Activity: Measurement and uncertainty
In this activity on Measurements and Uncertainties, you will be introduced to measuring with a Vernier caliper, estimate uncertainty, practise the (max - min)/2 method, distinguish random and systematic errors, process data with Excel, draw graphs with Logger Pro, understand the benefits of linearisation in identifying relationships and calculate the uncertainty in gradients.
Need to know
In this practical the mass and diameter of different balls of Plasticine will be measured in order to verify that the mass of a sphere is proportional to the cube of its diameter. This is a simple experiment but introduces the concepts of uncertainties, data processing and graphing.
Now the data has been entered into a spreadsheet it is a simple matter to perform calculations such as finding the average.
- Add header dmean/cm to the next column in your table (To get subscript highlight the text in the formula bar and right click, choose "format cells" and tick subscript).
- Click in the cell at the end of the first row of data.
- Type =ave this will open a list of formula beginning with ave, choose AVERAGE (double click).
- Highlight the row of data that you want to find the mean of.
- Enter
To copy the formula to all the rows
- Select the cell with the formula in it
- Click on the lower right hand corner (you know when you are clicking the right place because the cursor will become a +)
- Drag down to fill all the cells (Excel automatically changes the formula so that it refers to the relevant column).
Calculating dmean3
- Add the header dmean3/cm3 to the next column.
- Type = then click the cell you want to process (in this case it would be G3)) this adds the relevant cell to the formula.
- To calculate d3 type ^3 and enter (the final formula will be =G3^3 but =G3*G3*G3 would also work)
- Copy the formula to all cells in the column as before.
Calculating dmax3 and dmin3
To calculate the uncertainty in d3 you need to know the maximum and minimum possible values. Excel will do this for you with the MAX and MIN functions.
- Add the header dmax3/cm3 to the next column.
- Type =ma and select the formula MAX by double clicking.
- Highlight the values of d.
- Close the bracket and type ^3
- You will probably get an error message (!) informing you that you didn't highlight the cell next to the formula, get rid of this by highlighting the column, clicking the ! and selecting "ignore error"
Now add another column for the minimum value.
Upload an image of your Excel spreadsheet and an image of your final graph plotted in LoggerPro
Using evidence from your graph, comment on the random errors in your measurements.