How Is the Initial Upward Acceleration of a Weather Balloon Calculated?

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To calculate the initial upward acceleration of a weather balloon with a radius of 2.5m and mass of 15 kg, the volume of the balloon is first determined using the formula for the volume of a sphere. The density is calculated by dividing mass by volume, and buoyancy is established as greater than weight. The initial upward acceleration is derived from the buoyant force equation, leading to an acceleration of approximately 42 m/s². However, the balloon eventually reaches terminal velocity, which is calculated to be about 3 m/s². The discussion highlights the importance of correctly applying buoyancy and acceleration equations in solving such problems.
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Homework Statement



assume the balloon is a spherical shape whose radius is 2.5m and total mass of 15 kg

a) what is the initial upward acceleration of the balloon when it is released from sea level


Homework Equations





The Attempt at a Solution



i know the volume of a sphere is =4/3 (pi)r3
so can calculate the volume
i know the density of the balloon is

p=m/v
and that the buoyancy is going to be greater than the weight
i reaaranged the equation and substituted m=pv into fb=ma

to get fb=pva

but i don't think this is the right way to do it
where am i going wrong and how do i finish the equation?

cheers
 
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i had a similar problem i solved for the force then the volume and manipulated the equation to read a=f/pv i got a reasonable answer
 
ye i got the answer in the end. the acceleration comes out as about 42 m/s^2 but the next part of the question was to find where it reaches terminal velocity and it reaches it at 3m/s^2
 
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