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Re: [Phys-l] real-world mechanics problem



Visualizing the dynamics of a tuned circuit, I recall that increasing the
value of one reactive element increases Q, increasing the amount
of the other decreases Q.
For a tuned circuit of some Q the amplitude for constant drive increases
until the losses equal the drive power. Fishing round for some vestigial
memory of the homologies between electrical and mechanical effects,
I grasp at the thought that
Fr = 1/(2pi root( l.c)) and Fr = 1/(2pi root( l/g))
from which I suppose that placing a penny above the bob decreases
the radius of gyration, essentially decreasing the (effective) length l
and increasing Fr. That would decrease Q, I suppose.

If this tortuous line of reasoning were justified, it would then still be necessary
to know the shape of that 77kg bob and the length from its com to the pivot
to deduce the change.
One could balance the pendulum on a knife-edge to find the prior CoM
(which is particularly not good for dividing the pendular mass
in two equal parts, in this case :-)
But a guess? < .03% half amplitude decease.

Brian W

On 2/3/2011 12:32 PM, Bob Sciamanda wrote:
?BC,
I don't quite follow all of this, BUT
Why are you using the kinematics of CONSTANT ACCELERATION for a pendulum
bob?
-Bob (not a pendulum bob :)

-----Original Message-----
From: Bernard Cleyet
Sent: Thursday, February 03, 2011 11:53 AM
To: Forum for Physics Educators
Subject: Re: [Phys-l] real-world mechanics problem

"Speaking" of non-imaginary world problems.

I have one. A friend wishes to know the effect on the amplitude by adding
three quarters on the top of a 77kg pendulum bob (the tower clock at the
county building in Santa Barbara.*


The period change was quite obvious and measurable.** However, there was no
detectable change in the amplitude. After some cogitation (I'm a bit slo
these days.) I conclude that adding mass on the "down swing" will do
nothing, but on the upswing will reduce the amplitude. I found the KE at
BDC and concluded the energy to lift the quarters (~ 0.02kg) is so little
the reduction in height, (h = L(1-cos(A)), is on the order of microns, and,
therefore, not measurable by his method. [speed as measured by a photogate
at BDC]

Here's my prob. Using the kinematic equations for constant acceleration
etc. I fond the formula for speed at BDC (and the work-energy principle)

X dot = sqrt.(g*L) A as a means of measuring the amplitude.

I obtain the same formula by using the total energy of the P. using 0.5(M
L^2 * theta dot) and m*g*h h = L(1-cos(theta) and using E = PE at the max
deflection (amplitude). However, and this is my prob. To obtain the same
equation I must use the approximation cos =~ 1 - theta^2 / 2!

Nice, and not satisfactory.

bc


* http://www.bisnoschallgallery.com/Home.html

No weight tray (the std. method of adjusting "high end" clocks).

** http://www.bisnoschallgallery.com/Clock_Data.html

The data for that experiment is in the archive, if there is one.