Calculating Work Done by Upward Buoyant Force on Hot Air Balloon

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SUMMARY

The discussion focuses on calculating the work done by the upward buoyant force on a hot air balloon with a mass of 425 kg, which ascends with an acceleration of 1.25 m/s² for 25 seconds. The participant correctly identifies the need to calculate the net force, which includes the buoyant force and the weight of the balloon. The displacement is determined to be 390.625 m, and the participant contemplates using the potential energy formula PE = mgh to find the work done. The discussion emphasizes the relationship between work, force, and displacement in the context of buoyancy and motion.

PREREQUISITES
  • Understanding of Newton's Second Law (F = ma)
  • Familiarity with the concepts of work (W = fd) and kinetic energy (KE = 1/2mv²)
  • Knowledge of gravitational potential energy (PE = mgh)
  • Basic principles of buoyancy and forces acting on objects in fluid
NEXT STEPS
  • Calculate the buoyant force acting on the hot air balloon using Archimedes' principle
  • Explore the relationship between work done and energy transformations in fluid dynamics
  • Learn about the kinematic equations for uniformly accelerated motion
  • Investigate the effects of varying mass and acceleration on the work done in similar scenarios
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and buoyancy, as well as educators seeking to enhance their understanding of work and energy concepts in real-world applications.

azhang40
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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 ?
 

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