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