A. Calculate the terminal velocity for a pollen grain falling through the air us

Question

A. Calculate the terminal velocity for a pollen grain falling through the air using the drag force equation. Assume the pollen grain has a diameter of 4 µm and a density of 0.3 g/cm3.

B. If this grain is released from the top of a tree (height 11 m), estimate the time it will take to fall to the ground. Hint: The pollen grain will reach its terminal velocity very quickly and will have this velocity for essentially the entire motion. Your answer will explain why pollen stays in the air for a very long time. (Assume the density of air to be 1.3 kg/m3.)

Please answer both parts of the question.

Explanation / Answer

part a:

terminal velocity=sqrt(2*m*g/(pho*A*Cd))

where m=mass of the grain=volume*density

=(4/3)*pi*radius^3*density

=(4/3)*pi*(4*10^(-6)/2)^3*300 kg=1.0053*10^(-14) kg

g=acceleration due to gravity=9.8 m/s^2

pho=density of air=1.3 kg/m^3

Cd=drag coefficient=0.47

A=surface area=4*pi*radius^2=4*pi*(4*10^(-6)/2)^2=5.0265*10^(-11) m^2

then terminal velocity=sqrt(2*1.0053*10^(-14)*9.8/(1.3*0.47*5.0265*10^(-11)))=0.0801 m/s

part b:

time taken to reach ground=distance/terminal velocity

=11/0.0801=137.33 seconds

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.