Physics Labs & Error Calculation

[Monocerotis]

Homework Statement

This is just a question regarding error calculation in physics labs. I've never before in my career as a student done any lab work, this is a 1st year undergraduate physics course.

For this lab we were required to create an experiment that would illustrate acceleration due to gravity with a cart rail on an air track.

My lab partner and I conducted several runs where we would give the cart an initial push up the air track, and then gather data with motion sensors and then import that data into DataStudio.

Very smooth runs, no exaggerated spikes in the graph that according to our limited info would constitute an error.

I have position time and velocity time graphs of all the runs.

From that we extracted the slope, y int, r, mean squared and root MSE for our runs.

Homework Equations

a = g * sin(theta)

Front of book forumlas:

Δy = a(Δx)

Δy = nx^(n-1)Δx

y = x1+x2+x3+...; y = x1+x2-x2...; y=x1-x2-x2...;y=x1-x2+x2...;etc.
Then Δy= (sqrt) Δx1^2 + Δx2^2 + Δx2^2...

y = ax1 (+-) bx2 where a and b are constants.
Δy = (sqrt) a^2(Δx1^2) + b^2(Δx2^2)

y = cos (ax) where a is a constant
Δy = asin(ax)Δx; Δx expressed in radians

The Attempt at a Solution

I really have no idea where to begin with error calculation. It was never discussed in the labs, we didn't have any lab prep session where error calculation was discussed. In the front of our lab books we are given ambiguous formulas which we've been told to use in error calculation.

This really isn't so much of a straight forward homework question as it is a "what am I supposed to do because I'm completely lost here" type situation.

any help appreciated.

 

[anathema]

Dear student,

Thank you for reaching out to us for help with your lab work. Error calculation is an important aspect of any scientific experiment, as it helps to determine the accuracy and reliability of your results. It is understandable that you may feel lost and unsure of how to proceed, especially since it was not covered in your lab sessions.

Firstly, it is important to understand that there are different types of errors that can occur in an experiment. These include systematic errors, which are consistent and can be corrected for, and random errors, which are unpredictable and cannot be corrected for.

To calculate the errors in your experiment, you will need to first identify the sources of error. This could include factors such as sensor accuracy, human error, or environmental conditions. Once you have identified the sources of error, you can then use the appropriate equations and formulas to calculate the error for each data point.

For example, if the source of error is the sensor accuracy, you can use the formula Δx = x ± Δx, where Δx is the error in your measurement and x is the measured value. This formula takes into account the uncertainty in your measurement.

If the source of error is human error, you can use the formula Δx = (Δx1^2 + Δx2^2 + ...)^1/2, where Δx1, Δx2, etc. are the individual errors in each measurement. This formula takes into account the cumulative effect of multiple measurements.

It is also important to note that when calculating errors, you should use the appropriate units for each measurement. For example, if your measurement is in meters, your error should also be in meters.

I would also recommend consulting with your lab instructor or a more experienced peer for guidance on error calculation. They may be able to provide you with more specific instructions and tips for your particular experiment.

I hope this helps to clarify the process of error calculation for you. Good luck with your lab work!