A balloon rises slowly into sky. If the balloon has a diameter of 23.1 cm when a child lets go, what is its diameter at an altitude of 1410 m?
MIT 8.01 Physics I Classical Mechanics, Fall 1999
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This question could be solved by applying the ideal gas law. Using the reciprocal proportionality of P and V.
First assume the ballon is perfectly heat-isolated, then calculate the volume of the ballon is 4/3*pi*r^3, the assume the air pressure on the place the ballon has arised as 1 atmosphere pressure(atm).
Because the air pressure between height of 1410m and 0m varies, and no particular formula could be used. Here is the link for the graph of the relationship between height and pressure. But the graph didn't use the atm as its air pressure unit.
Finally you get the volume at the height of 1410m by using this: P1*V1 = P2*V2
P1- Pressure of the baloon in ground level V1- volume of the baloon in ground level
P2- " " " " in 1410m V2- " " " " in 1410m
R1- Radius of the baloon in ground level R2- Radiaus of the baloon in 1420m
we need to find out the diameter so
V2=P1*V1/P2 --- A V2=4/3PiR2^3 ---B V1=4/3PiR1^3----- C
4/3PiR2^3= 4/3PiR1^3 * P1/P2
R2^3=R1^3 * P1/P2------- D
To find the radius we need to find out the presure ratio between pressure at the ground level and 1410 m .. according to first answer we can find the pressure what we need by a graph but when we are finding a ratio, pressure unit wont be a prblem. but i was anable to find that graph and if there any graph we can solve this problem by solving the equation 'D'
then 2 * R2= Diameter at 1410m