Up is a 2009 American computeranimated comedyadventure film

Up is a 2009 American computer-animated comedy-adventure film produced by Pixar which premiered on May 29, 2009. The film centers on an elderly widower named Carl Fredricksen and an earnest young Wilderness Explorer named Russell who fly to South America by floating in a house attached to thousands of helium balloons.

Suppose the weight of the house is W = 320000 N. The density of air is D = 1.29 kg/m³, and the density of helium is d = 0.179 kg/m³. The total volume of helium in the balloons is V. For this situation, assume that the house has negligible buoyancy force acting on it, and that the balloon material is very light.

(a) Write an expression for the buoyant force on the balloons in terms of D, d, g, and V.

F_B = ________

(b) Write an expression for the total weight of the house-balloons system in terms of W, D, d, g, and V.

W_Total = ________


(c) Determine the total volume of helium required to lift the house.

________________ m³

(d) A single balloon has a volume of 0.015 m³. How many balloons are required to lift the house? (Round to the nearest integer.)

__________________ balloons

Solution

a) F= (D-d)gV

b) W=(D-d)gV

c) From (b), solving for V we have,

V = W/(D-d)g = 320000/(1.29-.179)*9.8 = 293907m^3

d) No of balloons: 19593796