A plate of mass M is moved with constant velocity v = 40m/s against powder of dust particles moving with constant velocity u = 40m/s in opposite direction stick to plate as shown. The density of the dust is
ρ = 10 –3 kg/m 3 and plate area is A = 10m 2 Find the force F required to keep the plate moving uniformly.
Text Solution
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Force F on plate = force exerted by dust particles
= force on dust particles by the plate
= rate of change of momentum of dust particles
= mass of dust particles striking the plate per unit time × change in velocity of dust particles.
= A (v+ u) ρ × (v + u) = A ρ (v + u) ρ A(u + v) 2
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