If the glass beads used for the mass measurements were significantly smaller in
ID: 485450 • Letter: I
Question
If the glass beads used for the mass measurements were significantly smaller in
diameter than the beads used for the volume measurements, how would the
value of the experimental density of the glass beads be affected? Give
your reasoning. Would this be a systematic or a random error? Give
your reasoning.
Statistical Analysis of Experimental Density Data Final Mass (g) Mass of Initial Mass (g) (Dev)42 32.7363 35.641 38.4215 41.2054 44.021 29.887 32.7363 35.641 38.4215 41.2054 10 Beads (g)Deviation 2.8493 2.9047 2.7805 2.7839 2.8156 0.0225 0.0779 0.0463 0.0429 0.0112 0.00050625 0.00606841 0.00214369 0.00184041 0.00012544 4 Mean Mass 2.8268 g Std.De 0.05168220197 Cl (Single Value) = Cl (Mean)= 0.2379448578 g 0.1064121754 g Final Volume (mL) Volume of 10 Beads (mL) Initial Volume (mL) Deviation (Dev)A2 24.71 23.52 22.41 23.52 22.41 21.21 1.19 0.02333333333 0.0005444444444 1.11 -0.056666666670.003211111111 1.2 0.03333333333 0.001111111111 Mean Volume - 1.166666667 mL Std.Dev.= 0.04932882862 CI (Single Value) Cl (Mean) = 0.4895886241 mL 0.2826641239 mL Density = Random Error of Density = 96 Error = 2.422971429 g/mL 0.5940895947 g/mL 0.9571428571 %Explanation / Answer
Density is given by, density = Mass/ volume
According to the data given, the mass and volumes have been determined independently for beads from a given lot. It is thus assumed that all the beads have same diameters.
If the glass beads used for the mass measurements were significantly smaller in diameter than the beads used for the volume measurements, then Mass observed < Mass expected and Volume observed > volume expected
Since the mass of the beads with smaller diameter is going to be less than those with larger diameters, the experimental density would be lower than actual density.
The type of error will depend on the experimental procedure followed while selecting beads for mass and volume analysis. If one has randomly picked up beads from the same lot for mass and volume measurements, it will result in random error. In such a situation, with each measurement the error can fluctuate in either direction depending on whether the beads chosen for mass analysis have average diameter larger or smaller than those chosen for volume analysis. In this case, taking more data will help in minimizing the error by averaging over a large number of observations.
If however, the volume analysis was always performed with the same lot of smaller beads, it will result in a systematic error. This is because if we use the same beads again and again, then no matter how many times we do the measurement, we will always get a lower experimental density value that the actual value. Thus the error will always be in the same direction and taking average over different observations will not reduce the error.