Post on 14-Dec-2015
PT NotesUnit 1 - Force
Unit 1 - Subunit 1 Mechanical Force
Linear
Force = Mass x Acceleration
F = m x aUnitsAm.St. [lb] = [slugs] x [ft/s2]
S.I. [N] = [kg] x [m/s2]
acceleration due to gravitygravity = a
a = 32 ft/s2 Am. St.
a = 9.8 m/s2 S.I.
Torque = Force x Lever Arm
T = F x L Units
Am. St. [lb·ft] = [lb] x [ft]
S.I. [N·m] = [N] x [m]
PT NotesUnit 1 - Force
Unit 1 - Subunit 2 Fluid Force
Mass Density = _Mass_
Volume
D = _m_
VUnits Am. St. [slugs/ft3] = [slugs] / [ft3]S.I. [g/cm3] = [g] / [cm3] [kg/m3] = [kg] / [m3] [g/mL] = [g] / [mL]
Weight Density = _Weight_
Volume
*ρ w = __W__
VUnits Am. St. [lbs/ft3] = [lbs] / [ft3]S.I. [N/cm3] = [N] / [cm3] [N/m3] = [N] / [m3]
* “ρ” - Rho is a Greek letter
Specific Gravity = Density of "stuff"
Density of H2O
sp. gr. = Dstuff
Dwater
****NO UNITS FOR SPECIFIC GRAVITY****Density of H2O = 1 g/cm3 = 1,000 kg/m3
= 62.4 lb/ft3
1 cc = 1 cm3 = 1 mL
Pressure = Force
Area
P = F_ A
Units Am. St. [lb/ft2] = [lb] / [ft2] [p.s.i.] = [lb] / [in2] S.I. [Pa*] = [N] / [m2]
*Pa = Pascal
Pressure = weight density x height
P = ρw* x h
* weight density Units
Am. St. [lb/ft2] = [lb/ft3] x[ft] S.I. [N/m2] = [N/m3] x [m]
1 atm (atmosphere) = 14.7 lb/in2 (psi)= 2117 lb/ft2
= 1.013 x 105 N/m2 or Pascal (Pa)
= 33.92 ft. of H2O= 760 mm of Hg (mercury) (Chem
- torr)
= 29.92 in of Hg
Units of Atmospheric Pressure (at sea level)
Absolute Pressure =
Total Pressure =
GaugePres. + AtmosphericPres.
Pascal’s Principle
PLarge = Psmall
_FL_ = _FS_
AL AS
Buoyant Volume weight Force = displaced X
density
FB = Vdisplaced x ρw Units
Am. St. [lb] = [ft3] x [lb/ft3]
S. I. [N] = [m3] x [N/m3]
PT NotesUnit 1 - Force
Unit 1 - Subunit 3 Electrical Force
Voltage –Prime Mover
Series Circuit: Dimmer 1 out others out Vsource = VL1 + VL2
Voltage –Prime Mover
Parallel Circuit:•Brighter•1 out others stay on•Vsource = VL1 = VL2
PT NotesUnit 1- Force
Unit 1 – Subunit 4Thermal Force
Temperature – Molecular Motion
F = 9/5 C + 32
C = 5/9 (F – 32)
PT NotesUnit 2 - Work
Unit 2 – Subunit 1Mechanical Work
Linear
Work = Force x Distance
W = F x dUnitsAm. St. [ft·lb] = [lb] x [ft]S.I. [J] = [N] x [m]
J = Joule = N·m
Torque Work = Torque x radians
WT = T x θ*
UnitsAm. St. [ft·lb] = [lb·ft] x radians (unitless)
S.I. [J] = [N·m] x radians (unitless)
* θ = (theta) is a Greek letter used to label angles
Angular(rotational)
1 rotation = 360 = 2 radians
2 = 6.28
1 radian = 57.3
Efficiency = Workout
WorkinNote: UNITLESS the units
cancel!!
Efficiency is usually
given as a percent
Multiply by 100 and add a “%” sign
Unit 2 - Subunit 2
Fluid Work
Fluid Work = Volume X Pressure Change Change
WF = Δ V x Δ P
UnitsAm.St. [ft·lb] = [ft3] x [lb/ft2]S.I. [J] = [m3] x [N/m2]
Formulas
Area of circle = r2
Volume of cylinder = hr2
= h(area of circle)
Unit 2 - Subunit 3
Electrical Work
Electrical = Change x quantity
Work in Voltage of charge
WE = ΔV x q
Units Am.St. [J] = [V] x [C] & S.I.
C = coulomb 1 coulomb = 6.25 x 1018 electrons = 1
A·sec
Charge = Current x Time
q = I x tUnitsAm.St. [C] = [A] x [sec]& S.I.
A = Amperes = Amps
Electrical=change in x Current x Time Work Voltage
WE = Δ V x I x tUnitsAm.St. [J] = [V] x [A] x [sec]& S.I.
1 J = 1 V·A·sec = V·C
PT NotesUnit 3 – Rate
Unit 3 - Subunit 1 Mechanical - Rate
Linear Rate
Velocity = distance_ time
v = l__ t
Units Am.St. [mi/hr or mph] = [mi] /
[hr] [ft/sec] = [ft] / [sec]
S.I. [km/hr or kph] = [km] / [hr]
[m/sec] = [m] / [sec]
velocity - has magnitude and direction(vector)
speed - has magnitude only(scalar)
average velocity = displacement/time
average speed = total dist. traveled
/time
Acceleration= final velocity – initial velocity
time = Vf - Vi
tUnits
Am. St. [ft/sec 2] = [ft/sec] – [ft/sec]
[sec]
S.I. [m/sec2 ] = [m/sec] – [m/sec]
[sec]
Angular Rate
Angular Rate = number of rotations time ω = θ tUnitsAm. St. [rev/min] or rpm= [rev] / [min]& S.I. [rot/sec] = [rot] / [sec] [rad/sec] = [rad] / [sec]
Angular Acceleration angular = final rate – initial
rate acceleration time
= ωf - ωi
tUnitsAm. St. & S.I. [rev/min2] = [rev/min] / [min]
[rot/sec2] = [rot/sec] / [sec] [rad/sec2] = [rad/sec] / [sec]
PT NotesUnit 3 – Rate
Unit 3 - Subunit 2
Fluid - Rate
Volume Flow Rate = Volume Time
QV = V t
UnitsAm. St. [gal/min] = [gal] / [min]
[ft3/sec] = [ft3] / [sec]S.I. [L/min] = [L] / [min]
[m3/hr] = [m3] / [hr]
Mass Flow Rate = Mass
Time QM = m
tUnitsAm. St. [lb/hr] = [lb] / [hr]
S.I. [kg/hr] = [kg] / [hr]
Area of TrapezoidArea = 1/2( base 1 + base 2 ) x
heightBase 2
Height
Base 1
Volume of a Trapezoid
Volume = 1/2( base 1 + base 2) x height x distance
Base 1
Distance
Base 2
Height
PT NotesUnit 3 – Rate
Unit 3 - Subunit 3 Electrical - Rate
Current = Quantity of Charge time
I = q t
UnitsAm.St. [A] = [Coulombs] & S.I. [sec]
*this is an old formula from Unit 2 rearranged q = I x t
Frequency = number of cycles time f = # cycles tUnitsAm. St. [Hz] = [cycles]& S.I [sec]
Period = time # of Cycles
T = t # of cyclesUnitsAm. St. [sec/cycle] = [sec]& S.I. [cycle]
f = 1 / T frequency & period are
T = 1 / f inverses of each other
1 sec = 1,000 milliseconds [msec]
1 sec = 1,000,000 microseconds [μsec]
Oscilloscope sine waves square waves triangle waves saw-tooth waves
Vertical - measures voltage
Horizontal - measures period
PT NotesUnit 3 – Rate
Unit 3 - Subunit
4 Thermal - Rate
Heat Flow = Heat Energy Transferred Rate Elapsed Time
QH = H t
UnitsAm. St. [Btu/hr] = [Btu] / [hr] S.I. [cal/min] = [cal] / [min] [J/sec] = [J] / [sec]
Do not confuse Heat with
Temperature
Heat is Energy!!!
1 calorie = the amount of heat
required to raise temperature
of 1 gram of water 1° C
1 British Thermal Unit (Btu) =
the amt of heat required to raise the temperature of 1 lb. of water 1 F
1 Btu = 252 cal
1 cal = 4.18 J
1 kcal = 1,000 cal
1kcal = 1 Cal
Big “C” is food calories
SpecificHeat = Mass * Heat * Δ Temp Constant
H = m * c * Δ TUnitsAm. St. [Btu] = [lb] * [Btu/lb·F°] * [F°]S.I. [cal] = [g] * [cal/g·C°] * [C°]
Heat Thermal Flow Conductivity Rate = constant * Area * ΔTemp
Thickness
QH = k * A * ΔT lUnitsAm. St. [Btu/hr] = [(Btu·in) / (hr·ft2·F°)] * [ft2] *
[F°][in]
S.I. [cal/sec] = [(cal·cm) / (sec·cm2·C°)] *[cm2] * [C°]
[cm]
Lab book p. 96 has table of specific heat
constants (“c”)
Lab book p. 99 has table of thermal conductivity
constants (“k”)
This is the only method of heat transfer in opaque solids. If the temperature at one end of a metal rod is raised by heating, heat is conducted to the colder end, but the exact mechanism of heat conduction in solids is not entirely understood. It is believed, however, to be partially due to the motion of free electrons in the solid matter, which transport energy if a temperature difference is applied. This theory helps to explain why good electrical conductors also tend to be good heat conductors (see Conductor, Electrical). Although the phenomenon of heat conduction had been observed for centuries, it was not until 1882 that the French mathematician Jean Baptiste Joseph Fourier gave it precise mathematical expression in what is now regarded as Fourier's law of heat conduction. This physical law states that the rate at which heat is conducted through a body per unit cross-sectional area is proportional to the negative of the temperature gradient existing in the body. The proportionality factor is called the thermal conductivity of the material. Materials such as gold, silver, and copper have high thermal conductivities and conduct heat readily, but materials such as glass and asbestos have values of thermal conductivity hundreds and thousands of times smaller, conduct heat poorly, and are referred to as insulators.
Temperature Change Versus Heat Added: Water