Calculating Acceleration of Rising Balloon

[iseidthat]

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?

 

[redargon]

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?

 

[thomate1]

Your attempt at a solution is incorrect because the question is asking for the acceleration of the balloon, not the acceleration due to gravity (g). The ratio of air density inside and outside the balloon affects the buoyancy force acting on the balloon, which then determines the acceleration of the balloon. The correct approach to solving this problem would involve using the buoyancy equation: Fb = ρVg, where ρ is the density of air, V is the volume of the balloon, and g is the acceleration due to gravity. Using this equation, you can determine the acceleration of the balloon based on the given ratio of air densities. It is also important to note that the mass of the balloon fabric and basket should not be neglected, as they also contribute to the overall mass of the system and affect the acceleration.