Accelleration of a static body in wind

[petef]

Homework Statement

I drop a 50mm sq concrete cube fom a notional tower into a steady horizontal wind stream of 10m/sec.

Homework Equations

How long before the cube reaches the wind spead
What is the accelleration
How far will the cube have traveled down range

The Attempt at a Solution

 

[Delta2]

The exact solution of this problem would use fluid dynamics and take into account the dimensions and shape of the object (50mm cube).

However if the object is very small (50mm is not so small but anyway) and the velocities involved are also small we can make an approximation and model the force from the wind as
$\vec F=-k\vec V_{rel}$
where $\vec V_{rel}$ the relative velocity of the object to the wind and k a constant that depends mainly on the density of the air (and on the dimensions and shape of the object).

So by using Newton's 2nd law and considering the forces in x and y-axis we would have

$m\frac{dv_x}{dt}=-k(v_x-10)$ (1)

$m\frac{dv_y}{dt}=mg-kv_y$ (2)

where m is the mass of the small object.

 

[petef]

Thanks D2