Collisions; elastic and inelastic collisions; impulse, momentum, kinetic energy, and work
Box of matches per group
Distribute a box of matches to each group. Challenge them: can you drop the box on its end from 1 foot (30 cm) above the desk so that it does not fall over?
They will try and try, and some may even manage to luckily make the box bounce and land back upright. But overall it cannot be done consistently. Unless, that is, some enterprising students find the trick.
After a while, show them the trick. (The trick only sometimes works for me, but it gives a much better chance than without.) Slide open the matchbox so that the sleeve lands first and the drawer closes by momentum. The friction of the drawer sliding shut absorbs the kinetic energy of the falling matchbox, making the collision more inelastic (the matchbox stops dead rather than bounces). The kinetic energy of the falling box is absorbed gradually, over a relatively long time and distance, rather than quickly. I have found that it helps to put more mass in the matchbox, using a small coin, washer, nail, or pebble.
The greater the matchbox’s speed v or the greater its mass m, the more difficult it is to stop. What do we mean by “difficult”? Its momentum mv and its kinetic energy ½ mv2 must be reduced to zero. Both momentum and kinetic energy become greater as mass and speed become greater. To change momentum requires an impulse Ft, where F is an applied net force and t is the time over which it is applied. To change kinetic energy requires work Fd, where F is the applied net force and d is the distance over which it is applied. Both of these require a force, but the needed force is smaller as the time t and distance d are longer. The acceleration, or rate at which the velocity changes, is F/m. When the matchbox is open, only the sleeve stops immediately upon impact. The majority of the mass, in the drawer, slows and stops over a longer time and distance, with less force and acceleration.
Copyright © 2004, Richard Barrans
Revised: 21 December 2016; Maintained by Richard Barrans.