Re: bouncing ball or car acceleration

[Gary Turner <turner@MORNINGSIDE.EDU>]

I thought this statement, while correct for the skater, was incomplete for
the bouncing ball.

In the latter case, you know the energy of deformation - it is the kinetic
energy of the ball.  The force that deforms the wall is the same force
that 'decelerates' the ball.  The deformation distance * force is the work
done on the ball (which is negative).  That is momentarily stored as
elastic potential energy, before being transferred back to kinetic energy
in the ball.

Knowing the energy, the average force is proportional to k.  From impulse,
then the time of collision is inversely proportional to k

> so if we are given any known force F, the
> energy of deformation is inversely proportional
> to k.  Brick walls are proverbial for their
> large k values.  This implies negligible energy
> transfer.

Only for a given force (I know you said that - just wanted to clarify).  In
collisions, brick walls also have the tendency to provide very large
forces - so transfer a similar amount of energy as, say, a wooden wall.

> =================
>
> BTW note the correspondence in the form of equations
> [2] and [3] to the energy of a capacitor at constant
> charge and constant voltage, respectively.