Calculating Acceleration of Rising Balloon

AI Thread Summary
To calculate the acceleration of a rising hot-air balloon with an outside-to-inside air density ratio of 1.30, one must consider the buoyant force acting on the balloon. The buoyant force is proportional to the difference in density between the outside air and the air inside the balloon. The acceleration cannot simply be calculated by multiplying the density ratio by gravitational acceleration, as this does not account for the net forces involved. The correct approach involves applying Newton's second law and factoring in the effective weight of the balloon based on the density difference. Thus, a more detailed calculation is required to determine the actual acceleration of the balloon.
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Homework Statement



What is the acceleration of a rising hot-air balloon if the ratio of the air density outside the balloon to that inside is 1.30? Neglect the mass of the balloon fabric and the basket.


Homework Equations


g=9.81 m/s^s

The Attempt at a Solution



I thought it would just be 1.3 times g=
1.3(9.81)=12.75 m/s

my homework says it is wrong...why?
 
Physics news on Phys.org
if the ratio was 1:1 the acceleration would be 9.81m/s^2 downwards. So how much lighter is the air in the balloon actually?
 

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