E. Measurement Systems: Temperature, Volume and Mass

1. E. Measurement Systems: Temperature, Volume and Mass Math 10: A and W

2. Key Terms: • Find the definition of each of the following terms: • Conversion Factor • Mass • Weight • Temperature • Volume • Capacity

3. 1. Converting Temperature • 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.

4. Math on the Job – p. 138 • Read through together and solve.

5. 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.

6. 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.

7. 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.

8. 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.

9. 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.

10. 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.

11. 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.

12. Activity 4.2 – Develop a Conversion Formula p. 139 • Read through together and solve

13. Mental Example • The thermometer on the outside of your house reads 20°F. Estimate what the temp would be if expressed in degrees Celsius.

14. Discuss the Ideas – Separation of Crude Oil p. 140 • Read through and solve on your own then we will go over as a class.

15. Example • 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.

16. Example • 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?

17. 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.

18. Building your Skills • Ex. 4.1 (p. 143) #1-6

19. 2. Volume • Math on the Job p. 124 • Read through together and solve.

20. a) In the SI, the base unit for measuring volume is the liter (L). It is also the base unit for capacity. • 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.

21. SI Units of Measurement (volume) SI Prefix Symbol Combined Symbol kilo hecto deca meter deci centi milli

22. L and ML will be used most often but this gives you a good look at the difference between the two.

23. 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 (

24. What is the formula for calculating volume? • It depends on what you are trying to find the volume of: • Rectangle - • Cylinder - (h=height of cylinder) • Cone - (h=height of cone) • Triangular Prism - (h=height of triangular base and l=length of prism)

25. 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. • 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.

26. 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.

27. Imperial Units of Measurement (volume and capacity) UnitAbbreviation fluid ounce/ounce teaspoon tablespoon cup pint quart gallon

28. 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.

29. 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.

30. Discuss the Ideas – DART p. 95 • Read through together • Can you think of any recent disasters that have needed Canadian Aid? • Solve

31. Think about, or look at, your favorite drink containers. What are the sizes of the bottles? • The sizes are 355mL, 591mL, 237mL, etc.

32. 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.

33. Discuss the Ideas – Packaging p. 125 • Read through together and solve

34. Activity 3.9 – Converting a Recipe p. 126 • Get into partners and we will work through this as a class.

35. Example • 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?

36. Example • 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?

37. Example • Val built 24 wood planters for her garden. The inside of each planter measures 4’ long, 2’ deep, and 1’ wide. She needs to order soil to fill the planters. At K & R soils, potting soil sells for $17.00/, while Bob’s Best Buy sells potting soil for $21.50/. Where should Val but her soil?

38. Activity 3.10 – Driveway Construction p. 130 • Read through together and solve

39. Building your Skills • Ex. 3.4 (p. 132) #1-6, 7 challenge

40. 3. Mass in the Imperial System • 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.

41. Math on the Job p. 146 • Read through together and solve

42. Although people often use the terms mass and weight interchangeably, there is a difference between them.

43. 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

44. Weightis 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.

45. 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.

46. * • 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 • On the moon, you would weigh of what you weigh on earth.

47. 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.

48. 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.

49. 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.

50. 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.