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Question

The terminal velocity of a 3×10^−5 kg raindrop is about 9 m/s . Assume a drag force FD=−bv.

a) Determine the value of the constant b. Express your answer using one significant figure.

b= _____ kg/s

Determine the time required for such a drop, starting from rest, to reach 63% of terminal velocity. Express your answer using one significant figure.

_____________s

Answer 1

Let's start with part A... draw a free-body diagram!

↑ F_Drag

•

↓ F_Gravity

We're interested in what happens when the falling raindrop is at terminal velocity, or in other words, when the drag force from the air exactly balances the force due to gravity. F_Drag = F_Gravity

The equation for F_Drag is given to you as F_Drag = -bv

The equation for F_Gravity, like any force, can be written as F_Gravity = ma

We have two forces that are equal to each other, and four variables. Can you figure out which values to use to solve the equality for b?