Calculating Work Done by Upward Buoyant Force on Hot Air Balloon

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To calculate the work done by the upward buoyant force on a hot air balloon, first determine the net force by combining the buoyant force with the weight of the balloon. The balloon ascends with an acceleration of 1.25 m/s² for 25 seconds, resulting in a displacement of approximately 390.625 meters. The work done can also be calculated using the potential energy formula PE = mgh, where h is the height reached. The discussion highlights the need to clarify the relationship between net force, displacement, and work in this context. The calculations and concepts presented guide the approach to solving the problem effectively.
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Homework Statement


A hot air balloon of mass 425 kg ascends from the ground level and accelerates at a rate of 1.25 m/s/s for 25 seconds. How much work is done by the upward buoyant force on the balloon?

(conceptual) A certain amount of work W is required to accelerate a car from rest to a speed of v. How much work is required to accelerate from rest to a speed of v/2?

Homework Equations


W=fd
Fnet=ma
KE=1/2mv^2


The Attempt at a Solution



I tried to find Fnet first, so would it be the upward buoyant force (what is trying to be solved)+mg (weight)= 425x1.25. Then find the displacement using one dimensional motion, getting 390.625 m traveled. Is all this right? How do I proceed?

Rearranged W=1/2m(v/2)^2 to 4w=1/2mv^2. How do I proceed? I'm solving for work required.
 
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Cant you simply compute the height the balloon reached and then use PE=mgh ?
 

Thread 'Magnitude of buoyant force in fluids of different densities'

The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?
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