To an order of magnitude, how many helium-filled toy balloons would be required to lift you? Because helium is an irreplaceable resource, develop a theoretical answer rather than an experimental answer. Assume that you have a mass of approximately 70 kg, the radius of a balloon is 12.5 cm, the helium is at STP and it is immersed in air at 0°C and 1 atm.
__________My work now___ I assumed that the balloon was a sphere, so 4/3*pi*(r^3) = 0.008181231 m^3. I used 0.125 m for the radius. Also the weight of the person is equal to m*g=686 Newtons.
Thus, the force needed to lift up the person is 686 Newtons. I found the density of air at STP to be 1.2754 kg/m^3. So the buoyant force is density of air * g * Volume of air displaced which is the same as the volume of one balloon. Thus, the buoyant force for one balloon is is 1.2754 x 9.8 x 0.008181231 m^3.
The weight of the person was 686 newtons, so 686/force of one balloon = # of balloons, which is 6710 balloons. This is INCORRECT. Also, I thought the question stated "what order of magnitude" so I guessed 7,000 balloons, but my online homework still said, "response differs from the correct answer by more than 10%".
Please help explain if you can how to solve this problem.
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