Testing Newton's First Law

t_1   --- the time it took the cart to pass through the first photogate
t_t    --- the total time recorded by the photogate timer for the cart to pass through the first and second gates
t_2   --- computed from t_2=t_t-t_1 to get just the time for the cart to pass through the second gate
v_1  --- the average velocity of the cart during the time it went through the first gate; v_1 = L/t_1
v_2  --- the average velocity of the cart during the time it went through the second gate; v_2 = L/t_2
%diff --- the percent difference between the first and second velocity computed by %diff=100%*(v_1-v_2)/v_1

In this lab, we measured the velocity of a cart on an air track at two different points along the track after pushing it with our hands. By our pushing, we gave the cart an initial horizontal velocity. Using Newton's laws and the fact that ideally no force is acting in the horizontal direction once the cart leaves our hand, we expect that the velocity will remain the same.

As a measure of how constant the velocity was, we computed the percent difference between the initial and final velocities. This percent difference reflects the error of the experiment as ideally it would be zero. We ran the experiment three times with different carts and with the gates in different positions to help randomize the errors (see below). For these three trials, the average percenter difference was 25%. This value seems rather high, but I expect that the errors described below account for it.

Ideally, the air track eliminates friction by supporting the carts with air. However, the carts are still exposed to drag, as well as some friction with the track because the air flow out of the holes is not uniform. This error would manifest itself as a slowing down of the carts, which is indeed what we saw. If we had seen the velocity go up, then this error would help explain nothing.

Another possible source of error is the timers. Inasmuch as possible, I tried to test the timers by comparing to my watch. while this certainly would not indicate small errors, the timers seemed to work for long periods. I would imagine that the error presented by the timers is small.

More importantly though, I believe the fact that the air track was somewhat bowed (as evidenced when we tried to level the track and the cart would slide to the low spot) contributed the most error to this experiment. Indeed, because of our observation of this possible error, in trial #3, we purposefully placed the photogate timers symmetrically about the bow so as to minimize its effect on the results. While this is in some sense rigging the experiment, it seemed the best method with such equipment. The results yielded the lowest percent difference as would be expected. Overall, we are confident Newton's laws hold, and would expect as friction is decreased and 'bow'ness is removed, the percent difference would go to zero.