Correctness of A particular Lab Experiment

[azaharak]

Hi

I've been reading through different laborator manuals on the same experiment, you may be familiar with the experiment.

Using a tape timer, or spark timer to measure the velocities and acceleration of a moving body, assuming its moving with constant acceleration.

The lab utlizes the fact that the average velocity will be equal to the instantaneous velocity at the midpoint of a time interval, the spark or tape timers make regularly timed dots which you can obtain the average velocities from.



The problem/issue is that One of the manuals instructs you to compute the instantansous velocities for every other set of dots or odd dots, for instance

Vavg1=(x2-x0)/(t2-t0), and this is the instanteous velocity at time t1
Vavg3=(x4-x2)/(t4-t2), and this is the instanteous velocity at time t3
Vavg5=(x6-x4)/(t6-t4), and this is the instanteous velocity at time t5

and so on


The other lab manual instructs you to compute all of them.

Vavg1=(x2-x0)/(t2-t0), and this is the instanteous velocity at time t1
Vavg2=(x3-x1)/(t3-t1), and this is the instanteous velocity at time t2
Vavg3=(x4-x2)/(t4-t2), and this is the instanteous velocity at time t3
Vavg4=(x5-x3)/(t5-t3), and this is the instanteous velocity at time t4

Although the 2nd method appears to give you more data, I believe it is slightly flawed because you adjacent velocites will not necessarily be independent from an error point of view.

Can anyone else give some insight into which method is correct, I really appreciate it.

 

[diazona]

I don't see anything wrong with either method. Sure, the uncertainties in the different velocities are not independent, but why does that matter, unless you're averaging them or something?

And in fact, I believe that the uncertainties in the even numbered velocities are correlated only with each other, not with the uncertainties in the odd numbered velocities. For example, since both v3 and v1 depend on x2 and t2, their uncertainties will be correlated, but v3 and v2 are not calculated from any of the same data so their uncertainties would be independent. If this is the case, the second procedure may be better because in the end it incorporates twice as many independent degrees of freedom.

 

[azaharak]

But what if you consider the following

The instantaneous velocity V3 depends on positions x4 and x2

the instantaneous velocity V4 depends on positions x5 and x3


Assume it is a car sliding down a track,
If for instance the car that is sliding down the track hits a slight bump between x4 and x2,
specifcially between x3 and x2

this will skew the result for v3 away from theory, and v4 as well!.

Wheras the first method does not introduce this double skew.

I have come across several manuals that perform it the 1st way, there must be a reason beacuse it is not trivial to leave half the data out.

Any other suggestions?

 

[azaharak]

Please, I appreciate your input, preparing lab. Thanks