Concept explainers
(a)
The appropriate model to describe the system when balloon is stationary.
(a)
Answer to Problem 33AP
The appropriate model to describe the system is particle in equilibrium.
Explanation of Solution
The mass of the balloon is
If a system remains stationary, the sum of all forces acted on a system in all direction vertical as well as horizontal is equal to zero. This condition is also called is equilibrium condition.
Conclusion:
Therefore, appropriate model to describe the system is particle in equilibrium.
(b)
The force equation for the balloon for this model.
(b)
Answer to Problem 33AP
The force equation for the balloon for this model is
Explanation of Solution
In equilibrium condition, sum of all forces in vertical direction is equal to zero.
Here,
Conclusion:
Therefore, the force equation for the balloon for this model is
(c)
The mass of the string in terms of
(c)
Answer to Problem 33AP
The mass of the string in the terms of
Explanation of Solution
From equation (I),
The buoyant force act on the balloon is equal to the displaced volume of the air by the balloon.
Formula to calculate the buoyant force acting on the balloon is,
Here,
Formula to calculate the weight of the balloon is,
Here,
Formula to calculate the weight of the helium gas is,
Here,
Formula to calculate the weight of the string is,
Here,
Substitute
Formula to calculate the mass of the helium gas is,
Here,
Substitute
Rearrange the above expression for
Conclusion:
Therefore, the mass of the string in terms of
(d)
The mass of the string.
(d)
Answer to Problem 33AP
The mass of the string is
Explanation of Solution
From equation (II),
Substitute
Conclusion:
Therefore, the mass of the string is
(e)
The length
(e)
Answer to Problem 33AP
The length
Explanation of Solution
From equation (II),
The mass of the string of height
Substitute
Substitute
Conclusion:
Therefore, the length
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Chapter 14 Solutions
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