# Wind and f=ma

1. Oct 14, 2009

### brandy

i'm currently discussing this with a friend.
anyway.

here is the conversation:
he said
It started as "If something doesn't have a mass, it cannot have a force", due to Newton's second law, F = ma (Force = Mass x Acceleration). Logically, if you substitute 0 in for the Mass, you will get a result of 0 Force. My brother then argued that there are things which have no mass but still have a force and the main example we discussed was wind. Does wind have a mass? After a while we got to the fact that wind is just heat. After long debating about "does heat have mass" we got to the fact that heat is just energy. Now we are at "does energy have mass". Apparently there are conflicting arguments all over the place with this. I believe for there to be energy, it must have mass, due to Einstein's formula E = mc^2 (Energy = Mass x Speed of Light^2). As with F = ma, if you substitute 0 in for the Mass, you will get a result of 0 Energy.

My thinking:
my understanding is that hot air rises because it is less dense than air that is colder. which is a change in pressure, which is what causes air particles to move. hence wind. so heat causes wind but that doesnt mean wind is heat. is my understanding screwed?

my understanding of heat is that it is a form of energy and that heat does not have a mass and that there must be a flaw in his logic of wind being heat.

So i said that he is overcomplicating things and that the air particles have a mass.

he said:
Well yes, but the thing moving that air... does it have a mass? Because it is able to move the air, meaning it exerts a force, which Newton's Second Law tells us must mean it has a mass. Although this heat, as I said, energy, so the question is, does energy have mass...?

So he doesn’t actually want to know about wind but the force on wind. i asked him how wind was heat and he couldn’t remember.

so the force that causes wind is the force that causes heat i guess. unless the name of that force is wind. in which case I’m thoroughly confused. I think I need a scientific definition of wind here

so now i'm asking you about your opinion of the force that causes wind being heat and how heat is energy and about the force that causes heat

And also I guess this could be related to convection currents.

2. Oct 14, 2009

### xxChrisxx

F=ma applies...

Wind is merely small air particales moving into your face/body etc. Air has mass.

As for convection and generally air movement, there are tons of threads discussing movement of air. Both from a system opint of view and from a particaly pov.

3. Oct 14, 2009

### Jimmy

Net Force is also equal to the rate of change of momentum:

$$\mathbf{F} = \frac{d \mathbf{p}}{dt}$$
(first derivative of momentum with respect to time)

For example, photons are massless, but they do possess momentum and can impart force. The momentum of a photon is equal to Planck's constant divided by the photon wave length:

$$p = \frac{h}{\lambda}$$

However, air consists of particles that do have mass so the above doesn't really apply in this case. I just wanted to point out that things without mass can have momentum and cause force and pressure.

I'm not a meteorologist but that sounds reasonable. Warmer air rises and cooler air moves in to take its place.

Last edited: Oct 14, 2009
4. Oct 14, 2009

### HallsofIvy

Wind is moving air. And, of course, air has mass. Not only the mass of the atoms of Nitrogen and Oxygen, etc. making up the air but small particles of dirt, insects, etc. all have mass.

5. Oct 14, 2009

### tuoni

Wind is the motion of packets of air from a region of high pressure to a region of low pressure, it is the effect, not the cause, of the phenomenon.

$$F = ma = \frac{mv^{2}}{2s} = \frac{V\rho v^{2}}{2s} = \frac{As\rho v^{2}}{2s} = \frac{A\rho v^{2}}{2}$$

A -- cross-sectional area of region in motion
ρ -- mass density of medium
v -- velocity of region

Further derivation yields algorithms for fluid stress (dynamic pressure) and drag, two very useful concepts.