This is a GO problem, Chapter 11 problem 103 The hot air inside the balloon has

Question

This is a GO problem, Chapter 11 problem 103
The hot air inside the balloon has a densityof 0.97 kg/m3, andthe cool air outside the balloon has a density of 1.25kg/m3.

What is the algebraic expression for the upwardacceleration ay of the balloon?Express your answer in terms of thedensity C of the cool airoutside the balloon, thedensity H of the hot air insidethe balloon, and the magnitude g of theacceleration due to gravity. Upward is the positivedirection. ay=?
what is the valueof ay=?


The hot air inside the balloon has a densityof 0.97 kg/m3, andthe cool air outside the balloon has a density of 1.25kg/m3.

What is the algebraic expression for the upwardacceleration ay of the balloon?Express your answer in terms of thedensity C of the cool airoutside the balloon, thedensity H of the hot air insidethe balloon, and the magnitude g of theacceleration due to gravity. Upward is the positivedirection. ay=?
what is the valueof ay=?

Explanation / Answer

Considering the weight of balloon is negligible as compared toweight of hot air , Let volume of balloon be V Then mass of hot air inside it = Density *volume = 0.97V So weight of hot air inside= mg = 0.97Vg (downward) Also Buoyant force =weight of displaced fluid Here displaced fluid is cold air Weight = mg =volume *density of cold air *g =1.25Vg (upwards ) Net upward force = 1.25Vg-0.97Vg=0.27Vg Also mass of hot air = 0.97V We know , acceleration =Force /mass = 0.27Vg / 0.97V = 2.73m/s2

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