# How molecules in the air cause air resistance in car travelling at high speed

1
by LutaArya

2015-09-21T22:27:53+05:30

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The air molecules have small masses m.  A Car has a large mass.  But still are significant when vehicles at high speeds V collide with them.  Molecules in air are travelling in all directions with a speed v.  When they are hit by the car, their momentum and energy get changed. They get rebounded with almost same speed.  So momentum becomes opposite in direction.  Let us assume that there is no energy loss in the collision and it is elastic.

M V - m v =  M V' + m v
M (V - V') = 2 m v

1/2 M V² - 1/2 M V'² = loss in KE   of car = gain in KE of air molecules
= 1/2 m ( 4 v² - v²)
1/2 M (V² - V'²) = 3/2 m v² = 3m/2  * [M (V - V')/2m]²
V + V' = 3 M  ΔV  / 4m

ΔV  ≈  8 m V / (3 M)

Thus the change in the velocity of the car, ie., is proportional to the velocity of the car.  Thus a resistance faced by the car is proportional to its speed.

At small speeds, the resistance may not be clear and apparent.  But at very high speeds, it is significant.  This is often called drag.  There is an effect called viscosity in fluids. That affects the velocity of an object travelling in a liquid or gas.  The molecules touching the surface of the car  on all sides exert a drag force - called a damping force on the vehicle.  That force is proportional to  the velocity of the object like car.

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