Suppose a balloon of constant mass M contains a bag of sand of mass Mo experiences a constant force upward thurst C. Initially it is in equilibrium and that sand is released at a constant rate a(alpha), so that all of it is released in time to, set up equation of motion for Balloon.

Classical Dynamics of Particles and Systems
5th Edition
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter2: Newtonian Mechanics-single Particle
Section: Chapter Questions
Problem 2.2P
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Suppose a balloon of constant mass M contains a bag of sand of mass Mo experiences a constant force upward thurst C. Initially it is in equilibrium and that sand is released at a constant rate a(alpha), so that all of it is released in time to, set up equation of motion for Balloon. 

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