Boeing 747

Question:

How would you weigh a Boeing 747 without using scales?

.

.

C

A

P

T

A

I

N

I

N

T

E

R

V

I

E

W

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Solution: There are many solutions to this puzzle. For many interviewers, the intended response is that you put the jet on a large boat, say an aircraft carrier, and paint a mark on the hull where the water line is. Now remove the jet and the boat rises in the water. Finally, load the boat with items of known weight, say one hundred 100-pound bags of cement, until the boat sinks to the waterline mark you previously painted. The total weight of the items loaded on the boat equals the weight of the jet.

Dale Fedderson, a career counselor at a Los Angeles–based career center, considers the following solution even more elegant. As a former teacher, he used this technique to get his students to measure the weight of his automobile. Fedderson explains:

Measure the square inches of tire rubber contacting the tarmac for all tires (easy to do with a ruler and a thin straight edge), measure the tire pressure, and multiply pressure times square inches. That is the total weight of the plane. In the case of a Boeing 747-400, assume there are 16 landing gear tires and two nose gear tires, with each tire representing 175 square inches of tarmac contact. Further, assume the tire pressure to be 125 pounds per square inch. The calculation, then, is 18 tires 175 square inches 125 pounds per square inch 393,750 pounds.

Because a tire is a flexible support, so long as the vehicle is not actually resting on the rims, the rubber contacting the road is all that holds it up, and the rubber does that by pressure—“pounds per square inch”—which necessarily has to counteract and be equal to the weight of the vehicle.

Smart-aleck responses, such as looking up the technical specifica-tions for the 747 on the Boeing Web site, are not recommended. In fact, the specifications are there, and they reveal that the typical operating (empty) weight for a Boeing 747-400 is 398,780 pounds (an answer that corresponds amazingly well with Fedderson’s calculation).

Answer: Many solutions are possible. Two agreeable ones are to calculate weight by displacement of water or combined air pressure on tires.

Extra credit: The weight of the plane can also be derived this way: Calculate the volume of that portion of the ship between the first water level (without the jet) and the second water level (with the jet). Multiply that volume by the density of water, and you will also get the weight of the jet.

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