Upthrust in gases is the upward force exerted on an object immersed in a gas, which opposes the object’s weight. It arises from the pressure difference between the top and bottom of the object due to the gas’s density. This concept is similar to upthrust in liquids but involves the behavior of gases, which are much less dense than liquids.
When an object is placed in a gas, the pressure at the bottom of the object is greater than the pressure at the top. This difference in pressure results in an upward force (upthrust). The size of this force depends on the volume of the displaced gas and the density of the gas.
Just like liquids, gases exerts upthrust on objects that are in them. Air is the most common gas of interest. We float objects on air. Sometimes, as human beings, we use parachutes to float in air.
The upthrust in air is small because air has lower density compared to most of substances.
The density of air is about 1.3kgm-3 or 0.0013gcm-3.
A balloon can float in air if it contains a gas with a lower density than air. For example hydrogen has a density of 0.09 kgm-3 whereas helium has a density of 0.18kgm-3. Therefore a balloon filled with helium or hydrogen will rise on air provided density of the balloon fabric and air will be less than density of air.
Problems involving upthrust in gases
Consider the figure below that illustrates a balloon filled with air .
If we consider the balloon filled with air to a certain volume, the weight of air in the balloon plus its fabric is greater than the weight of air displaced. This is because the volume of air in the balloon is nearly equal to the volume of air displaced.
The upthrust force on the balloon due to the air is thus less than the weight. The balloon thus stay grounded because the it’s weight is less than the upthrust force that could set it up to float on air.
That is W-U > resultant downward forces.
If the balloon is filled with a gas that has a lower density than air, the gas and balloon fabric weigh less than the displaced air. The upthrust force U exerted by the air on the balloon is greater than the weight W of the inflated balloon. This results in the upthrust force being larger. The resultant upward force is greater than W-U and hence the balloon sets to accelerate upward.see the illustrations below.
Example Question
A meteorological balloon has a volume of of 55m3 and is filled with a helium gas of density 0.18kgm-3. If the weight of the balloon fabric is 170N, calculate the maximum load the balloon can lift given that density of air is 1.3kgm-3
solution
Volume of air displaced by the balloon is 55m3 which is volume occupied by the balloon.
mass of air displaced by the balloon = 55m3 x 1.3kgm-3 = 71.5kg
weight of air displaced =71.5kg x 10 Nkg-1 = 715N
mass of helium in the balloon = 55m3 x 0.18kgm-3 = 9.9Kg
weight of helium in the ballon = 9.9kg x 10 Nkg-1 = 99N
Total weight of the inflated balloon = 170N + 99N = 269 N
From the law of floatation, upthrust is the weight of air displaced which should also be weight of the balloon plus the weight of load it will carry. hence,
upthrust = weight of the balloon + load in the ballon = weight of air displaced
269N + load in the ballon = 715N
load in the balloon = (715-269)N=446N
So the total mass of the goods to be included in the balloon should never exceeded 44.6kg.
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