PT Notes Unit 1 - Force Unit 1 - Subunit 1 Mechanical Force

Linear Force = Mass x Acceleration F = m x a Units Am.St.[lb] = [slugs] x [ft/s 2 ] S.I.[N] = [kg] x [m/s 2 ]

acceleration due to gravity gravity = a a = 32 ft/s 2 Am. St. Am. St. a = 9.8 m/s 2 S.I. S.I.

Torque = Force x Lever Arm T = F x L Units Units Am. St. [lb·ft] = [lb] x [ft] Am. St. [lb·ft] = [lb] x [ft] S.I. [N·m] = [N] x [m]

PT Notes Unit 1 - Force Unit 1 - Subunit 2 Fluid Force

Mass Density = _Mass_ Volume D = _m_ V Units Am. St. [slugs/ft 3 ] = [slugs] / [ft 3 ] S.I. [g/cm 3 ] = [g] / [cm 3 ] [kg/m 3 ] = [kg] / [m 3 ] [g/mL] = [g] / [mL]

Weight Density = _Weight_ Volume * ρ w = __W__ V Units Am. St. [lbs/ft 3 ] = [lbs] / [ft 3 ] S.I. [N/cm 3 ] = [N] / [cm 3 ] [N/m 3 ] = [N] / [m 3 ] * “ρ” - Rho is a Greek letter

Specific Gravity = Density of "stuff" Density of H 2 O sp. gr. = D stuff D water ****NO UNITS FOR SPECIFIC GRAVITY**** Specific Gravity = Density of "stuff" Density of H 2 O sp. gr. = D stuff D water ****NO UNITS FOR SPECIFIC GRAVITY**** Density of H 2 O = 1 g/cm 3 = 1,000 kg/m 3 = 62.4 lb/ft 3 1 cc = 1 cm 3 = 1 mL 1 cc = 1 cm 3 = 1 mL

Pressure = Force Pressure = Force Area Area P = F_ P = F_ A Units Units Am. St. [lb/ft 2 ] = [lb] / [ft 2 ] Am. St. [lb/ft 2 ] = [lb] / [ft 2 ] [p.s.i.] = [lb] / [in 2 ] [p.s.i.] = [lb] / [in 2 ] S.I. [Pa*] = [N] / [m 2 ] S.I. [Pa*] = [N] / [m 2 ] *Pa = Pascal

Pressure = weight density x height P = ρ w * x h * weight density Units Am. St. [lb/ft 2 ] = [lb/ft 3 ] x[ft] S.I. [N/m 2 ] = [N/m 3 ] x [m] Am. St. [lb/ft 2 ] = [lb/ft 3 ] x[ft] S.I. [N/m 2 ] = [N/m 3 ] x [m]

1 atm (atmosphere) = 14.7 lb/in 2 (psi) = 2117 lb/ft 2 = x 10 5 N/m 2 or Pascal (Pa) = ft. of H 2 O = 760 mm of Hg (mercury) (Chem - torr) = in of Hg Units of Atmospheric Pressure (at sea level)

Absolute Pressure = Total Pressure = Gauge Pres. + Atmospheric Pres.

Pascal’s Principle P Large = P small _F L _ = _F S _ A L A S

Buoyant Volume weight Force = displaced X density F B = V displaced x ρ w Units Am. St. [lb] = [ft 3 ] x [lb/ft 3 ] S. I. [N] = [m 3 ] x [N/m 3 ]

PT Notes Unit 1 - Force Unit 1 - Subunit 3 Electrical Force

Voltage –Prime Mover Series Circuit: Dimmer Dimmer 1 out others out 1 out others out V source = V L1 + V L2 V source = V L1 + V L2

Voltage –Prime Mover Parallel Circuit: BrighterBrighter 1 out others stay on1 out others stay on V source = V L1 = V L2V source = V L1 = V L2

PT Notes Unit 1- Force Unit 1 – Subunit 4 Thermal Force

Temperature – Molecular Motion  F = 9/5  C + 32  C = 5/9 (  F – 32)

PT Notes Unit 2 - Work Unit 2 – Subunit 1 Mechanical Work

Linear Work = Force x Distance Work = Force x Distance W = F x d Units Am. St. [ft·lb] = [lb] x [ft] S.I. [J] = [N] x [m] J = Joule = N·m

Torque Work = Torque x radians W T = T x θ * W T = T x θ *Units Am. 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  = radian = 57.3 

Efficiency = Work out Work in Note: 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 W F = Δ V x Δ P Units Am.St. [ft·lb] = [ft 3 ] x [lb/ft 2 ] S.I. [J] = [m 3 ] x [N/m 2 ]

Formulas Area of circle =  r 2 Volume of cylinder = h  r 2 = h(area of circle) Area of circle =  r 2 Volume of cylinder = h  r 2 = h(area of circle)

Unit 2 - Subunit 3 Electrical Work

Electrical = Change x quantity Work in Voltage of charge W E = ΔV x q Units Am.St. [J] = [V] x [C] & S.I. C = coulomb · 1 coulomb = 6.25 x electrons = 1 A · sec

Charge = Current x Time q = I x t Units A [C] = [A] x [sec] & S.I. Units Am.St. [C] = [A] x [sec] & S.I. A = Amperes = Amps A = Amperes = Amps

Electrical=change in x Current x Time Work Voltage W E = Δ V x I x t Electrical=change in x Current x Time Work Voltage W E = Δ V x I x t Units Am.St. [J] = [V] x [A] x [sec] & S.I. 1 J = 1 V·A·sec = V·C 1 J = 1 V·A·sec = V·C

PT Notes Unit 3 – Rate Unit 3 - Subunit 1 Mechanical - Rate

Linear Rate Velocity = distance_ time time v = l__ tUnits Am.St.[mi/hr or mph] = [mi] / [hr] [ft/sec] = [ft] / [sec] [ft/sec] = [ft] / [sec] S.I.[km/hr or kph] = [km] / [hr] [m/sec] = [m] / [sec] [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 time = V f - V i = V f - V i t Units Am. St. [ft/sec 2 ] = [ft/sec] – [ft/sec] [sec] S.I. [m/sec 2 ] = [m/sec] – [m/sec] [sec]

Angular Rate Angular Rate = number of rotations time time ω = θ ω = θ tUnits Am. St. [rev/min] or rpm= [rev] / [min] & S.I. [rot/sec] = [rot] / [sec] [rad/sec] = [rad] / [sec] [rad/sec] = [rad] / [sec]

Angular Acceleration angular = final rate – initial rate acceleration time angular = final rate – initial rate acceleration time  = ω f - ω i tUnits Am. St. & S.I. [rev/min 2 ] = [rev/min] / [min] [rot/sec 2 ] = [rot/sec] / [sec] [rot/sec 2 ] = [rot/sec] / [sec] [rad/sec 2 ] = [rad/sec] / [sec] [rad/sec 2 ] = [rad/sec] / [sec]

PT Notes Unit 3 – Rate Unit 3 - Subunit 2 Fluid - Rate

Volume Flow Rate = Volume Time Q V = V t Units Am. St.[gal/min] = [gal] / [min] [ft 3 /sec] = [ft 3 ] / [sec] S.I. [L/min] = [L] / [min] [m 3 /hr] = [m 3 ] / [hr]

Mass Flow Rate = Mass Time Q M = m t Units Am. St. [lb/hr] = [lb] / [hr] S.I. [kg/hr] = [kg] / [hr] Mass Flow Rate = Mass Time Q M = m t Units Am. St. [lb/hr] = [lb] / [hr] S.I. [kg/hr] = [kg] / [hr]

Area of Trapezoid Area = 1/2( base 1 + base 2 ) x height Base 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 Notes Unit 3 – Rate Unit 3 - Subunit 3 Electrical - Rate

Current = Quantity of Charge time I = q I = q tUnits Am.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 t Units Am. St. [Hz] = [cycles] & S.I [sec]

Period = time # of Cycles T = t # of cycles Period = time # of Cycles T = t # of cycles Units Am. St. [sec/cycle] = [sec] & S.I. [cycle]

f = 1 / T frequency & period are T = 1 / f inverses of each other f = 1 / T frequency & period are T = 1 / f inverses of each other 1 sec = 1,000 milliseconds [msec] 1 sec = 1,000 milliseconds [msec] 1 sec = 1,000,000 microseconds [μsec] 1 sec = 1,000,000 microseconds [μsec]

Oscilloscope sine waves sine waves square waves square waves triangle waves triangle waves saw-tooth waves saw-tooth waves

Vertical - measures voltage

Horizontal - measures period

PT Notes Unit 3 – Rate Unit 3 - Subunit 4 Thermal - Rate

Heat Flow = Heat Energy Transferred Rate Elapsed Time Q H = H t Units Am. St. [Btu/hr] = [Btu] / [hr] S.I. [cal/min] = [cal] / [min] [J/sec] = [J] / [sec] Heat Flow = Heat Energy Transferred Rate Elapsed Time Q H = H t Units Am. 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 thetemperature of 1 lb. of water 1  F

1 Btu = 252 cal 1 Btu = 252 cal 1 cal = 4.18 J 1 kcal = 1,000 cal 1kcal = 1 Cal Big “C” is food calories

Specific Heat = Mass * Heat * Δ Temp Constant H = m * c * Δ T Specific Heat = Mass * Heat * Δ Temp Constant H = m * c * Δ T Units Am. St. Am. St. [Btu] = [lb] * [Btu/lb·F°] * [F°] S.I.[cal] = [g] * [cal/g·C°] * [C°]

Heat Thermal Flow Conductivity Rate = constant * Area * ΔTemp Thickness Q H = k * A * ΔT l Heat Thermal Flow Conductivity Rate = constant * Area * ΔTemp Thickness Q H = k * A * ΔT l Units Am. St. [Btu/hr] = [(Btu·in) / (hr·ft 2· F°)] * [ft 2 ] * [F°] [in] S.I. [cal/sec] = [(cal·cm) / (sec·cm 2· C°)] *[cm 2 ] * [C°] [cm] [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. Conductor, ElectricalConductor, Electrical

Temperature Change Versus Heat Added: Water