Motion and Force

Date: 11/28/2004 at 22:16:48
From: Sarah
Subject: Force in pounds hitting an object

You are a 50 pound person riding in a bus going 45 MPH, when the
driver suddenly stops.  If you were to "fly" out of your seat, how
many pounds of force would you hit the windshield with?

I'm in 7th grade, and I am just not sure how to figure this out.  Is
there a formula that would solve this?

I have discussed this with my parents and they are not sure if you 
are able to just multiply the weight times the speed of the bus, or 
if there is another factor or factors involved.  This is not a 
homework assignment--just something that I was wondering one day while 
riding home from school.  Thank you for your help.

Date: 11/29/2004 at 08:43:24
From: Doctor Rick
Subject: Re: Force in pounds hitting an object

Hi, Sarah.

This is much more complicated than you may think.  The force with 
which you hit depends on what you hit and how.

The product of your weight and your velocity is called MOMENTUM, and 
it indicates how hard it is to stop you.  A heavy object moving slowly 
(perhaps a car starting to roll down a hill) can be just as hard to 
stop as a light object moving very fast (say, a bullet), if they have 
the same momentum.

One way of viewing FORCE is as a RATE OF CHANGE of momentum.  I could 
bring the momentum down to zero quickly (by slamming you into a brick 
wall) or slowly (by putting a stack of pillows in your path).  The 
first way would cause a much greater rate of change of momentum (your 
momentum changes faster), thus generating a much greater force.

An example of this is an egg toss--did you ever participate in that 
messy game?  Teams of two people face each other and one tosses an egg 
to the other, who must catch it without breaking it.  You all take a 
step back then toss again, and the team that gets farthest apart 
without breaking their egg wins.  One trick that helps you win is to 
pull your hands back, in the direction the egg is moving, as you 
catch it.  This spreads the momentum change out over a longer time, 
and thus puts less force on the egg.

I can't say what force you would exert on the glass because I don't 
know how long it takes to break the glass, nor how much of your 
momentum is absorbed in the process.  (You'll still be moving, 
probably, after you break through the glass; your momentum will not 
yet be zero, and you'll have to hit something else in order to stop.)

While I haven't exactly answered your question, but I hope I've given
you something to think about, both in terms of physics (the science of 
motion and force) and car safety.  Wear your seat belt!

- Doctor Rick, The Math Forum
  http://mathforum.org/dr.math/