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Sears and Zemansky's University Physics with Modern Physics | 13th Edition | ISBN: 9780321696861 | Authors: Hugh D. Young; Roger A. Freedman; A. Lewis Ford
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Answer: A hot-air balloon consists of a basket, one

Chapter 4, Problem 56P

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QUESTION:

Problem 56P

A hot-air balloon consists of a basket, one passenger, and some cargo. Let the total mass be M. Even though there is an upward lift force on the balloon, the balloon is initially accelerating downward at a rate of g/3. (a) Draw a free-body diagram for the descending balloon. (b) Find the upward lift force in terms of the initial total weight Mg. (c) The passenger notices that he is heading straight for a waterfall and decides he needs to go up. What fraction of the total weight must he drop overboard so that the balloon accelerates upward at a rate of g/2? Assume that the upward lift force remains the same.

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QUESTION:

Problem 56P

A hot-air balloon consists of a basket, one passenger, and some cargo. Let the total mass be M. Even though there is an upward lift force on the balloon, the balloon is initially accelerating downward at a rate of g/3. (a) Draw a free-body diagram for the descending balloon. (b) Find the upward lift force in terms of the initial total weight Mg. (c) The passenger notices that he is heading straight for a waterfall and decides he needs to go up. What fraction of the total weight must he drop overboard so that the balloon accelerates upward at a rate of g/2? Assume that the upward lift force remains the same.

ANSWER:

Solution 56P

Total mass is M.

The initial acceleration of the balloon downwards was g/3.

There is an upward lift by the air drag.

So, the final equation for this system can be written as,

-----------------(1)

a)

The free body diagram is given below,

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