PT Notes Unit 1 - Force Unit 1 - Subunit 1 Mechanical Force.
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Transcript of PT Notes Unit 1 - Force Unit 1 - Subunit 1 Mechanical Force.
![Page 1: PT Notes Unit 1 - Force Unit 1 - Subunit 1 Mechanical Force.](https://reader037.fdocuments.net/reader037/viewer/2022103121/56649c785503460f9492dd06/html5/thumbnails/1.jpg)
PT NotesUnit 1 - Force
Unit 1 - Subunit 1 Mechanical Force
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Linear
Force = Mass x Acceleration
F = m x aUnitsAm.St. [lb] = [slugs] x [ft/s2]
S.I. [N] = [kg] x [m/s2]
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acceleration due to gravitygravity = a
a = 32 ft/s2 Am. St.
a = 9.8 m/s2 S.I.
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Torque = Force x Lever Arm
T = F x L Units
Am. St. [lb·ft] = [lb] x [ft]
S.I. [N·m] = [N] x [m]
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PT NotesUnit 1 - Force
Unit 1 - Subunit 2 Fluid Force
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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]
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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
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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
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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
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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]
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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)
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Absolute Pressure =
Total Pressure =
GaugePres. + AtmosphericPres.
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Pascal’s Principle
PLarge = Psmall
_FL_ = _FS_
AL AS
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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]
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PT NotesUnit 1 - Force
Unit 1 - Subunit 3 Electrical Force
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Voltage –Prime Mover
Series Circuit: Dimmer 1 out others out Vsource = VL1 + VL2
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Voltage –Prime Mover
Parallel Circuit:•Brighter•1 out others stay on•Vsource = VL1 = VL2
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PT NotesUnit 1- Force
Unit 1 – Subunit 4Thermal Force
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Temperature – Molecular Motion
F = 9/5 C + 32
C = 5/9 (F – 32)
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PT NotesUnit 2 - Work
Unit 2 – Subunit 1Mechanical Work
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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
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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)
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1 rotation = 360 = 2 radians
2 = 6.28
1 radian = 57.3
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Efficiency = Workout
WorkinNote: UNITLESS the units
cancel!!
Efficiency is usually
given as a percent
Multiply by 100 and add a “%” sign
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Unit 2 - Subunit 2
Fluid Work
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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]
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Formulas
Area of circle = r2
Volume of cylinder = hr2
= h(area of circle)
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Unit 2 - Subunit 3
Electrical Work
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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
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Charge = Current x Time
q = I x tUnitsAm.St. [C] = [A] x [sec]& S.I.
A = Amperes = Amps
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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
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PT NotesUnit 3 – Rate
Unit 3 - Subunit 1 Mechanical - Rate
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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]
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velocity - has magnitude and direction(vector)
speed - has magnitude only(scalar)
average velocity = displacement/time
average speed = total dist. traveled
/time
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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]
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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]
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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]
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PT NotesUnit 3 – Rate
Unit 3 - Subunit 2
Fluid - Rate
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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]
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Mass Flow Rate = Mass
Time QM = m
tUnitsAm. St. [lb/hr] = [lb] / [hr]
S.I. [kg/hr] = [kg] / [hr]
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Area of TrapezoidArea = 1/2( base 1 + base 2 ) x
heightBase 2
Height
Base 1
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Volume of a Trapezoid
Volume = 1/2( base 1 + base 2) x height x distance
Base 1
Distance
Base 2
Height
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PT NotesUnit 3 – Rate
Unit 3 - Subunit 3 Electrical - Rate
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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
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Frequency = number of cycles time f = # cycles tUnitsAm. St. [Hz] = [cycles]& S.I [sec]
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Period = time # of Cycles
T = t # of cyclesUnitsAm. St. [sec/cycle] = [sec]& S.I. [cycle]
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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]
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Oscilloscope sine waves square waves triangle waves saw-tooth waves
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Vertical - measures voltage
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Horizontal - measures period
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PT NotesUnit 3 – Rate
Unit 3 - Subunit
4 Thermal - Rate
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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]
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Do not confuse Heat with
Temperature
Heat is Energy!!!
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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
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1 Btu = 252 cal
1 cal = 4.18 J
1 kcal = 1,000 cal
1kcal = 1 Cal
Big “C” is food calories
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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°]
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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]
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Lab book p. 96 has table of specific heat
constants (“c”)
Lab book p. 99 has table of thermal conductivity
constants (“k”)
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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.
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Temperature Change Versus Heat Added: Water