what’s the uncertainty in the density of the wood?

Question

a block of wood is measured to be 4cm x 5.7cm x 12.9 cm each +/- 0.1 the mass is 335.42g measured on a centigram balance so +/- 0.02 g so what’s the uncertainty in the density of the wood?

Answer 1

If we use the measures without error, volume V=294.12cc and mass M=335.42g, so density D=335.42/294.12=1.1404.

The maximum error limits of the density D=M/V are when M is maximum and V is minimum, and when M is minimum and V is maximum.

The minimum M=335.40g. The maximum V=4.1×5.8×13.0=309.14cc.

The maximum M=335.44g. The minimum V=3.9×5.6×12.8=279.552cc.

The corresponding densities are M/V=1.0849 (min) and 1.1999 (max).

So 1.0849≤D≤1.1999. The nominal D without error=1.1404g/cc.

1.1404-1.0849=0.0555, and 1.1999-1.1404=0.0595g/cc.

Therefore the error in the density is about 0.06g/cc.