Q31 of 31 Page 95

Consider a rectangular block of wood moving with a velocity v0 in a gas at temperature T and mass density ρ. Assume the velocity is along x-axis and the area of cross-section of the block perpendicular to v0 is A. Show that the drag force on the block is 4ρ Avo , where m is the mass of the gas molecule.

Given:


Velocity of rectangular block wrt. Gas =


Temperature of gas=T


Mass density =ρ


Area of cross section of block = A


V=rms speed of gas molecules


Relative speed of molecules wrt front face=


Momentum transferred to block in one collision


m=mass of a single molecule


n=no. of molecules per unit volume


no. of collisions in time Δt



⇒ Momentum transferred from front surface in time Δt



Similarly, momentum transferred from back surface



Net force acting is equal to rate of change of momentum


i.e



From kinetic theory of gases




Therefore, force is given by



Which is the drag force acting on the particle


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