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Analysis of inclined Air-track experiment

First lets write down the formulae for the motion which we analyzed on the inclined air track. When I started off the clock the cart had zero velocity and it was at the origin for our x-axis. This implies that
eqnarray30
This implies then that
 equation32
Rather than use the acceleration that we determined graphically I'll use one of our primary measurements, namely the time at which we reached a distance of 4 m from x=0. To determine the only unknown remaining constant, a I solve equation 8 for the acceleration:
equation38
The expression makes sense since a gets larger for smaller t and larger x. Putting in numbers I obtain:
equation42
A result which is consistent with what we derived from our graphical analysis.

Now I would like to emphasize that by suitable manipulation of eq 2 you can handle any problem involving motion with constant acceleration. However you will find yourself often repeating certain symbolic manipulations of formulae. To avoid this it can be useful to use the following expressions which are easily derived once and for all as described in the book:
 eqnarray47
As compared to the book you will notice that I have suppressed tex2html_wrap_inline276 assuming that my clock always runs from zero time (tex2html_wrap_inline278). The last of these formulae is quite obvious when we look at the parabolic x(t) curve we got for the inclined track. You will find that it comes in very handy in problem 30 due this Monday. The second of these formulae is also very important and comes in handy. It is always the one to use when the time taken to perform the motion is not of interest. An example:



Collin Broholm
Fri Sep 12 13:43:28 EDT 1997