- #1
karamsoft
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Hi, I came across this question in a physics review pamphlet:
A balloon for a county fair is designed to carry four
100-kg passengers when it is expanded to its maximum
volume. The designers assumed the balloon would
operate in ordinary spring temperatures. If, on the day
of the fair, the temperature reaches a record-breaking
maximum: (air density: 1.2)
A) the balloon will not be able to achieve its maximum
volume.
B) more sandbags will be needed for proper operation of the
balloon.
C) the total weight the balloon is able to carry will be
reduced.
D) once in flight, the balloon cannot be lowered until the
ambient temperature drops.
FB,net = (1.2— air heated)x volume of balloon
FG= mg
The book says the answer is C because Warmer air is less dense than cooler air. Less dense air will give a smaller buoyant force and the balloon will be able to carry less weight.
However, using the equation FB,net = (1.2— air heated)x volume of balloon
it is obvious that the less dense air will result in a larger difference between the the densities (of the cold and hot air) which will ultimately result in a larger buoyant force. Hence, we will need a larger downward force to compensate (force of gravity) by adding sandbags (so answer choice B, which is the opposite of C).
Thanks,
Homework Statement
A balloon for a county fair is designed to carry four
100-kg passengers when it is expanded to its maximum
volume. The designers assumed the balloon would
operate in ordinary spring temperatures. If, on the day
of the fair, the temperature reaches a record-breaking
maximum: (air density: 1.2)
A) the balloon will not be able to achieve its maximum
volume.
B) more sandbags will be needed for proper operation of the
balloon.
C) the total weight the balloon is able to carry will be
reduced.
D) once in flight, the balloon cannot be lowered until the
ambient temperature drops.
Homework Equations
FB,net = (1.2— air heated)x volume of balloon
FG= mg
The Attempt at a Solution
The book says the answer is C because Warmer air is less dense than cooler air. Less dense air will give a smaller buoyant force and the balloon will be able to carry less weight.
However, using the equation FB,net = (1.2— air heated)x volume of balloon
it is obvious that the less dense air will result in a larger difference between the the densities (of the cold and hot air) which will ultimately result in a larger buoyant force. Hence, we will need a larger downward force to compensate (force of gravity) by adding sandbags (so answer choice B, which is the opposite of C).
Thanks,