Does "Up" Defy Physics?
Can balloons be used to lift a house?
Can balloons be used to lift a house? According to the Disney Pixar movie "Up" they can. For those of you who don't know what "Up" is here is the premise in why Carl made a flying house(I'll try to keep this SPOILER free!):
The movie starts with a young Carl in the movies watching a documentary on his adventurous hero Charles Muntz. In the end of the flick Muntz heads to Paradise Falls. Though this wasn't inspiration enough to go to Paradise Falls, when he meets another adventurous mind in the form of Ellie they decide that they want to move to Paradise Falls. Something happens Ellie and they are unable to go together, but Carl still wants to go! Due to Carl's immense attachment to his house he decides, "I'll just bring my house with!"
And he does it! With some will-power and little physics Carl floats his house to Paradise Falls with balloons. How many balloons does Carl use? How effective would they be?
How heavy is the house?
Pixar reports to have animated 20,622 for the liftoff scene. Other floating scenes have just 10,297. Let's take 20,622 into rather than the later.
Using a force sensor a 13 party balloons I was able to find the average force that a single party balloon would exert on the house (Special thanks to Mr. Schmitt and Ms. Jacobs and Ms. Science-Over-looker for all the help!)
Total Force = .341N Upward Force of 13 balloons
Average Force = .0262N Upward Force of one balloon
That is a small force. So to do a quick double check use Archimede's Principle to approximately solve for the force.
F=(helium density)(acceleration due to gravity)(volume of a balloon with a radius of 6in)
F = .1785(kg/m^3) * 9.8(m/s^2)*.01483(m^3)
To put this into perspective it would take 20,000+ balloons to lift Mrs. Jacobs!
With the average mass of a house being from 80,000lbs-160,000lbs, the force needed to lift a smaller house would more than 355,858N = 13.6 million party balloons. On the high end it would need to be more than 711715.4592N = 27.2 million party balloons!
How many balloons would it take on another planet?
By substituting the force that I found a single balloon to exert back into Archimedes' Equation I was able to fine the average volume of these balloons: .0150m^3 = V
The tricky thing with this is due to the gravity change there will be a different weight of the house, therefor a different force needed to lift the house. Also, the atmospheric density is different. All this considered here are the result to Venus and Mars!
The gravity on Mars is 3.711m/s^2
The atmospheric density of .0155kg/m^3
RED FLAG! HALT! No matter how many balloons you use on Mars it would be impossible to lift the house through the air. Even though the house will be much lighter than on earth the air density on Mars is so low that the balloons would actually sink!
Gravity of Venus is 8.87m/s^2
Atmospheric density is 65kg/m^3
Now here is a perfect example of a planet that is ideal for helium balloon travel. With the crazy rise in atmospheric density the amount of buoyant force that each balloon exerts jumps from .0262N to 8.61N.
The force that Venus exerts on the house would be ranging from 322.088N to 644,175N.
Only 37,409 balloons to 74,818 balloons would be needed!
WAS "UP" ON VENUS?
Of course these are merely models though. And these models are far from complete. There are a few open ended questions, though, that I would like to keep you pondering:
Where did the balloons come from anyway?!
How would the hotter temperature of Venus affect the balloons?
How high would the balloons travel before coming to a rest or bursting?
How does the gravity affect the net force between the house and the balloons?
"Gases - Densities." Gases - Densities. N.p., n.d. Web. 16 Dec. 2014.
":: NASA Quest Aerospace ::." :: NASA Quest Aerospace ::. N.p., n.d. Web. 15 Dec. 2014.
Rastogi, Nina. "How Many Balloons Would It Take to Lift a House like the One in Pixar's Up?" N.p., n.d. Web. 16 Dec. 2014.