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A review of Determining DensityAt a local pawn shop a student finds a medallion that the shop owner insists is pure platinum. However, the student suspects that the medallion may actually be silver and thus much less valuable. The student buys themedallion only after the shop owner agrees to refund the price if the medallion is returned within two days. The student, a chemistry student, then takes the medallion to her lab and measures its density as follows. She firstweighs the medallion and finds its mass to be 55.64 g. She then places some water in a graduated cylinder and reads the volume as 75.2 mL. Next she drops the medallion into the cylinder and reads the new volume as77.8 mL. Is the medallion platinum (density =21.4 g/cm3) or silver (density =10.5 g/cm3)?SolutionThe densities of platinum and silver differ so much that the measured density of the medallion will show which metal is present. Because by definition Density = mass/volume To calculate the density of the medallion, we need its mass and its volume. The mass of the medallion is 55.64 g. The volume of the medallion canbe obtained by taking the difference between the volume readings of the water in the graduated cylinder before and after the medallion was added. Volume of medallion 77.8 mL -75.2 mL = 2.6 mL The volume appeared to increase by 2.6 mL when the medallion was added, so 2.6 mL represents the volume of the medallion. Now we can use the measured mass and volume of the medallion to determine its density: Density of medallion mass/volume = 55.64/2.6 = 21 g/mL = 21 g/cm3The medallion is really platinum.Do these Problems: (separate sheet of paper)1. If 89.2 mL of a liquid has a mass of 75.2 g, calculate the liquid’s density.2. A cube of metal weighs 1.45 kg and displaces 542 mL of water when immersed. Calculate the density of the metal.3. The density of pure silver is 10.5 g/cm3 at 20 °C. If 5.25 g of pure silver pellets is added to a graduatedcylinder containing 11.2 mL of water, to what volume level will the water in the cylinder rise?4. Suppose your car is rated at 45 mi/gal for highway use and 38 mi/gal for city driving. If you wanted to writeyour friend in Spain about your car’s mileage, what ratings in kilometers per liter would you report?5. You are in Paris, and you want to buy some peaches for lunch. The sign in the fruit stand indicates thatpeaches are 11.5 francs per kilogram. Given that there are approximately 5 francs to the dollar, calculatewhat a pound of peaches will cost in dollars.Doing area conversions: Use the conversion factors, but square them!!Example: How many square feet are there in 3.3 square yards? The conversion factor is 1ft = 3 yards. To get square feet we need to square everything on one side of the equation but if we do that we need to square everything on the other side too.3ft = 1yd so (3ft)2 = (1yd)2 so 9ft2 = 1yd2Doing volume conversions: Use the conversion factors, but cube them!!Example: How many cubic feet in 3.3 yds3? The conversion factor is 1ft = 3 yards. To get cubic feet we need to cube everything on one side of the equation but if we do that we need to cube everything on the other side too.The True StoryOn July 23, 1983, Air Canada Flight 143 was flying at an altitude of 26,000 ft from Montreal to Edmonton. Warning buzzers sounded in the cockpit of the Boeing 767. One of the world's larger planes was now a glider-the plane had ran out of fuel! Like all Boeing 767s, the plane had a sophisticated fuel gauge, but it was not working properly. However, the plane was still allowed to fly, because there is an alternate method for determining fuel. The Mechanics have a dip stick, calibrated in centimeters, and translated into volume in liters. The Mechanics calculated the three tanks had a total of 7682L of fuel. Pilots always calculate fuel quantities in mass, because they need to know the total mass of the plane before takeoff. Air Canada pilots had always calculated the mass in pounds, but the new 767s fuel consumption was given in kilograms. This involved using the fuel's density to convert 7682 L to a mass in kilograms, so that the pilot could calculate the mass of fuel that had to be added. The First Officer of the plane asked the Mechanic for the conversion factor to calculate volume-to-mass conversion, and the Mechanic replied "1.77". Using that number, the officer and the Mechanic calculated that 4917 L of fuel should be added. The required amount for the trip was 22,300 kg. The mechanic never gave the First Officer the conversion units which was for pounds per liter, not kg/liter as the First Officer assumed. The rest of the story is that the Pilot could not make it to the nearest airport, Winnipeg, but to a little town Gimli which had a former Royal Canadian Air Force runway converted to a race track. For 30 minutes the plane glided to Gimil and managed to land.The Problem (6) The Gimli Glider was a Boeing 767 that ran out of fuel. Read the story above, then verify that the ground crew should have added 20,163 L of fuel instead 4916. The crucial piece of information is the density of the fuel. The crew used 1.77, but did not recognize the units were pounds per liter. To solve the problem you need first to find the density in units of kilograms per liter (Hint: 1 lb = 454 grams).The Problem reworded On July 23, 1983 Air Canada Flight 143, flying at 26,000 feet from Montreal to Edmonton, ran out of fuel because the first officer ask the mechanic for the conversion factor of mass to volume at Montreal. The mechanic gave the first officer the answer 1.77 with no units. The plane had 7682 L of fuel at Montreal. The pilot knew he needed 22,300 kg of fuel to make the trip. The mechanic's answer of 1.77 was pounds per liter not kilograms per liter caused the error such that only 4917 L of fuel was added. If there are 2.205 pounds in a kilogram, how many liters of fuel were needed for the trip? How many liters minimum of fuel should have been added at Montreal before takeoff? Problem 7 Before 1982 the US Mint cast penny coins from an alloy of copper and zinc. A 1980 Penny weighs 3.051 g and contains 2.898 g of pure copper. In 1982 the US Mint stopped making copper pennies, because the price of copper was worth more than the penny. The post 1982 penny contains only a layer of copper over zinc. A 1990 penny weighs 2.554 g and contains 2.490 g of zinc. If the mint melted down one pound of 1980 pennies, how many 1990 pennies can be made from the total copper from the 1980 pennies? Problems 8 An Olympic size swimming pool is 50.0 m long and 25.0 m wide. How many gallons of water ( d = 1.0g/mL )are needed to fill the pool to an average depth of 5.5 feet. Problem 9 A furniture factory needs 29.5 ft2 of fabric to upholster one chair. A Europen supplier sends the fabric in bolts of exactly 200 m2. What is the maximum number of chirs that can be upholstered by three bolts of fabric. Hint: 1 m - 3.281 ft)? Problem 10 My throw away car gets 23.4 mi/gal and hold 70.1 L of gasoline. How far can I drive on a tankful of gas? If gas cost $2.20/gal; how much does a tankful of gas cost? If the average speed on a trip is 92.2 km/hr, How many hours may I drive the car on the trip before I run out of gas? Problem 11 A material will float on the surface of a liquid if the material has a density less than that of the liquid. Given that the density of water is approximately 1.0 g/mL, will a block of material having a volume of 1.2 x104 in.3 and weighing 3.5 lb float or sink when placed in a reservoir of water? ................
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