Take a breath

Classical Mechanics Level 3

A healthy fully grown man stands on a very sensitive balance in an open, airy environment and looks at the reading to measure his weight. He then breathes in to the fullest and looks at the balance again. Then, the new reading on the balance _ _ .

remains unchanged, that is, the same as the original value can either be less o r or more than the previous value increases, that is, becomes more than the previous value decreases, that is, becomes lower than the previous value

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Rishav Koirala by Rishav Koirala , 22, Singapore

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4 solutions

Rishav Koirala
May 30, 2014

This problem, though easy requires a little in-depth analysis. Taking in air does not increase the weight of the person as much as it increases the volume. This increased volume in turn increases the upthrust of the air on the body of the person, thereby reducing his weight a little.

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Actually, the critical but unsaid detail is whether or not the pressure of the air inside the lungs is the same. For example, a balloon inflated with room air has slightly higher internal air pressure because of stretched balloon, so it would appear "heavier" on a sensitive scale. Otherwise, an empty box filled with room air with a sealed lid or unsealed lid weighs the same on the scale. As it is unlikely that air inside the lungs is ever less than ambient pressure, it's unlikely that a person will appear to "weigh" less on a scale by inhalation.

To make this problem easier to understand, let's imagine we have a test tube under water, upside down with a pocket of air at the top, and a sliding stopper inside the tube, so that there is some water and that pocket of air contained by the stopper. This test tube will have a certain hydrostatic weight under water. If the sliding stopper leaks, so that as we slide it up or down, the volume and pressure of that pocket of air remains the same, and the test tube will have the same hydrostatic weight as before. However, if the sliding stopper does not leak, so that we can change the pressure and volume of the pocket of air, we can change the hydrostatic weight of the test tube, namely, if we push in the stopper so that the volume of the pocket of air decreases, the hydrostatic weight will increase, and vice versa. Submarines work on the same principle.

Michael Mendrin - 7 years ago

The answer given by you is wrong, as the pressure in the lungs is higher so not much volume change and also you have to consider anatomy of the body, when we breath there is more expansion in the diaphragm internally than externally. Weight will increase.

Rohan Chowdhary - 6 years, 10 months ago

When you take a breath your muscles contract first, to allow the air in and then the get "stiff" again. So, exhaling does not require effort. The pressure in the lungs is probably greater than the enviroment air pressure.

So, when the man takes the breath we have 2 forces. The weight of the air and the boyance force. Since the volume of the air in the lungs is smaller than the original volume of the air, the boyance force will be lower than the air's weight. So i believe the reading will increase.

Please correct me :)

Konstantinos Manos - 6 years, 12 months ago
Mayank Holmes
May 31, 2014

if he inhales some air the density of his body decreases............ consequently air is able to apply more up-thrust on the body and hence the net force of gravity acting downwards is somewhat countered by the up-thrust in the upward direction and hence his weight decreases!!!!!

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Utkarsh Gautam
Nov 20, 2014

This is a problem of fluid mechanics and air needs to be thought of as a fluid.By breathing in air the volume of his chest increases, thereby increasing the volume of air displaced by his body.So by Archimedes' Principle air as a fluid applies more buoyant force,decreasing the overall downward force.

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Mahmoud Fathy
Jul 15, 2014

Well I don't know whether my thinking is correct or not but I guess that breathing to the fullest will take up many air molecules which sround him,now the pressure made by the molecules in getting him down will decrease as their density decrease so the Random collisions of air molecules with his body will decrease and so less weight readings

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