Question

Difference between Weight and Force in fluids?
So I have a sample problem in my book. It gives you the dimensions of a room, and asks you to find the weight of the air in the room at 1.0 atm. They use the equation: Density=m/V
m=(Density)(V)
But we need weight so:
mg=(Density)(V)(g)
My question is why can't we use P=F/A or (F=PA)?
F=mg right?
So why is it that when I multiply pressure (in Pa) by area (in m^2) I get a completely different answer?

Answer 1

Here are the values
floor dimensions: 3.5m by 4.2m
height: 2.4m
pressure: 1.0 atm=101.325 Pa
A=(3.5)(4.2) =14.7m^2
V=35.28m^3
Density=1.21kg/m^3

Answer 2

First way: mg=PVg
mg=(35.28m^3)(35.28m^3)(9.81m/s^2)
mg=418 N

Second way: F=PA
F=(101.325 Pa)(14.7m^2)
F=1489 N ????

This shows that F≠mg is the weight of air different somehow because it is a fluid? Is it because of density?
Vg should equal A; is this right? Please explain.

Thank-you

Answer 3

I made a mistake when writing the first way. The P is actually density, but I used the density of air, not water, which was actually 1.21kg/m^3. So mg is actually (1.21)(35.28)(9.81) which is 418 N, the correct answer. But I don't get what you're saying about the second one. Where does the surface of water come in?

Answer 4

weight of WATER = force of gravity on water. -> that is what you did in the first step in the second one, you are finding the force exerted by AIR on the surface of water. those are completely different from eachother.

Answer 5

F = ma
Weight = mg
Basically, the difference is in regards to the specificity of what acceleration is. In falling objects, this is gravity. But in problems with say, sliding objects, it's often the acceleration of the object which is being acted upon by a force.

Answer 6

But isn't the acceleration of the air in the room due to gravity?

Answer 7

Yes. Weight is a force downward that opposes motion. But when we say F=ma, we're referring to forces trying to alter the position of an object / do work that aren't necessarily related to the downward direction/gravity.

Answer 8

So force is not necessarily equal to weight?

Answer 9

Force downward is related to weight. But no, force isn't, necessarily. :)