Physics question: Very small objects, such as dust particles, experience a linea

Question

Physics question:

Very small objects, such as dust particles, experience a linear drag force. D = (bv, direction opposite the motion), where b is a constant That is, the quadratic model of drag of the equation given below fails for very small particles. For a sphere of radius R. the drag constant can be shown to be b = 6pi eta R, where eta is the viscosity of the gas. D = (1/2 CAv2, direction opposite the motion). Find an expression for the terminal speed v term of a spherical particle of radius R and mass m falling through a gas of viscosity eta. Express your answer in terms of the variables m, eta, R, and appropriate constants. Suppose a gust of wind has carried a 52-mu m -diameter dust particle to a height of 310m. 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 25 degree C air is 2.0 times 10-5 N middot s/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

A) 6(pi) (eta)r v = mg... so v= mg/6(pi) (eta)r

B) mass of the particle is pie(r^2) * density =5.73* 10^-6

terminal velocity by above formula = 5773 m/sec.

time required = 310/ v = 0.05 secs

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