The Disney movie \"Up\", is all about buoyancy. In the movie clip (which you don

Question

The Disney movie "Up", is all about buoyancy. In the movie clip (which you don't really need to watch), the main character's wife has passed away. He is scheduled to move to an assisted living home, but has other plans. Since he used to sell helium filled balloons, he ties a mess of them to his house. When the assisted living home comes to pick him up, he releases the balloons and the house rises and flies across the sky. Unknown to him, a nice little Boy Scout was stowed away in his house when it lifted off. The two of them go on an adventure and save some rare bird This is an aside of how measurements were made. From the picture, the house door = 3ft = 1m, so the house is about 21 ft. (7 meters) wide. The balloon bunch has a radius of about 3 houses or 20 meters to give a total volume of 32.000 m^3, but the balloons only fill half the volume due to packing density of 0.5. (i.e. a sphere inside a box of the same dimension only fills in roughly half the volume.. So the balloons take up a volume of 16,000 m^3. In the picture to the right, the house with all the helium balloons is shown. The overall goal is to find the combined mass (in kg) of the house. Consider the house and all the balloons as the object. Assume the balloons are filled with helium gas Draw a force diagram in the box to the right. Be sure to include both the weight of the house and the weight of the helium in the balloons. Assume the house is stationary. Write Newton's second law for the object. From the diagram and a bit of measuring, the total volume of the balloons is approximately, 16,000 m^3. (This is approximately 12,000 balloons-5 foot diameter balloons, at least that what the picture shows above.) Use this volume along with the density of air and the density of helium to determine the weight of the house.

Explanation / Answer

Upward force : V(pg - pa)g (according to archimedes principle)

V - total volume of balloons

pg - Density of helium

pa - density of air

Downward force = (mh + mb)g

mh - Mass of house

mb - Mass of balloons

Newtons Second laww of motion (since acceleration is zero)

upward force = downward force

(mh + mb)g - V(pg - pa)g = 0

V = 16000 m3

density of air = 1.225 kg/m3

density of helium = 0.164 kg/m3

So the combined mass

m = 16000*(1.225-0.164) = 16976 kg

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