DATA SHEETS AND GRAPHS

RECORDING MEASUREMENTS If you are doing any measuring process, you must record all measurements you’ve got. Recorded measurements with their errors can be given as – TABLE or – GRAPH

TABLE (DATA SHEET) It’s easy to build table if you have only two variables: – into one column we write values of indipendent variables (independent variables answer the question "What do I change?“) – into second column we write values of dependent variables (dependent variables answer the question "What do I observe?") Variables can also be controlled (Controlled variables answer the question "What do I keep the same?")

EXPERIMENT Student measured the speed of the body. During 6 seconds he observed the distance traveled by the body (preciseness ±5m) after every second (±0,2s) Data, he recorded: – t 1 =1s; s 1 =31m – t 2 =2s; s 2 =56m – t 3 =3s; s 3 =91m – t 4 =4s; s 4 =119m – t 5 =5s; s 5 =147m – t 6 =6s; s 6 =186m Build up the data sheet of that experiment

t (s); ∆t=±0,2s s (m); ∆s=±5m 0,0 1,031 2,056 3,091 4,0119 5,0147 6,0186 Calculate: -Speed of the body -Absolute and relative errors of the velocity

t (s); ∆t=±0,2s s (m); ∆s=±5m v (ms -1 ) ∆v (ms -1 ) 0,00 1,031 2,056 3,091 4,0119 5,0147 6,0186

GRAPH Graph is the line, that shows functional dependence between independent and dependent variables When representing data as a graph, we represent uncertainty in the data points by adding error bars.

Axis t (independent variable) Axis s (dependent variable)

Error bars: absolute error of time ±0,2s, absolute error of lenght ±5s

Some rules to draw error bars Add error bars only to the first and last points Only add error bars to the point with the worst uncertainty Add error bars to all points but use the uncertainty of the worst point Only add error bars to the axis with the worst uncertainty

Trend line, you draw, must NOT hit every point, but MUST hit every “error cross” (in MS Excel command „linear trendline“)

Find trendline’s function (MS Excel’s command „Display trendline’s equation“ NB! Excel uses more percise calclulation of the slope).

Draw steepest possible gradient and shallowest possible gradient just add error bars to the first and last point, and then draw a straight line passing through the lowest error bar of the one point and the highest in the other (steepest) and vice versa (shallowest).