Re: Work - impulse


Peter wrote:
. In both cases, the puck stops completely on impact with the lever,


This you have not shown. This is in fact counter to experiment.

That was empirically determined. The setup used proved to be extremely
sensitive; thus, the data reported are completely reliable. It is not
difficult to replicate, taking all the usual precautions.

Then you need to publish your experimental results, because your
experimental results are counter to other experimental results. By the
way, other experimental results are consistent with what theory
predicts.

Here is what theory predicts:

M = mass of lever
L = length of lever, from end to end
I = ML^2/12, for lever pivoted in center
m = mass of puck
v = initial velocity of puck
v' = final velocity of puck
r = distance of closest approach of line of motion of puck to pivot
w = final angular velocity of lever

We will solve for the value of r that requires v'=0.
We will assume a completely elastic collision.

Conservation of angular momentum:
mvr = mv'r + Iw = mv'r + (ML^2/12)w
and because v'=0
mvr = (ML^2/12)w (1)

Conservation of energy:
mv^2 = m(v')^2 + Iw^2 = m(v')^2 + M(L^2)(w^2)/12
and because v'=0
mv^2 = M(L^2)(w^2)/12 (2)

sqrt[12(m/M)]v/L = w (3)

Put (3) into (1)
mvr = sqrt[12(m/M)](ML^2/12)v/L
r = sqrt[(M/m)/12]L

This says that for M/m = 1, r = (L/2)/sqrt(3).
And for M/m = 2, r = (L/2)/sqrt(4/3).


You claim to find values of r that are different than these values of
r.
You claim to find for M/m = 1, r = (L/2)/3
And for M/m = 2, r = (L/2)/(5/2).

On the basis of your experimentally determined values of r, you are
saying that the principles used in the calculation above must be wrong
somewhere, and I take it you have a problem with the conservation of
energy --- or at least that your experimental results suggest that this
is the one that must be wrong.

I suggest strongly that you do the following:
a) Document all your sources of systematic error and use that to
estimate error bars on your measured value of r.
b) Do a literature search on experiments that test completely elastic
collisions with mixed linear and rotational motion and compare your
experimental sensitivity with theirs.
c) If your experimental sensitivity is comparable to that of the
competing papers, submit it to a journal for peer review.

Since your experimental results conflict with other experimental
results, you will have to be *very careful* in your execution of these
steps to be absolutely sure you're right.

PD

.

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