Modern commercial airliners are largely made of aluminum a...

Modern commercial airliners are largely made of aluminum, a light and strong metal. But the fact that aluminum is cheap enough that airplanes can be made out of it is a bit of historical luck. Before the discovery of the Hall-Héroult process in 1886, aluminum was as rare and expensive as gold. What would happen if airplanes had to be made of steel? The fuselage of the Boeing 777, which can carry 305 passengers, is approximately a hollow aluminum cylinder without ends, 64.0 m long, 6.2 m wide, and 2.5 mm thick (see sketch at right). Suppose this fuselage was made of steel (density 7.87 g/cm³) instead of aluminum (density 2.70 g/cm³), and let's say the average passenger has a mass of 79 kg. We'll also assume the engines can't lift any greater mass than they already do. Calculate the number of passengers that the Boeing 777 could carry if its fuselage was made of steel.

Transcript

00:01 Okay, so here we know that commercial airliners are typically made out of aluminum, but we wanted to know what would happen if they were made of steel instead.

00:10 So normally, the airplane can carry 400 passengers, and we know the measurements of the airplane, we're going to assume it's a hollow cylinder.

00:28 That is 70 .7 meters long, 6 .5 meters long.

00:41 Wide and 2 .5 millimeters thick.

00:51 Now one thing to note about a cylinder is if it's hollow and if there's no end caps, if you actually cut the cylinder, it's going to actually form a sort of rectangle.

01:05 So you can, if you need help visualizing this, imagine a toilet paper roll, the cardboard piece.

01:11 If you cut down the middle of that and then flattened the roll, it's going to form a rectangle slash square shape.

01:19 So here what's we really have is a rectangle that's 70 .7 meters long, 6 .5 meters wide, and then we know the thickness is 2 .5 millimeters.

01:42 So instead we want to know if this fuselage was made of steel instead of aluminum, how much, how many passengers could it carry? so right now we know that it can carry 400 passengers and each passenger is 80 kilograms.

02:00 So what we can do is we can calculate the total mass that the airplane can carry when it's made out of aluminum.

02:06 And then we can see how much mass it is when it's made out of steel instead, and then divide the remaining mass that it can carry by 80 to see how many passengers it can carry.

02:18 So the total mass that the airplane can carry first is 400 passengers plus the weight of the aluminum.

02:24 So 400 passengers, and we know that one passenger is 80 kilograms.

02:34 So this will tell us the mass of the passengers of the airplane carries, which is 32 ,000 kilograms.

02:44 And then we want to add this to the kilograms of aluminum that the airplane also carries.

02:51 So to find that, we first need to know some information about aluminum.

02:57 We're given the density of aluminum, which is 2 .70 grams per cubic.

03:02 Centimeter.

03:04 So we know how to relate mass and volume of aluminum, but we just want the mass.

03:09 So a way that we can cancel out this volume is to see what volume of aluminum that we actually have.

03:15 And because we have the measurements of the plane, we can actually calculate this volume...

Question

Please give Ace some feedback