – dist. Bet. The 1st and 2nd object
Motion of Satellites
v = √GmE /r (circular orbit)
T = 2πr/v = 2πr3/2/√Gm
E – one period
Periodic Motion
-motion that repeats itself in a definite cycle
T=1/ƒ – period on full cycle ƒ=1/T - # of cycles per unit time Density
= m/v ρ
FLUID MECHANICS Pressure
P = F/A ; force per unit area Unit for pressure: Pascal Continuity Equation
-the mass of the moving fluid doesn’t change as it flows.
A1v1 = A2v2 (continuity Eq.)
Where:
A – Stationary cross-section area v – Speed of the fluid
V = Av – Volume flow rate TEMPERATURE and HEAT TF = 9/5TC + 32°
TC = 5/9 (TF - 32°)
TK = TC + 273.15
**Constant-volume gas thermometer T2/T1 = P2/P1
T in Kelvin P – pressure
Kelvin – absolute temp. scale
T = 0K = -273.15 °C – absolute zero Thermal Expansion
-expansion due to change in temperature
Linear thermal Expansion L = L
Δ α OΔT ;
where
. – coefficient. of linear thermal α
expansion
LO – initial length
Volume Thermal Expansion V = V
Δ β OΔT;
Where
- coefficient of volume thermal β
expansion
VO – initial Volume
Specific Heat Capacity
Q = mc T; c – specific heat of aΔ material
Phase Change Q = ±mL Where:
(+) – heat entering – used when materials melt
(-) – heat leaving – used when it freezes
LF – heat of fussion
m – mass
MECHANISMS OF HEAT TRANSFER Conduction
-occurs w/in a body or bet. Two bodies in contact
H=kA ((TH-TC)/L) (heat current in
conduction) Where:
A - cross-sectional area of the rod K - thermal conductivity of the material
TH-TC – temperature difference on the
rod
L – length of the heat flow path Large k – good conductors of heat Small k – poor conductors or insulators Thermal insulation in buildings:
H=A (TH-TC)/R; R = L/k
Where:
R – Thermal resistance of a slab (material)
Convection
-transfer of heat by mass motion of a fluid from one region of space to another.
Types:
Forced Convection
-the fluid circulated by a blower or pump
Free/natural Convection
-the flow is caused by differences in density due to thermal expansion, such as hot air rising
Radiation
-the transfer of heat by electromagnetic waves such as visible light, infrared, and UV radiation.
H=Ae Tσ 4 (heat current in radiation)
Where: A – surface area e – emissivity T – absolute Temp – Stefan-Boltzmann constant σ =5.67051 x 10 σ -8 W/m2 * K4
***Emissivity is often larger for dark surfaces than for light ones.
THERMODYNAMICS
-interaction with the surroundings, or environment, in the least two ways, one w/c is heat is transfer.
First law of thermodynamics
-the change in internal energy of a system during any thermodynamic process depends only on the initial and final states, not on the path leading from one to the other.
Denoted by: ∆U = Q – W Where: U – internal energy Q – quantity of heat W – work
**If it is an isolated system (one that does no work on its surroundings and has no heat flow to or from its surroundings)
W=Q=0 Therefore, U2-U1=∆U = 0
Kinds of thermodynamic processes Adiabatic Process
-no heat transfer into or out of a system
Q=0 ∆U = Q
**when a system expands adiabatically, W is (+) (system does work on its surroundings), so ∆U is (-) & internal energy decreases.
**when a system compressed adiabatically, W is (-) (work done on the system by the surroundings) and U increases.
Isochoric Process
-constant volume process
**when volume is constant, it does no work in its surroundings. So W=0.
∆U = Q
Isobaric Process
-constant pressure process **∆U,Q,W = 0
But calculating the work W=p(V2-V1)
Isothermal Process
-constant temperature process **∆U,Q,W are non-zero.
Molar heat capacity of ideal gas CP = CV + R
Where
CP – molar heat capacity at constant
pressure
CV - molar heat capacity at constant
volume
R – 8.315 J/mol * K Ratios of Heat Capacity
= C γ P / CV
Capacitance
-the measure of the ability of a capacitor to store energy
C = Q/Vab (definition of capacitance)
Where:
Q – magnitude of the charge of the conductor
Vab – Voltage of the battery
SI unit – farad = 1 C/V = 1 coulomb/volt Capacitance of a parallel-plate capacitor in a vacuum C = єOA/d Where: єO = 8.85 x 10-12 F/m
A – Area of each plate
d – distance bet. Two capacitors Capacitors in Series 1/Ceq = 1/C1 + 1/C2 + 1/C3 + … Capacitors in Parallel Ceq = C1 + C2 +C3 + … POWER P = IV Where: I – current V – voltage Voltage V = IR SI - Volts Where: R – Resistance R = L/Aρ - resistivity of material ρ L – length A – cross-section Area = E/J ρ
E – magnitude of electric field J – Current density Resistors in Series Req = R1 + R2 + R3 + … Resistors in Parallel 1/Req = 1/R1 + 1/R2 + 1/R3 + … SI - ohms Index of Refraction n = c/v where
c – speed of light in free space(3x108
m/s)
v – index of refraction of the medium Image Formation on PLANE MIRRORS(PM)
-the distance of the object and the image from a plane mirror is always equal
s – object distance from PM s’ – image distance from PM s = - s’
y – height of the object y’ – height of the the image
m – lateral magnification (ratio of y’ over y)
m = y’/y if:
m is positive – image is real(upright) m is negative – image is inverted Lenses
Converging lenses – positive focal point
- Image produce:real Miniscus lenses – one part concave other convex
Diverging Lenses – negative focal point
- Image produce:virtual
Focal length (f) – distance from a lens to its focal point
Depends on:
Index of refraction (n) Radii of curvature (R1 & R2)
Radii of curvature is (+) – convex (curved outward)
Radii of curvature is (-) – concave (curved inward)
1/f= (n-1) (1/ R1 + 1/ R2)
Lenses have two focal points:
Near focal point – w/c the light come form
Far focal point – other side of the lense FOR CONVERGING LENSES
OBJEC T IMAGE APPEARAN CE EXAMPLE BET. F & O BEHIN D THE LENS VIRTUAL, ERECT, LARGER THAN THE OBJECT MAGNIFYI NG GLASS
AT F NONE NONE LIGHTHOU
SE
BET. F
& 2F BEYOND 2F’ REAL, INVERTED, LARGER THAN OBJECT PROJECTO R AT 2F AT 2F’ REAL, INVERTED, SAME SIZE AS OBJECT OFFICE COPIER BEYON D 2F BET. F’ & 2F’ REAL, INVERTED, SMALLER THAN OBJECT CAMERA AT INFINI TY F AT F’ REAL, INVERTED, SMALLER THAN OBJECT CAMERA
For Diverging Lenses: For all locations:
-virtual, erect and smaller than the object
Interference
- The variation of wave amplitude that occurs when waves of the same or different frequency come together. -Either constructive or destructiove Double Slit
-Produces an interference pattern of light and dark lines
Diffraction Grating
-it produces sharper and brighter interference patterns than a double slit
Diffraction – a wave behavior in w/c waves bend around the edge of an obstacle in their path
Covalent Bonding – The mechanism by which electron sharing holds atoms together to form molecules
TYPES OF CRYSTALLINE SOLIDS TYPE COVALE
NT IONIC MOLECULAR METALLIC BOND SHARED ELECTR ON ELECTRIC ATTRACTI ON VAN DER WAALS FORCES ELECTR ON GAS PROPERTI ES Very hard; high melting point; soluble in a very few liquid Hard; High melting point; may be soluble in polar liquid such as water Soft; low melting and boiling point; soluble in covalent liquids Ductile; metallic luster; ability to conduct heat and electric current readily Example Diamon
d Sodium Chloride Methane Sodium
Radioactive Decay Alpha Particles -the nuclei of 4
2He atoms
Beta particles
-w/c are electrons or positrons(+ charged electrons)
Gamma Rays
-photons of high energy Electron Emission nO →p+ + e -Positron Emission p+ →nO + e -Electron Capture p+ + e- →nO RADIOACTIVE DECAY DECAY NUCLEAR TRANSFORMATI ON ALPHA A ZX → A-4Z-2Y + 4 2He ELECTRO N EMISSION A ZX →AZ+1Y + e -POSITRO N EMISSION A ZX →AZ-1Y + e -ELECTRO N CAPTURE A ZX + e- → AZ-1Y GAMMA A ZX → AZX + γ
