A little more on this weeks Physics assignment

Hi folks,

A few folks have written looking for help on this week's assignment.  Use the "What if" article as a guide.  Find a topic and apply some physics concepts/formula to the topic.  Students in other classes have used the power generated by a punch from the Hulk, the momentum of Thor's hammer, the amount of bees it would take to hold up a jet liner, and how many toasters could Spiderman power compared to the amount of energy he exerted to hold a subway car.  I've also seen an article calculating the speed that Santa Claus would have to travel at to deliver gifts on Xmas Eve (and, if he traveled at that speed, what would happen to him and the reindeer!).

If you just apply one formula, you'll get credit for the assignment, but if you apply several formulas or look at the situation from different angles (ie. Yoda's power and how many houses could be powered with that power)  you'll get extra credit.

I've included a superb essay from a student in a separate class.  This one is worth a full 10 points of extra credit.

Have fun!

Jim Mueller

How many bees would it take to lift up a plane?

In the Bee Movie, there is a crucial scene in the movie where seemingly thousands of Bees manage to lift and land a plane. After brutally knocking out the pilot and copilot of the plane, a rogue bee and his crazed human girlfriend manage to hijack a plane. They then use thousands of bees to land it after they remember they cannot fly a plane. But, is this actually possible? How many Bees would it take to gather enough force to carry a plane?

First, we need to calculate how much force it would take to lift up the plane in the first place. Then, we will need to find the force of a bee.

To find how much force it would take to lift up a plane, we need to find the mass of it. We'll need to find the model of plane used in the movie to get more accurate data.

The model of plane used in the movie is from a company called 'Flyover Air', an airline that does not exist in the real world. However, we do know it is a commercial aircraft, and we can compare it to other commercial aircraft that do exist and find the closest match.

The plane used in the movie has 2 jets on each wing. It also has 34 windows on each side of the plane, and in an earlier scene we can see that there are 3 seats per window.

34 * 2 * 3 = 204. This means the plane can fit about 204 passengers. The Bee Movie was also created in, and most likely set in, the U.S.A. Along with all that, the movie was released in 2007, meaning we can use no models of planes created after then. This is all crucial data for finding the commercial aircraft the plane was based off of.

A Boeing model of plane first seemed like a possibility. It is a model of commercial aircraft that usually operates in Europe and America, and that can carry a large number of passengers. However, Boeing models only have one jet per wing, and can usually fit up to twice as many passengers as the plane in the movie.

Another possible model seemed to be the Airbus A340-200, as it can fit about 200 passengers, and has two jets per wing. However, it doesn't operate in the U.S.A, also taking it out of the equation.

The main problem with all of this is that commercial aircraft that use two jets usually fit about twice the amount of passengers the plane in the movie does, at the least. I can not find a close enough model of plane that operates in America. But, I did manage to find a model of plane that is close enough in all other categories, and will likely have a similar weight to the plane in the movie. So, we are using the Airbus A340-200 after all.

This model of plane's maximum landing weight is 185,000Kg (Source), which is the mass of the plane we will use in our equations. Converted to Newtons, it would take about 1,814,230.25N to lift and land the plane.

Now that we know how much force it would take to land the plane, we need to find the force of a Bee.

In the movie, the bee's used to land the plane are special 'Pollen Jocks', an extra strong type of bee in the movie. They collect pollen for the hive. The closest type of Bee to this in the real world is a type of worker bee, a forager bee. They don't differ in size from any other honey bee, so we will just use the size of a normal Western honey bee.

On average, honey bees weigh one tenth of a gram , or 0.0001 kilograms. A bee can carry up to 100mg in pollen, or 0.0001kg. So, they can carry about their own weight. We know all we need to know to solve for how many bees it would take to lift a plane now, we just need to divide the weight of the plane by how much weight a bee can carry. 185,000Kg/0.0001kg = 1,850,000,000.

It would take 1,850,000,000 bees to lift the weight of the plane. That's pretty insane! But would the plane used in the movie actually be able to fit that many bees under it? Let's find out.

In the movie, the bees all lift up the plane just from the underside. So, we will only calculate the area of the underside of the plane. First, we have to find the area of the underside of the  plane, and then the area of that many bees.

We know the model of the plane is an Airbus A340-200. From the company's website (here), we know the total wingspan, height and length of the plane. Using the website we used earlier, we know it has a total wing area of 363.1m2. It also have  a cabin width of 5.64m, and a length of 59.40m. Multiplying those together and adding the wing area gives us a total area of about 698m2.

Now, to find the area of that many bees. The length and size of bees can vary, but for honey bees, this stays relatively consistent. Worker honeybees have an average length of about .5 inches, but I couldn't find much about the width of the bee, so we are going to also use this chart for reference.

 The length of the bee is about the same as before, and the width seems to bee about .8cm. Converted, they have a length of about 0.013 meters and width of about 0.008 meters. Using the formula for area, (length x width), this gives honeybee workers an area of about 0.000104 meters2. But, this is all approximate, because the size of bees can vary.

Now, we just need to multiply the area of a bee by 1,850,000,000….oh goodness. 0.000104 * 1,850,000,000 gives us an area of 192,400 m2.

So, the surface area of 1,850,000,000 bees squished together is actually about 275.6 times the area of the plane used!  The creators of this movie obviously didn't do their bee-search (I know, very funny).

But in comparison, the area of a regulation sized football field is 17556.48m2! 1,850,000,000 bees has the same area as about 11 football fields.  Wow!