Transcript E. Measurement Systems: Temperature, Volume and Mass

E. MEASUREMENT SYSTEMS:
TEMPERATURE, VOLUME AND
MASS
Math 10: A and W
Key Terms:
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Find the definition of
each of the following
terms:
Conversion Factor
Mass
Weight
Temperature
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Volume
Capacity
1. Converting Temperature
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Have you ever been travelling and heard that the
temp was 40° and assume it would be hot.
However, when you arrived you found it to be quite
cool, why would that be?
The temp was measured in Fahrenheit, not Celsius.
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Math on the Job – p. 138
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Read through together and solve.
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Do you know what temp system your stove at home
uses?
It is probably Fahrenheit and if it does have both
then Fahrenheit is probably the primary temp.
If you look at the cooking instructions on a box of
frozen chicken wings (or anything) it will give you
cooking temp in Fahrenheit as a primary temp and
Celsius as the secondary probably in brackets.
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The reason for these past 2 statements is the result
of where we live.
Temp is measured using thermometers that may be
calibrated to different scales.
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In Canada, we use the SI system, so we measure
temp is Celsius scale, but in some cases we do use
the Fahrenheit scale which is the imperial system.
The Celsius and Fahrenheit scales are the 2 most
commonly used scales used in daily lives and the
workplace.
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For example, trades people who work outdoors
have to know the external temp is order to calculate
the setting time of solvents, adhesives and paints.
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The USA uses Fahrenheit and because of our
proximity to the USA and the fact the Canada used
Fahrenheit till the 1970s when we adopted the SI
system we still see Fahrenheit used.
You will probably hear your parents or
grandparents still talk about temp is Fahrenheit or
at least be able to approximate back and forth
between the two systems very easily.
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Because the Celsius system is a 100 step scale from
the boiling point to the freezing point of water, it is
sometimes referred to as centigrade.
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Activity 4.1 – Temperature Graph
p. 139
Use a scale of 10 for x and y axis
Put Celsius on the x axis and Fahrenheit on the y.
0° to 100° on the x-axis (Celsius)
Put the graph in the middle of your graph paper
You may work with a partner but you both need to
have a graph of your own at the end.
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Activity 4.2 – Develop a Conversion Formula p. 139
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Read through together and solve
Mental Example
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The thermometer on the outside of your house reads
20°F. Estimate what the temp would be if expressed
in degrees Celsius.
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Discuss the Ideas – Separation of Crude Oil p. 140
Read through and solve on your own then we will go
over as a class.
Example
1.
Kevin is transporting frozen food from LA to
Vancouver in a refrigerated truck. The external
temp in LA is 90°F when he leaves. He knows that
the safest temp for preserving the frozen food is
between 0°F and -4°F. When he arrives at the
Canadian Border, the border guard determines
that the temp of the truck to be -19°C. Is this
within the acceptable range of temperature for
preserving frozen food? Give answer to the
nearest half a degree.
Example
2.
While travelling in the US, Jenn and Rich are
concerned because their daughter Isabella has a
temp of 39°C, so they take her to the medical
clinic. The nurse takes Isabella’s temp on the
Fahrenheit scale. What is Isabella’s temp in
Fahrenheit?
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Activity 4.3 – Cooking at Higher Altitudes p. 143
We will not be using the internet
However for every 305m above sea level water
boils at 1°C less than at sea level.
Now lets read through together and solve.
Building your Skills
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Ex. 4.1 (p. 143) #1-6
2. Volume
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Math on the Job p. 124
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Read through together and solve.
a) In the SI, the base unit for measuring volume is the
liter (L). It is also the base unit for capacity.
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A liter is one-thousandth of a cubic meter.
Using liters as the base unit we use the same
prefixes as we did with length.
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SI Units of Measurement (volume)
SI Prefix
kilo
hecto
deca
meter
deci
centi
milli
Symbol
Combined Symbol
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L and ML will be used most often but this gives you
a good look at the difference between the two.
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Why is volume measured in cubic units?
When we are finding volume we are finding how
many cubes (of a certain size) will fill the object
(𝑚3 )
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What is the formula for calculating volume?
It depends on what you are trying to find the volume of:
Rectangle - 𝑉 = 𝑙 × 𝑤 × ℎ
Cylinder - V = 𝜋𝑟 2 × ℎ (h=height of cylinder)
Cone - V =
1
𝜋𝑟 2
3
×ℎ
(h=height of cone)
1
2
Triangular Prism - 𝑉 = 𝑏 × ℎ × 𝑙 (h=height of
triangular base and l=length of prism)
b) In the imperial system, the base unit for measuring
volume and capacity is the pint, but volume can also
be measured in cubic inches, cubic feet or cubic yards.
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In Canada, we use the term imperial units to mean
British imperial units. The US also uses an imperial
system, but the sizes of its units for volume and
capacity are different from the British units.
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A British gallon is equal to 4.54609L; a US gallon
equals 3.785L. Because British and US gallons are
different sizes, so are all the related volume and
capacity measures.
For example, a British pint is 20 fluid ounces, while
a US pint contains 16 fluid ounces.
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Imperial Units of Measurement (volume and capacity)
Unit
fluid ounce/ounce
teaspoon
tablespoon
cup
pint
quart
gallon
Abbreviation
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In many industries, volume and capacity are
measured in imperial units rather than SI units. For
example, in the food industry ingredients are often
measured in teaspoons, cups and ounces.
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A building contractor estimating the amount of
concrete needed for a job may find one supplier
who delivers concrete by the cubic meter and
another who delivers it in cubic yards.
The contractor would need to know how to convert
between the 2 systems to ensure that she is getting
the best price for her client.
This is the case for many jobs or industries.
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Discuss the Ideas – DART p. 95
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Read through together
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Can you think of any recent disasters that have
needed Canadian Aid?
Solve
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Think about, or look at, your favorite drink
containers. What are the sizes of the bottles?
The sizes are 355mL, 591mL, 237mL, etc.
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The reason for this is that many containers are
manufactured to US specifications and are then
labeled with Canadian SI equivalents.
So rather than having drink containers with a round
number like, 250mL or 500mL, we have seemingly
strange numbers of milliliters for many of our
containers.
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Discuss the Ideas – Packaging p. 125
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Read through together and solve
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Activity 3.9 – Converting a Recipe p. 126
Get into partners and we will work through this as a
class.
Example
1.
Nigel imported a vehicle that was made in Britain.
The capacity of the gas tank is 22 gallons. If the
price of gasoline is $1.20 a liter, how much will it
cost Nigel to fill his tank when it is empty?
Example
2.
The cooling system of a car’s 6-cylinder,
250-cubic-inch displacement engine has a
capacity of 3½ gallons. To protect the engine
against freezing temps, an antifreeze solution of
5/8 water is added to the cooling system. If the
cooling system is filled to capacity with the
antifreeze solution, how many quarts of ethylene
glycol are in the cooling system?
Example
3.
Val built 24 wood planters for her garden. The
inside of each planter measures 4’ long, 2’ deep,
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and 1 ’ wide. She needs to order soil to fill the
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planters. At K & R soils, potting soil sells for
$17.00/𝑦𝑑 3 , while Bob’s Best Buy sells potting soil
for $21.50/𝑚3 . Where should Val but her soil?
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Activity 3.10 – Driveway Construction p. 130
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Read through together and solve
Building your Skills
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Ex. 3.4 (p. 132) #1-6, 7 challenge
3. Mass in the Imperial System
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As we discussed earlier many older Canadians
grew up using the imperial system, therefore they
are used to using those units for weight, temp,
distance, etc. Even though Canada has switched
over to the SI system.
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Math on the Job p. 146
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Read through together and solve
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Although people often use the terms mass and
weight interchangeably, there is a difference
between them.
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Mass refers to the quantity of matter in an object.
Mass is usually measured using a balance to
compare a known amount of matter to an unknown
amount of matter
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Weight is a measure of the force of gravity on an
object.
Weight is therefore a measurement of the heaviness
of a body, the force with which a body is attracted
to a planet or moon, and is equal to the product of
the objects mass and the acceleration of gravity.
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So what does this mean?
Simply stated, it means that where ever an object is
its mass will remain constant. However, the further
away it is from the center of gravity, the less it will
weigh.
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You have studied the planets in Science, and know that
on other planets, because the force of gravity is
different than it is on earth, on object will weigh a
different amount.
You have seen astronauts in space and they look the
same as they do on earth (same shape, size and mass)
but they are weightless because there is no gravity in
space
1
6
On the moon, you would weigh of what you weigh on
earth.
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So mass does not change unless the object changes
but weight can change depending on where you
are in the universe.
Measuring weight and mass are necessary tasks for
many trades. For example, crane and hoist
operators weigh material to determine whether it
can be lifted safely and they often use imperial
units.
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In the imperial system, the slug is the unit of mass
and the pound is the unit of wieght.
The slug is not often used, and we have come to use
the pound as a base unit for both mass and weight
Many Canadians and some trades still measure
weight in pounds even though we have converted to
SI. For example forklift operators and building
constructors.
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In the imperial system, there are 3 commonly used
units of weight: the ounce, the pound and the ton.
The pound is the base unit of weight.
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1 ton (tn) = 2000 pounds
An adult buffalo can weigh 1 ton.
1 pound (lb)
A football weighs approx. 1 lb.
16 ounces (oz) = 1 lb.
One slice of bread weighs approx. 1 oz.
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In order or determine what a pound is, we need a
standard with which to compare it.
The pound is actually defined in terms of the SI
system as the rounded value of 0.45359237
kilograms.
So a pound is slightly less than ½ a kilogram.
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Discuss the Ideas – Weight of Waste p. 148
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Read through together and solve.
Example
1.
You manage a recycling collection company and
there are 2 different companies that want to
purchase some recycled computer paper from you
to make different products. One companies pays
by volume, $270 per cubic yard, and the other by
weight, $200 per 500lbs. Which is the better sell
for you? What do you have to consider right of
the start?
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Activity 4.4 – Choosing Imperial Units
Read through and work through with a partner if
you choose.
Example
2.
Stephan is building a rectangular water cistern so
that he can collect rainwater for his garden. The
inside dimensions of the finished cistern will be 10
feet 8 inches by 8 feet 4 inches by 4 feet 6 inches.
A cubic foot of water weighs about 62 pounds 8
ounces. If the cistern is completely filled with
water, what will be the weight of the water
expressed in tons?
Example
3.
George estimates that each bale of hay in his
field weighs 62.5 pounds on average. There are
892 bales to be picked up. If his truck can carry 8
tons on one trip, how many trips will he have to
make to move his bales?
Mental Example
1.
Dakota works as a fishing guide in the NWT. On a
recent trip, her client caught 2 chinook salmon.
One salmon weighed 20lb 7oz and the other
weighed 21lb 9oz. What is the total weight, in
pounds, of the two salmon?
Building your Skills
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Ex. 4.2 (p. 151) #1-6, 7 challenge
4. Mass in the SI
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Medications come in different dosages and often
both mass and volume need to be considered to
determine the correct dosage.
Emergency Medical Attendants (EMA’s) are trained
to administer a drug based on the strength of the
drug and its volume and/or weight. They are
usually supplied with tables that indicated the
volume and weight of medications to administer
according to the weight of the patients.
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Math on the Job p. 154
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Read through together and solve
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In the last section, we discusses the difference
between mass and weight and determined that in
the imperial system, we tend to use the term pound,
(unit of weight) for both weight and mass.
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In the SI units, we do the opposite. The correct term
for a unit of weight is the newton, but we use the
term kilogram, a unit of mass, to refer to both mass
and weight.
One kilogram weighs 9.8 newtons, however we will
use the kilogram to represent both weight and mass
as that is how you will see it (unless you get into
higher level physics and chemistry) in your life and
careers.
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Activity 4.5 – Using SI Prefixes p. 154
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Work through with a partner.
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A megagram is generally referred to as a tonne, a
metric ton, or a long ton; will be using tonne.
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Activity 4.6 – Equivalent Masses p. 155
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Work through with your partner
Example
1.
You and your five friends want to use your boat to
cross the lake and you are the only one who can
drive the boat. The max capacity of the boat is
listed at 0.55 tonnes. You weigh 75kg and your
friends weigh 76kg, 82kg, 63kg, 68kg, and 78kg
respectively. You also have 104kg of supplies.
How many trips will you have to make in order for
everyone (and your supplies) to get across the
water safely? Give reasons for your answer.
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Discuss the Ideas – Gross Vehicle Weight Rating
p. 156
Read through together and solve
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Activity 4.7 – Protein vs. Fat Content p. 156
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Work through together with a partner.
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Activity 4.8 – Estimating Mass
Read through together and work through with a
partner.
Building your Skills
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Ex. 4.3 (p. 159) #1-5
5. Conversions
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In many jobs, people have to call upon their knowledge
from various areas in order to solve a problem.
That is, they may have to work with unit pricing,
conversion factors, and volume formulas in order to
solve work place problems.
For example, grain is measured and sold in bushels, a
volume measure, even though the SI measurement for
grain in Canada, the tonne, is measured of mass or
weight.
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A bushel is a unit of volume or capacity equivalent
to approximately 2220 cubic inches.
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Discuss the Ideas – Mass/Weight Conversions
between SI and Imperial units p. 157
Read through together and solve.
Mental Example
1.
a)
b)
What is the approximate weight of:
a 5 pound roast, expressed in kg?
A 62 kg person, expressed in lbs?
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Conversion Factors:
kilograms to pounds:
1kg = 2.20462lb
pounds to kilograms:
1lb = 0.4545kg
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Using these determine the relationship between a
tonne and a ton?
Also how many grams are there in a pound?
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Math on the Job
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Read through together and solve.
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p. 162
Louise had to calculate the number of bushels of
barley Jim bought. This is done by first finding the
weight of the barely and then using the conversion
factor.
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In the Math on the Job we needed the conversion
factor of 49.5 bushels per tonne of barely to help
Jim determine his payment.
Farmers grow many other types of crops and a
different conversion factor is needed for each of
type of grain
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This chart gives us those conversion factors:
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http://www.afsc.ca/doc.aspx?id=2225
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Why do you think we need different conversion
factors for different types of grain?
They weigh different
They each weigh different because of how they
absorb moisture
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Activity 4.9 – Using Conversion Factors p. 163
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Read through together and solve.
Example
1.
a)
b)
c)
Billy is catering a dinner for 20 people. She consults a
3
cookbook that tells her she will need approximately
4
lb of beef for each person and that it will take
approximately 20 minutes per pound to cook at
350°F.
Approx. how many kilograms of beef should Billy buy?
At what approx. temp Celsius should she cook it?
Approx. how many minutes per kg will she have to
cook the roast?
Building your Skills
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Ex. 4.3 (p. 159) #6-7
Ex. 4.4 (p. 165) #1-7, 8 challenge