Mass and Energy test 1

value

a measured or counted quality has a numerical value (2.47)

unit

whatever there are a number of

(feet, inches, seconds, etc)

dimension

a property that can be measured, such as length, time, mass, or temperature or calculated by multiplying or dividing other dimensions, such as length/time (velocity)

measurable units

specific values of dimensions that have been defined by convention, custom, or law, such as grams for mass, seconds for time, and centimeters or feet for length

two quantities may be added or subtracted only if

units are the same

numerical values and their corresponding units may always be combined by

multiplication or division

ex: 3N*4m = 12N*m

to convert a quantity expressed in terms of one unit to its equivalent in terms of another unit, multiply

the given quantity by the conversion factor

dimensional equation

stoichiometry

when using a conversion factor for s² to h², what do you do?

3600² s² / 1² h²

SQUARE 3600.

raising a quantity (or a conversion factor) to a power raises

its units to the same power

systems of units have what components

base units

multiple units

derived units

base units

for mass, length, time, temp, electrical current, and light intensity

multiple units

multiples or fractions of base units such as minutes, hours, and milliseconds, all of which are defined in terms of the base unit of a second

derived units

obtained in 2 ways

-by multiplying and dividing base or multiple units (cm², ft/min, kg*m/s²) derived units of this type are called compound units

-as defined equivalents of composed units (ex: 1 lbf = 32.174lbm*ft/s², 1erg= 1 g*cm/s²)

SI base units

m, kg, seconds, K, A (ampere)

SI prefixes: mega

M= 10^6

SI prefixes: kilo

k= 10³

SI prefixes: centi

c= 10^-2

SI prefixes: milli

m= 10^-3

SI prefixes: micro

u= 10^-6

SI prefixes: nano

n= 10^-9

SI prefixes: Giga

G= 10^9

SI prefixes: tera

T= 10^12

CGS system base units

cm, g, sec, K, A (ampere)

US customary system base units

ft, lbm, sec

lbm

pound mass

ampere (A)

electric current unit, for SI and CGS

what is common to both SI and CGS?

A (ampere), K, sec, cd (candela for light intensity)

candela (cd)

SI and CGS, light intensity

derived units: Volume

liter or L (SI and CGS)

1L= .001m³ or 1000cm³

derived units: force

N (SI) or dyne (CGS)

1N= 1 kg*m/s² = 1 g*cm/s²

derived units: pressure

pascal (SI)

1Pa= 1 N/m²

derived units: energy, work

joule (SI) or erg (CGS)

1J= 1 N*m= 1 kg*m²/s²

1 dyne*cm= 1 g*cm²/s²

1 gram-calorie (cal); 4.184 J= 4.184 kg*m²/s² (SI or CGS)

derived units: power

watt (SI or CGS)

1W = 1 J/s = 1 kg*m²/s³

what are the factors (numerical values and units) needed to convert nanoseconds to seconds?

1 ns=1*10^−9 s

what are the factors (numerical values and units) needed to convert square centimeters to square meters?

1 cm= 0.01 m

(1 cm)²=(0.01 m)²

1 cm²=1×10−4 m²

what are the factors (numerical values and units) needed to convert meters to millimeters?

1m = 1000mm

what are the factors (numerical values and units) needed to convert cubic feet to cubic meters?

1 ft= 0.3048 m

(1 ft)³ = (0.3048 m)³

1 ft³ = 0.0283168 m³

what are the factors (numerical values and units) needed to convert horsepower to British thermal units per second?

1 horsepower (hp)=0.7068 BTU/s

what is the derived SI unit for velocity? in CGS? in US customary units?

SI: m/s

CGS: cm/s

US: ft/s

force is proportional to

the product of mass and acceleration (length/time²)

or mass*(length/time²)

force units (SI)

kg*m/s²

force units (CGS)

g*cm/s²

force units (US)

lbm*ft/s²

1 N (SI)=

1 kg*m/s²

1 dyne (CGS)=

1 g*cm/s²

US customary derived force unit

pound-force (lbf)

1 lbf= 32.174 lbm*ft/s²

gc

conversion factor from natural to derived force units

gc= (1 kg*m/s²)/1N = (32.174 lbm*ft/s²)/ 1lbf

weight

the weight of an object is the force exerted on the object by gravitational attraction

W=mg

gravitational acceleration varies directly with

the mass of the attracting body (the earth in most problems you will confront)

gravitational acceleration varies inversely with

the square of the distance between the centers of mass of the attracting body and the body being attracted

g, gravitational acceleration in SI

sea level

9.81 m/s²

g, gravitational acceleration in CGS

sea level

980.1 cm/s²

g, gravitational acceleration in US

sea level

32.2 ft/s²

what is a force of 2 kg*m/s² equivalent to in newtons?

2 N

what is a force of 2 lbm*ft/s² equivalent to in lbf?

use 1 lbf=32.174 lbm⋅ft/s²

=.0622 lbf

if the acceleration of gravity at a point is g=9.8 m/s² and an object is resting on the ground at this point, is this object accelerating at a rate of 9.8m/s²?

No, the object is not accelerating if it's resting on the ground, even though gravity at that location is g=9.8 m/s²

• Gravitational acceleration (g): This is the acceleration an object would experience if it were in free fall (no opposing forces), due to Earth's gravity.

• But if an object is resting on the ground, it is not in free fall. There is a normal force from the ground pushing upward, exactly balancing the downward gravitational force.

suppose an object weighs 9.8N at sea level. a) What is its mass? b) would its mass be greater, less, or the same on the moon? c) how about its weight?

a) mass: W=mg

9.8 N/ 9.8m/s² ​=1 kg​

b) Mass is a measure of how much matter an object contains. It does not change based on location.

c) On the Moon, gravity is weaker:

gMoon≈1.6 m/s²

WMoon=m⋅gMoon=1 kg⋅1.6 m/s²=1.6 N

Weight on the Moon = less

suppose an object weighs 2lbf at sea level. a) What is its mass? b) Would its mass be greater, less, or the same at the center of the earth? c) How about its weight?

a) Weight of the object at sea level: 2 lbf (pound-force)

Gravitational acceleration at Earth's surface:

g=32.174 ft/s²

Weight=mass×g⇒mass=weight/g

mass= 2lbf/32.174 ft/s² ​≈0.0622 slug​

b) Mass depends only on the amount of matter, not on location.

c) Weight is the force due to gravity, and gravity decreases as you move toward the Earth's center.

At the exact center, gravity is zero (gravitational forces from all directions cancel out).

Weight at the center of the Earth = 0 lbf

US customary unit for mass

slug

water has a density of 62.4 lbm/ft³. How much does 2 ft³ of water weigh a) at sea level and 45 degrees latitude and b) in denver, colorado, where the altitude is 5374 ft and the gravitational acceleration is 32.139 ft/s²?

a) mass of the water: (62.4 lbm/ft³)(2ft³) = 124.8 lbm

weight of the water: W= (124.8 lbm)(g=32.174 ft/s²)(1lbf/32.174lbm*ft/s²)

(1lbf=32.174lbm⋅ft/s2 and you need to convert to lbf for your final answer since you’re calculating weight which is in force units)

b) in denver, use the g value given rather than the g value at sea level.

lbf is used for

force or weight

lbm is used for

Measuring the amount of matter in an object (its mass)

scientific notation

number expressed as the product of another number and a power of 10

ex: 2.3×10^-5

significant figures for a number are the digits from

the first nonzero digit on the left to either a) the last digit (zero or nonzero) on the right if there is a decimal point, or b) the last nonzero digit if there is no decimal point

how many sig figs does 2300 have?

2

how many sig figs does 2300. have?

4

how many sig figs does 2300.0 have?

5 (includes all zeros)

how many sig figs does 23,040 have?

4 (last zero is not considered since there is no decimal point.)

how many sig figs does 0.035 have?

2 (leading zeros are not considered)

how many sig figs does 0.03500 have?

4 (leading zeros not considered, zeros after nonzero values are since there is a decimal point)

when two or more quantities are combined by multiplication or division, the number of sig figs in the result should be equal to

the lowest number of sig figs of any of the multiplicands or divisors

How do you determine the number of significant figures when adding or subtracting numbers?

The result should be reported to the least number of decimal places (i.e., after the decimal point) among the numbers being added or subtracted.

12.11+0.0234+5.2=17.3334→17.3​

(5.2 has only 1 decimal place, so round the result to 1 decimal place.)

dimensionally homogenous

every valid equation must be dimensionally homogenous: that is, all additive terms on both sides of the equation must have the same dimensions

dimensionless quantities

can be a pure number or a multiplicative combination of variables with no net dimensions

process variables

temperatures, pressures, flow rates, concentrations, etc. as a rule, indirect techniques must be used to measure

how to generally measure process variables indirectly

measuring a quantity that varies in a known manner with the process variable and then calculating the process variable from that measured value

interpolation

estimating a value between tabulated values

interpolation equation

y-y1 / y2-y1 = x-x1 / x2-x1

extrapolation

estimating a value beyond the range of tabulated values

what is generally x and y in interpolation?

• x: The independent variable — this is the input or the value at which you're trying to estimate the function. It's the known point or the one you're interpolating at.

• y: The dependent variable — this is the output or value of the function at a given x. When interpolating, you're trying to find this value.

we are estimating a value of y for a value of x between tabulated points

when is linear interpolation inappropriate?

when the function is highly nonlinear

when data points are too far apart (must use curve fitting techniques)

fitting a straight line: equation

y= ax+b

a= y2-y1/x2-x1 (slope)

b= y1-ax1 or b=y2-ax2

fitting nonlinear data: equation

(qty 1)= a(qty 2)+b

y=qty 1; x=qty2

what would give me a straight line?

exponential form

y=ae^bx

exponential form linearized

lny = lna + bx

power law

y=ax^b

power law linearized

lny= lna + blnx

lnx=

2.3log10x

log paper

plots y directly on a logarithmic scale versus x on a rectangular scale

used for exponential (y=ae^bx)

log-log paper

plots y and x on a logarithmic scale

used for power law (y=ax^b)

if y versus x data appear linear on a semilog plot, then

lny versus x would be linear on a rectangular plot, and the data can therefore be correlated by an exponential function

if y versus x data appear linear on a log plot, then

lny versus lnx would be linear on a rectangular plot and the data can therefore be correlated by a power law

when you plot values of a variable x on a logarithmic axis and your plot yields a straight line through 2 points with coordinate values z1 and z2, replace

z2-z1 with ln(z2/z1)(=lnz2-lnz1) in the formula for the slope

1 kg= ___ lbm

2.205

when does lbf=lbm?

when you’re under earth’s standard gravity.

gc is 32.174lbmft/lbfs² or 9.81lbmm/lbfs²

g is standard or new gravity (like gravity on the moon)

process variable

a real-time measurement of a specific parameter in a process, such as temperature, pressure, or flow rate, that is monitored and controlled in industrial applications.

density

mass per unit volume of the substance (kg/m³, g/cm³, lbm/ft³, etc)

specific volume

volume occupied by a unit mass of the substance; inverse of density

densities of pure solids and liquids are independent of

pressure and vary relatively slightly with temperature.