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Get Full Access to University Physics - 13 Edition - Chapter 4 - Problem 56p
Get Full Access to University Physics - 13 Edition - Chapter 4 - Problem 56p

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# A hot-air balloon consists of a basket, one passenger, and

ISBN: 9780321675460 31

## Solution for problem 56P Chapter 4

University Physics | 13th Edition

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University Physics | 13th Edition

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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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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, Ma = Mg upward lift M × g/3 = Mg upward lift upward lift = Mg Mg/3 = Mg ---3-------------(1) a) The free body diagram is given below, b) the upward lift we found as, upward lift = Mg2 3 c) Now the balloon should go up at an acceleration of g/2. So the equation will be, 2 ma = Mg3 mg --------------------(2) Here m is the reduced mass after throwing some mass from the total mass M. So, let’s put the values in equation (2), mg/2 = 2Mg/3 mg mg/2 + mg = 2Mg/3 3mg / 2 = 2Mg / 3 2 2 4 m = 3× 3 = M .9 So the mass which has to be thrown is, M m = M M = M . 5 9 9 Conclusion: So, 5/9 th of the total mass has to be thrown out side to move upwards with an acceleration of g/2.

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##### ISBN: 9780321675460

Since the solution to 56P from 4 chapter was answered, more than 415 students have viewed the full step-by-step answer. This full solution covers the following key subjects: balloon, upward, lift, Force, passenger. This expansive textbook survival guide covers 26 chapters, and 2929 solutions. This textbook survival guide was created for the textbook: University Physics, edition: 13. University Physics was written by and is associated to the ISBN: 9780321675460. The full step-by-step solution to problem: 56P from chapter: 4 was answered by , our top Physics solution expert on 05/06/17, 06:07PM. The answer to “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.” is broken down into a number of easy to follow steps, and 112 words.

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