Difference in Weight?

[AaronPippin]

This was just a thought I had after this major storm has passed, with record breaking low pressure. Would a person or object weigh less, more, or stay the same in this situation?

Another question would be does the air itself weigh less?

Perhaps I may need to be more specific in my questions too if needed just ask.


Thanks,
Aaron

 

[rdale]

http://kids.earth.nasa.gov/archive/air_pressure/index.html

 

[Skip Talbot]

This was just a thought I had after this major storm has passed, with record breaking low pressure. Would a person or object weigh less, more, or stay the same in this situation?

Another question would be does the air itself weigh less?

Weight in this sense is just the influence of gravity on mass. The air would weigh less, since in times of lower air pressure, the air has less mass. Pressure does not change your mass, and so since your mass and Earth's gravity remain the same, you would weigh the same amount.

 

[Frank Kienast]

Pressure does not change your mass. However, with the air less dense, it weighs less, and thus has less buoyancy. So at a lower pressure, the scale is going to say a slightly higher weight for all solid objects, since they displace less air mass. Remember that the weight a scale displays is your actual weight (mass times gravity), minus the weight of the air you displace.

 

[Jeff Snyder]

Pressure does not change your mass. However, with the air less dense, it weighs less, and thus has less buoyancy. So at a lower pressure, the scale is going to say a slightly higher weight for all solid objects, since they displace less air mass. Remember that the weight a scale displays is your actual weight (mass times gravity), minus the weight of the air you displace.

I suppose you could include the effects of buoyancy -- for example, we "weigh" less in water as a result of buoyancy forces. Technically, even, one probably should include buoyancy, since the scale, as you noted, is actually measuring our weight (mass*gravity) minus the buoyancy force of the atmosphere on our bodies. However, the difference in average density between normal atmospheric conditions at sea level (~1 kg/m3) and the human body (~1000 kg/m3) is 3 orders of magnitude. If the surface pressure drops from 1000 mb to 955.2 mb, the buoyancy force will change (by ~4.5%), but this will be very small compared to our overall weight (mass*gravity); a 4.5% decrease in a buoyancy force that is 0.1% of our "total weight" is ~0.0045%. No bathroom scale would be able to measure the difference -- for a person who weighs 175 lb at 1000 mb, he/she will weigh ~175.0079 lb at 955 mb. However, props for bringing up a detail that technically is correct!

Another question would be does the air itself weigh less?

Using the ideal gas law (p = rho*Rd*T), lower pressure (keeping T the same and neglecting moisture effects, or keeping Tv the same) will result in lower density ("rho"). This means less mass per unit volume of air, which means less "weight" if we define weight as a measure of mass*gravity. A bathroom scale will read "0 lbs" in either case, though

 

[Greg Campbell]

Some back-of-the-envelope numbers.

Air density at sea level and 20C is about 1.2kg per cubic meter.
A person weighing 220 lb = 100 kg displaces about 100 liters = 1/10 of a cubic meter.
He therefore displaces 1.2kg / 10 = 120 grams of air.
Place this person in the core of a 900mb 'cane. Buoyancy drops by 10% = 12 grams.
The person's measured weight increases by 5 pennies.

 

[AaronPippin]

Thanks guys for some of these answers. It was partially my fault for not being specific enough about true weight obviously is mass*gravity. I knew that one. I was more talking about a change in weight due to buoyancy. Since the air would be less dense, I hypothesized that a person would displace less air, thus not being "held up" as much by the air, giving the impression that person or object weighed more. I just wanted someone else to confirm or agree with my hypothesis. Also I knew it was not a significant amount, nor probably even registerable on your typical scales. It was just something to think more deeply about.
Thanks,
Aaron