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?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.