Re: Air Track Experiments

[Richard Tarara <rtarara@SAINTMARYS.EDU>]

----- 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