A helium balloon \"floats\" because it displaces air, creating a buoyant force o
ID: 1451333 • Letter: A
Question
A helium balloon "floats" because it displaces air, creating a buoyant force on the balloon. This buoyant force is usually greater than the weight of the ballo and helium, so a tension force provided by a string is needed to keep it from floating away. Suppose a ballon at a party is a sphere with radius of 16.0cm. The density of helium at room temperature is Phe= 0.18kg/m^3, and the density of air is Pair= 1.29kg/m^3.
A) If the mass of the rubber in the ballo is 10g, what is the total weight of the helium filled ballon? The volume of a sphere is (4/3)(3.14)r^3
B) What is the magnitude of the buoyant force on the balloon?
C) What is the magitude of tensio in the string when the balloon is held stationary? You may want to draw a free body diagram for the balloon; then you ca use Newtons Second Law to solve.
Explanation / Answer
A)
volume of sphere V = (4/3)*pi*r^3
mass of the He = PHe*V
weight of He W1 = PHe*v*g = 0.18*(4/3)*pi*0.16^3*9.8 = 0.0303 N
mass ballon = 10 g = 0.01 kg
weight of the hte balloon = 0.01*9.8 = 0.098 N
total weight of the helium filled ballon W = 0.0303 + 0.098 = 0.1283 N
+++++++++++++++++++
B)
buoyantforce Fb = V*Pair*g = (4/3)*pi*0.16^3*1.29*9.8 = 0.2169 N
+++++++++
C)
along vertical
T = Fb - W
T = 0.2169-0.1283 = 0.0886 N
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