A grain of pollen (mass m) slides down a smooth, ?at, tilted solar panel (tilted
ID: 1894779 • Letter: A
Question
A grain of pollen (mass m) slides down a smooth, ?at, tilted solar panel (tilted at ? from horizontal) under the in?uence of gravity.(a) If the motion is resisted by a linear drag force f = kmv ?nd an expression for how far down the plane the grain slides in time t, assuming it is released from rest. Hint: Draw a free body diagram to start!
(b) Show that as the drag coe!cient becomes very small, your answer in part a reduces to a simple freshman physics result (which is what?) Comment brie?y on the similarities and differences between this problem and question 2. Hint: Here, I claim the useful Taylor expansion you’ll want will be e^x for x ? 1 And yes, you’ll really need to go all the way out to that x^2/2 term!
For you to think about. You do not have to write this up for credit, but we’ll revisit this idea again this term, it’s very important! The power x in e
x must be unitless. “Drag coe!cient” has units. So it cannot be exactly correct to say the “drag coe!cient becomes small”, without answering “small compared
to what”? What exactly is it that is really the “small thing, x” in this case?
Explanation / Answer
for time t f=mg-kmv s=0.5*f/m*t^2