Expert: Paul Soderman - 10/4/2009

Question
I'm meant to do a question and about a falling mouse and elephant on Excel - i meant to use number crunching instead of differentiation. so a mouse is falling down 2forces are acting uppwards: F=ma and Drag; and weight is acting downwards F=mg. We're meant to find velocity v, displacement x and acceleration a using Excel. can i assume that v and x are both zero for a=9.81 and then use for x=ut+at^2 and v=x/t. one last question for small mass - mouse- the accleration will decrease and then will be either positive or negative it will mean it's in free fall?  

Answer
Hi Jane
You can assume at time 0 both animals are held still so u(0) and x(0) are zero.  When you let go u = at and x = (at^2)/2.  (You could say x(t) = (at^2)/2 + u(0)t + x(0), but we already decided to make u(0)=0 and x(0)=0.)  With weight acting downward and drag acting upward,  a = (W-D)/m and W = mg from Newton's law, where g = 9.81 m/s^2 on Earth.  I assume you know the drag equation.  Of course you have to compute this for each time step because drag is changing.

When the drag reaches the value of W, acceleration is zero and the poor critters are in free fall at constant velocity.  They can both get there, but the mouse gets there first I assume, though I have never worked this problem to be sure.  Maybe the elephant falls faster and gets to free fall first.  Your code will find out.
Paul