General physics

Blowing off units. Throughout your physics course, your instructor will expect you to be careful with units in your calculations” Yet some students tend to neglect them and just trust that they always work out properly. Maybe this real world example will keep you from such a sloppy habit.

On July 23, 1983, Air Canada Flight I43 was being readied for its long trip from Montreal to Edmonton when the flight crew asked the ground crew to determine how much fuel was already on board. The flight crew knew they needed to begin the trip with 22 300 kg of fuel. They knew that amount in kilograms because Canada had recently switched to the metric system; previously fuel had been measured in pounds. The ground crew could measure the onboard fuel only in liters, which they reported as 7682 L. Thus, to determine how much fuel was on board and how much additional fuel was needed, the flight crew asked the ground crew for the conversion factor from liters to kilograms of fuel. The response was 1.77, which the flight crew used (1.77 kg corresponds to 1 L). (a) How many kilograms of fuel did the flight crew think they had? (In this problem, take all given data as being exact.) (b) How many liters did they ask to be added?

Unfortunately, the response from the ground crew was based on pre-metric habits -1.77 was the conversion factor not from liters to kilograms but rather from liters to pounds of fuel (1.77 lb corresponds to 1 L). (a) How many kilograms of fuel were actually on board? (Except for the given 1.77, use four significant figures for other conversion factors) (d) How many liters of additional fuel were actually needed? (e) When the airplane left Montreal, what percentage of the required fuel did it have?

En route to Edmonton, at an altitude of 7 .9 km, the airplane ran out of fuel and began to fall. Although the airplane had no power, the pilot managed to put it into a downward glide. Because the nearest working airport was too far to reach by gliding only, the pilot angled the glide toward an old, nonworking airport. Unfortunately, the runway at that airport had been converted to a track for race cars, and a steel barrier had been constructed across it. Fortunately, as the airplane hit the runway, the front landing gear collapsed, dropping the nose of the airplane onto the runway. The skidding slowed the airplane so that it stopped just short of the steel barrier, with stunned race drivers and fans looking on. All on board the airplane emerged safely. The point here is this: Take care of the units.

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