How Do You Calculate Uncertainty in Acceleration from Photogate Timer Data?

[Blues_MTA]

Homework Statement

I am doing a simple experiment using photogate timers and an elevated track to calculate velocity and acceleration. This experiment measures the time it takes for an index card attached to the top of a cart to pass through a photogate when going down an elevated track. By putting two photogates at two different places on the track we get two different time values and therefore two different velocity values. Both of which are calculted using the length of the card as the distance (the photogate timers track how long it takes the card to travel through each one)

Long story short I have my two velocity values and a percent error for each. I got this percent error by adding the percent error in the distance measurement of the care, and the percent error of the time values collected. So I have two different velocities with two different percent error values. In order to calculate acceleration i have to subtract these two velocities and divide by the total time spent onthe track. This value i also have a percent error for. I know when taking a quotient you have to add the two percent errors together, but what should i do with the Two velocity errors, I have

[(V2 (plus or minus its percent error))-(V1(plus or minus it's percent error))]/(time (plus or minus its percent error))

How do i find the uncertainty/percent error in acceleration?

Homework Equations

The Attempt at a Solution

 

[grzz]

a = {v$_{2}$ - v$_{1}$}/t

The numerator is a difference. Hence use rule for uncertainty in a difference to find the uncertainty in v$_{2}$ - v$_{1}$.
Then use rule to find the uncertainty in a quotient.

 

[gneill]

If you do a web search on "error propagation" or "error analysis" you will turn up copious resources which explain how to combine errors in your calculations.

Here's a few:

http://courses.washington.edu/phys431/propagation_errors_UCh.pdf
http://www.fas.harvard.edu/~scphys/nsta/error_propagation.pdf
http://teacher.pas.rochester.edu/PHY_LABS/AppendixB/AppendixB.html

 

[Blues_MTA]

thank you, my problem was that i had the two velocities and their Relative errors, i had to convert that to absolute error to complete the calculation in the numerator, then once that was complete convert that value to a relative error once again, then add the two, thank you very much!

 

[rwisz]

As a scientist, it is important to acknowledge and address sources of uncertainty in an experiment. In this case, there are several sources of uncertainty that can affect the accuracy of your calculated acceleration. Some possible sources of uncertainty in this experiment could include human error in timing the index card passing through the photogates, variations in the surface of the track, and possible friction in the cart's wheels.

To address these uncertainties, it is important to conduct multiple trials and take the average of your results. This can help to reduce the impact of any individual errors and provide a more accurate measurement of acceleration. Additionally, it may be helpful to use more precise equipment, such as a digital timer, to minimize human error.

In terms of calculating the uncertainty or percent error in acceleration, you can use the same approach as you did for velocity. This would involve adding the percent errors in the two velocity values and the percent error in the total time. However, it is important to note that this calculated uncertainty is only an estimate and may not reflect the true uncertainty in your experiment. It is always a good idea to discuss potential sources of error and their impact on your results in your conclusion.