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Re: Air Track Experiments



----- Original Message -----
From: David Abineri <dabineri@CHOICE.NET>
To: <PHYS-L@lists.nau.edu>
Sent: Tuesday, August 24, 1999 8:18 PM
Subject: Air Track Experiments


Rick, Thank you for your response to my question about air track
experiments.

In your response you indicate that the applied force is equal to mg.
Surely this is not the force applied to the cart because if it were,
then the forces on the hanging mass would cancel and there would be no
acceleration.



_______M_______
|
m |


mg is the weight of the suspended mass (and hanger)--sorry for the
confusion--I always use 'm' or m_sub_f for this falling mass and M or
M_sub_c for the mass of the cart. This force vertical force is transferred
to the cart via the recording tape and the pulley converts it to a
horizontal force.

Ultimately the algebra predicts: a = mg/(m+M) which is why it is
convenient to keep the mass of the system constant if you want ( a versus m)
to be linear. In a straight _confirmation_ of F = ma, plot mg versus a and
a linear plot with slope (m+M) is the confirmation. With the fixed falling
mass varied cart mass, a plot of acceleration versus the inverse of the
falling mass should be linear with a slope equal to the force.

I much prefer the experiment assuming no pre-knowledge of N2 and in fact no
pre-knowledge that the applied force (weight of the falling mass) can be
calculated as mg--rather, as described earlier, assuming only a
proportionality of force and falling mass. You can get a reasonable value
of 'g' from the analysis of the data (at least a slope with acceleration
units and within +/- 25% of g (known in our case from Galileo's preliminary
work--since we are taking a pre-Newtonian stance) ;-)


Given this and given that one is trying to demonstrate N2, one can't use
mg for weight anyway since that is N2.

Please correct me if I misunderstood your response.

By the way, whenever I have done this form of N2 (cart with wheels
pulled by hanging mass), most students are invariably confused by the
question as to, for example, whether the acceleration will be constant.
They say "of course it will be constant since falling object accelerate
constantly". I have, therefore tried to avoid the appearance of circular
logic and tried to avoid using falling masses.


Use the timing apparatus in a way that you measure the accelerations for
different distances travelled during the pull. It would seem an opportunity
to SHOW that indeed the acceleration IS constant.

Rick