Question

Part A

Calculate the buoyant force of air (density 1.20 kg/m3 ) on a spherical party balloon that has a radius of 14.6 cm .

Express your answer to three significant figures and include appropriate units

Part B

If the rubber of the balloon itself has a mass of 2.00 g and the balloon is filled with helium (density 0.166 kg/m3 ), calculate the net upward force (the “lift”) that acts on it in air.

Express your answer to three significant figures and include appropriate units.

Answer 1

a )

the buoyant force " F_B "

given

density 1.20 kg/m³ = and radius of 14.6 cm = r = 0.146 m

V = 4/3 r³

V = 4/3 X 3.14 X 0.146³

V = 0.013 m³

F_B = V g

F_B = 1.2 X 0.013 X 9.8

F_B = 0.15288 N

the buoyant force is F_B = 0.15288 N

b )

the net upward force is " F "

given m = 2 g = 0.002 kg

density 0.166 kg/m³ =

V = 4/3 X 3.14 X 0.146³

V = 0.013 m³  

gravity force F_G = m g + V g

gravity force F_G = 0.002 X 9.8 + 0.166 X 0.013 X 9.8

gravity force F_G = 0.0196 + 0.0211

gravity force F_G = 0.04074 N

the net upward force is F = F_B - F_G

F = 0.15288 - 0.04074

F = 0.11214 N

the net upward force is F = 0.11214 N