The dimensions of a steel plate used in the Physics 225: Capacitors lab are meas

Question

The dimensions of a steel plate used in the Physics 225: Capacitors lab are measured with a millimetre-ruled ruler, and found to be: l_best = 254 mm w_best = 156 mm What is the absolute uncertainty in the measurement of the length l of the steel plate? 254 +/- 1mm What is the absolute uncertainty in the measurement of the width w of the steel plate? 156 +/- 1mm What is the relative (fractional) uncertainty in the measurement of the length l of the steel plate? (1mm/254mm)*100 = 39% What is the relative (fractional) uncertainty in the measurement of the width w of the steel plate? (1 mm/156mm)*100 = 64% Write below the complete record of the measurement for the length and width of the steel plate. Calculate the best estimate value A_best for the area A of the steel plate and express the answer in scientific notation. Calculate the absolute and relative uncertainty delta A of the area A of the steel plate. Show all the details of your work.

Explanation / Answer

e

length=l=254 +/-1 mm

width=w=156+/-1 mm

f

A=l*w=39624 mm^2

g

dA/A=sqrt((dl/l)^2 +(dw/w)^2)

we got dA=298.08 mm^2=>(absolute)

relative=dA/A=7.5227*10^(-3) = 0.75 %

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