[pianotech] Force equivalents in different actions

[John Delacour]

At 13:32 -0500 24/3/10, Mike Spalding wrote:

>Energy is not equivalent to momentum.  Energy is mass times the 
>square of the velocity.

You mean kinetic energy, I suppose.

This is half what you say, namely HALF the mass times the square of 
the velocity.


So in the MKS system...

a mass of 10 grams travelling at 20 metres per second has kinetic 
energy of 2 joules.

1/2 * 10/1000 * 20 * 20 = 2.0

a mass of 12 grams travelling at 16.67 (20/12*10) metres per second 
has kinetic energy of 1.67 joules.

1/2 * 12/1000 * 16.67 * 16.67 = 1.67

a mass of 12 grams travelling at 18.25 metres per second has kinetic 
energy of 2.00 joules, the same as a mass of 10 grams travelling at 
20 metres per second

1/2 * 12/1000 * 18.25 * 18.25 = 2.00

This supposes the body moving in a straight line, which the piano 
hammer does not.  The effective mass and the (difficult to quantify) 
behaviour of the shank would also have to be factored in, and to 
arrive at a useful solution would require not only superhuman powers 
of observation but some rather complicated mathematics.  And, as so 
often, simple informed experimentation will find a better solution.

JD


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