Very small objects, such as dust particles, experience a linear drag force, D =

Question

Very small objects, such as dust particles, experience a linear drag force, D  = (bv, direction opposite the motion), where b is a constant. For a sphere of radius R, the drag constant can be shown to be b=6R, where is the viscosity of the gas.

Suppose a gust of wind has carried a 52-m-diameter dust particle to a height of 350 m . If the wind suddenly stops, how long will it take the dust particle to settle back to the ground? Dust has a density of 2700 kg/m3, the viscosity of 25C air is 2.0×105Ns/m2, and you can assume that the falling dust particle reaches terminal speed almost instantly.

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

We have been given the dust particle is moving terminal velocity.

So first of all we have to find out hte terminal velocity of the dust particle.

So, now applying force balance on the particle

mg=drag force

mg=6Rv

v=mg/6R

v=2700*4*(26*10-6)2/3*6*2*10-5

v=0.02028 m/s

Now we know that

v=x/t

t=x/v

t=350/0.02028

t=17258.38264 seconds or

t=4.79 hours

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