Raw Data: Washer Least Count Imm) Uncertainty (mm) #1 #2 #3 36.0 15.0 2.0 35.0 1

Question

Raw Data: Washer Least Count Imm) Uncertainty (mm) #1 #2 #3 36.0 15.0 2.0 35.0 16.0 2.0 34.0 15.0 2.0 0.5 Outer Diameter (mm Inner Diameter (mm) Thickness (mm) Uncertainty (s 12 east Count imm) Uncerta #1 #2 #3 .Outer Diameter (mm) 34.7 15.7 1.8 34.8 15.7 1.9 0.1 34.8 Inner Diameter (mm) 15.6 Least Countin uncertaintywi 0.00001 Thickness (mm) 0.0001 Mass( 12.010037 For Graduated Cylinder Measurement of Volume by Archimedes Method Least Count (ml) Uncertainty (mL) Initial Volume Final Volume Difference 1Volume (ml) 90 91

Explanation / Answer

given three sets of data

data 1: mass1 = 12g +- 1 g ( for acculab slab error in mass is 1 g)

volume 1 = pi(Do^2 - Di^2)*t/4

now Do = (36 + 35 + 34)/3 = 35 mm

Di = (15 + 16 + 15)/3 = 15.55 mm

t = 2 mm

V1 = 1543.62 mm^3

also from formula for error propogation

d(V1)/V1 = sqroot((dl/t)^2 + (2*dl/Dav)^2)

where dl = 0.5 mm

Dav = Do + Di /2 = 25.275 mm

hence dV1 = 390.70 mm^3

hence density rho1 = m1/v1 = 7.7739*10^-3 g/mm^3

and error in density d(rho1) = *rho1*sqroot((dm/m)^2 + (dV/V)^2) = 0.266*rho1 = 2.071*10^-3

hence rho1 = 7.7739*10^-3 +- 2.071*10^-3 g/mm^3

data 2: mass2 = 12.01g +- 0.0001 g ( for mettler toledo scaler error in mass is 0.0001 g)

volume 2 = pi(Do^2 - Di^2)*t/4

now Do = (34.7 + 34.8 + 34.8)/3 = 34.766 mm

Di = (15.7 + 15.6 + 15.7)/3 = 15.667 mm

t = (1.8 + 2 + 1.9)/3 = 1.9 mm

V2 = 1436.642 mm^3

also from formula for error propogation

d(V2)/V2 = sqroot((dl/t)^2 + (2*dl/Dav)^2)

where dl = 0.1 mm

Dav = Do + Di /2 = 25.2165 mm

hence dV2 = 76.466 mm^3

hence density rho2 = m2/v2 = 8.359*10^-3 g/mm^3

and error in density d(rho2) = *rho2*sqroot((dm/m)^2 + (dV/V)^2) = 0.4449*10^-3

hence rho1 = 8.359*10^-3 +- 0.4449*10^-3 g/mm^3

data3 : m3 = m2 = 12.01 +- 0.0001 g

V3 = 1*10^3 m^3

dV3 = 1*10^3 m^3

so rho = m3/V3 = 12.01*10^-3 g/mm^3

and d(rho) = sqroot((0.0001/12.01)^2 + (1)^2) = 1.000,000,007*rho

hence rho = 12.01*10^-3 +- 0.01201 g/mm^3

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