A parallel beam of particles of mass $m$ moving with velocities $v$ impinges on a wall at an angle $θ$ to its normal. The number of particles per unit volume in the beam is $n$ . if the collision of particles with the wall is elastic, then find the pressure exerted by this beam on the wall.

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Solution

The speed of particles in the direction perpendicular to the wall $= v c o s θ$ .
Since the collision is elastic, the change in velocity occurs in the direction perpendicular to the direction and equal to $Δ v = v c o s θ - (- v c o s θ) = 2 v c o s θ$
Thus the change in momentum for each particle $= 2 m v c o s θ$
Thus pressure exerted on the wall $= F o r c e p e r u n i t a r e a = T o t a l c h a n g e i n m o m e n t u m p e r s e c o n d p e r u n i t a r e a = \frac{Δ p}{A Δ t}$
$= n m Δ v \times 2 v c o s θ = 2 n m v^{2} c o s^{2} θ$

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