A balloon of mass M is floating at rest a distance H above theearth\'s surface.

Question

A balloon of mass M is floating at rest a distance H above theearth's surface. The rider throws out some ballast, and the balloonbegins to rise with an initial acceleration a. (a) What is the mass m of the ballast the rider throwsout? (b) Why is the word initial important in thedescription of the problem? What will cause this acceleration tochange as time passes? A balloon of mass M is floating at rest a distance H above theearth's surface. The rider throws out some ballast, and the balloonbegins to rise with an initial acceleration a. (a) What is the mass m of the ballast the rider throwsout? (b) Why is the word initial important in thedescription of the problem? What will cause this acceleration tochange as time passes?

Explanation / Answer

a) Let F be the upward air floating force since F-Mg=0 initally =>F=Mg F-(M-m)g = (M-a) a after throw m out, we have: =>F-Mg+mg =Ma - ma =>mg = Ma - ma =>m(g+a) = Ma m=Ma/(g+a) b) "initally" is very important for this question since itgive us the air floating force F. when the balloon goes up, the air floating forece may changeand that will cause the acceleration to change.

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