# The Effect of Temperature on Buoyant Forces

• karamsoft
In summary, the balloon will not be able to achieve its maximum volume if the temperature reaches a record-breaking maximum.
karamsoft
Hi, I came across this question in a physics review pamphlet:

## 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,

karamsoft said:
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)
How so?
The 1.2 is the density of the 'unusually warm' air, yes? So was the expected density more or less than 1.2? Roughly what density might the air in the balloon have? Is that altered by the unusually warm day?
You might find the table here useful: http://en.wikipedia.org/wiki/Density#Air

1 person
haruspex said:
How so?
The 1.2 is the density of the 'unusually warm' air, yes? So was the expected density more or less than 1.2? Roughly what density might the air in the balloon have? Is that altered by the unusually warm day?
You might find the table here useful: http://en.wikipedia.org/wiki/Density#Air

Thank you haruspex for your response,

I see what you mean. I was fixated on 1.2 kg/m3 as a constant value. Now I think about it, it is the other way around (that is the air heated inside the balloon will have the same density on whatever day since the temperature given by the fire is the same, right?). So on a warm day the density of the "ambient temperature" air will be less than 1.2 and the difference between the variables (densities) will be less and so the buoyant force will decrease as a result..
Awesome thanks!

## 1. What is the definition of buoyant force?

The buoyant force is the upward force that a fluid exerts on an object that is partially or fully submerged in it.

## 2. How does a balloon stay afloat in the air?

A balloon stays afloat due to the buoyant force exerted by the air around it. The air inside the balloon is less dense than the surrounding air, causing it to rise and the balloon to float.

## 3. What factors affect the buoyant force on a balloon?

The buoyant force on a balloon is affected by its size, shape, and the density of the fluid it is in. It also depends on the weight of the balloon and the weight of the displaced fluid.

## 4. Can a balloon sink?

Yes, a balloon can sink if the weight of the balloon is greater than the buoyant force exerted on it by the fluid. This can happen if the balloon is filled with a denser gas or if it becomes damaged and starts to leak air.

## 5. How is the buoyant force calculated?

The buoyant force is calculated by multiplying the density of the fluid by the volume of the displaced fluid and the acceleration due to gravity. This can be represented by the equation Fb = ρVg, where Fb is the buoyant force, ρ is the density, V is the volume, and g is the acceleration due to gravity.

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