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Consider a wind speed of $80kmh^{-1}$ towards the west, when this wind comes into contact with another body, it will obviously exert some force. However, what is the magnitude of this force? $F=ma$, as the wind is travelling at a constant velocity there is no resultant force acting on it, so the wind cannot have any force, so how does it exert a force on another body? Can we determine force given velocity, is there a relationship between them?

Qmechanic
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Quin Gardiner Bax
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    When it hits you, it changes its speed and direction. That interaction is causing the force, not the speed itself. – Sid Mar 12 '24 at 07:31

2 Answers2

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... the wind is travelling at a constant velocity ...

The wind is travelling at a constant velocity until it hits an object. At that point the wind changes its velocity - either in magnitude or direction or both. So the object must exert a force on the air in order to change the wind's velocity. And by Newton's Third Law the air exerts an equal and opposite force on the object.

Can we determine force given velocity, is there a relationship between them ?

Yes, structural engineers do this all the time to make sure that the structures they design are strong enough to withstand high winds. The exact relationship will depend on the aerodynamics of the object and the direction of the wind, but in general I would expect something similar to the drag equation in which the force is proportional to the square of the air speed.

gandalf61
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You are saying that the wind has constant speed 80 km/h, but that's only some sort of generalized, average statement. In fact the air particles that hit you cannot continue at their original velocity, they need to halt their motion or change their velocity (i.e., accelerate) to move around you. In other other words, the body being hit by the wind is exerting force on the wind particles - so by Newton's third law we can say that equivalently, the wind is exerting the same and opposite force on the body.

I can't give you an exact formula for this force. You can calculate this force assuming some sea-level air density, and that the wind hitting the body hits it head-on - but this calculation needs to be modified (the force reduced) by the "aerodynamic" nature of the body - how much of the wind can actually flow around the body without hitting it head-on - and on the other hand, the body's aerodynamic drag - how much "friction" the body has with the wind particles flowing past it. These things can have different values for different types of objects.

Nadav Har'El
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