Aluminum Sheet Length sys.unc. units ±0.05 l cm ± 0.05 | cm ±0.05 | cm Width s,

Question

Aluminum Sheet Length sys.unc. units ±0.05 l cm ± 0.05 | cm ±0.05 | cm Width s, unc. units 12.75 2 12.70 3 | 12.70 115.55 ±0.05 | cm 21 vs. 54 3 15.G 4 I 1560 5115-55 3 12.70 | 4 | /265 |5112.65 ±0.05 | cm | ±0.05 | cm | ±0.05 | | ±0.05 | cm | | ± 0.05 | cnn ±0.05 l cm +0.0001 m sys, unc. units ± 0.05 | ± 0.05 Hei ght -sys, unc units l Mass 1 6.0574000 cm 210,0 593 ±0.00051 em ! 2 20 o.o520 | | 3 | 27,09 | ±0.05 | g ± 0.0005 | cm 4 | 0.0454-0005- ± 0.00051 cm 5 | o.ey75 | Average Length-15593 cm-=0.062 Gedi.. Average Width-12.69 cm -001193.ngw- 0.065 Average Height = 0.0527 3 cm = o.os4110%-0. 004911(m Average Mass- 2 (2.9, -00 117m 0.163 9 S1709 V-LwH Volume of Aluminum Sheet- 10.4u7 cm 10.4u m Density of Aluminum Sheet 2.56

Explanation / Answer

Ans:1b) The density of Aluminuam obtained from the cylinder measurement is in a good consistance with the value provided in the hang book but the value which we obtained from the aluminum sheet calculation differ from the hand book value by 10%. So the density measured from the cylinder is a good result and the result obtained from the sheet is in 10% differ from the handbook data.

2a) The systematic uncertainties are the scale uncertains while measuring the length , width ,height, diameter, mass etc. This kind of uncertainty occures only due to the resolution of our measuring devices.Here for the measuring device we can say how much small scale we can measure a quantity.
2b) random uncertainty may occure due that present situation of the lab.i.e the temperature of the lab.A random error can also occur due to the measuring instrument and the way it is affected by changes in the surroundings. For example, a spring balance might show some variation in measurement due to fluctuations in temperature, conditions of loading and unloading, etc

3a) The volume of the cylinder is V=pi*(d/4)2*h where d is the diameter and h is the height of the cylinder.Here the volume depends on the square of the diameter so the uncertainty in the measurement of diameter contributes more in the ensity uncertainty.

3b)The volume of the sheet is V=l*b*h where the l, b, & h are the length, width and heigth of the sheet respectively. Here both the quantities are in linear power. So they contribute equally(with respect to power) to the density calculation.But the height has very small value compaired to the length and width. So the proportional error comes from the height will be higher then that of the length& width.So for the sheet measurement of height need more attention.

3c)The major source of uncertainty is the power domination of any quantity such as length, diameter etc.More over the quantity which has very small value, we have to calculate the uncertainty for that quantity very carefully because this quantity increases the relative error very much.
The another major set of uncertainty is in the mass measurement one have to measure the mass of both the cylinder and the sheet very care fully with the accure uncertainy measurement.

4)For the cylinder I will measure the diameter as accurate as I can to reduce its uncertainty contribution.And for the sheet I will measure the height of the sheet very carefully to reduce the uncertainty.Moreover I will take precise account of uncertainty for the mass measurement.

5)Here to know which one is more accurate we will take the ration of uncertainty with the measured value,So ,
for a) 1/1000 =0.001 ; for b)0.1/10=0.01 ; for c) 0.1/10 =0.01 and for d)1/1 =1 So we can see that the ratio is small for a so the measurement a is more accurate.

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