Key Inertia

[Richard Brekne]

Sarah Fox wrote:

> But if the hammer is more massive, it doesn't need ot hit the string with as
> much velocity to transfer the same amount of energy.  Energy imparted to the
> hammer shank is jack force times jack travel.  This is converted to kinetic
> energy of the hammer, which is proportional to mass.  Twice the hammer mass,
> while preserving the same jack force and stroke, would mean 2^.5 the
> velocity, true, but when the hammer hits the string, the same amount of
> kinetic energy is transferred to the string.
>

Ok Sarah... same kinetic energy.... but you demonstrated quite clearly below the
effect this (same energy for differeing mass* velocitycan have on what happenes
to the velocity of whats being hit.

So what now ?


Now, in our microgravity lab, we accelerate the bowling ball over a distance
of, say, 1 cm, with a force of 1 Newton.  We similarly accelerate the marble
over a distance of 1 cm with a force of 1 Newton.  Both now have the same
kinetic energy.  The bowling ball moves very slowly towards the wippen,
which is a super light 10 g, for simplicity sake.  The marble moves very
quickly towards an identical 10 g wippen.  When these balls hit their
respective wippens, the wippens bounce off of them.  We're interested in
finding out the wippen velocity.

When the marble strikes the wippen, the kinetic energy is transfered totally
to the wippen (assuming elasticity).  The marble is then halted, and the
wippen moves forward at the same velocity of the marble.  (It's like those
executive playtoys -- the racks of five hanging steel balls that click back
and forth.)

When the bowling ball hits its wippen, not much will happen to the
velocity of the ball.  The wippen will bounce off it and move forward at
approximately twice that velocity.

This is all well and good, and it might appear that the bowling ball is more
effective at moving its wippen.  However, consider that the bowling ball
wasn't moving very fast in the first place.  Kinetic energy being equal, the
marble would move Sqrt(1000), or approx 32, times as fast as the bowling
ball.  In the end, the ratio of wippen velocities would be 1:16, with the
marble's wippen moving much faster.






--
Richard Brekne
RPT, N.P.T.F.
UiB, Bergen, Norway
mailto:rbrekne@broadpark.no
http://home.broadpark.no/~rbrekne/ricmain.html
http://www.hf.uib.no/grieg/personer/cv_RB.html