We often ascribe weight due only to gravity. But, is there any effect of atmospheric pressure on the weight of a body?
Yes!
Remember Buoyancy?
According to Wikipedia, “Buoyancy is an upward force exerted by a fluid that opposes the weight of an immersed object.”
Atmosphere is composed of gases, which apply pressure on all the bodies present in it, owing to collisions of the gas molecules with their surfaces.
Effect of Atmospheric Pressure on the Weight is Insignificant
Consider a rectangular body, whose upper and lower surfaces have equal area.
The gas molecules will collide with all the surfaces of the body. Collision of gas molecules with the upper surface makes the gas apply downward pressure on the body, which is in the same direction as the force of gravity, while collision with the lower surface result in upward pressure.
For a body of ordinary size, the upper and lower surface are nearly at the same altitude, and so the frequencies of collisions with the two surfaces are practically the same. Therefore, the contribution of gas pressure almost cancels out, and is negligible compared to the contribution from gravitational force.
It is obvious that effects of gas pressure on the other surfaces of this body cancels out too, and thus can’t contribute to its weight.
However, it may sometimes have notable influence
Now, consider the case of a rectangular body whose upper and lower surfaces are wide apart, say 1 kilometer. In this case the frequencies of collisions of the gas molecules with the two surfaces differ considerably. As the atmosphere is denser the closer it is to the surface, the lower surface receives more collisions with the gas molecules than the upper surface.
Therefore, such a body is lighter due to the presence of the atmosphere. Nevertheless, the influence of atmosphere on the weight of the body would be insignificant, unless it has a very small mass.
For all practical purposes, therefore, the weight of a body depends only on the gravitational pull.
Buoyancy is more relevant in denser fluids, like liquids, as the frequency of collisions of the constituent molecules in these cases is many times greater, and thus its effect is substantial even in lighter bodies.
Let’s debunk an apparent paradox in this connection…
It is said that we are under the pressure of the atmosphere. Pressure of 1 bar at the sea level means every square centimeter of our body experiences a load of 1 kilogram.
Under the sea level, the pressure is even higher, about 100 bar at 1000 meter below the sea level. So, the deep-sea creatures at that level are experiencing a load of 100 kilogram per square centimeter of their body!
Then how come buoyancy makes us lighter?
This is because it requires an external agency to weigh a body. A body is light or heavy only to that agency.
From the viewpoint of the body, it gets battering from the fluid particles across all its exposed part. Hence, it feels like getting squeezed.
For the external agency, only the resultant force along the vertical direction matters in making a body lighter or heavier.
