# lab report

## lab report

Purpose:

We plan measure the density of a solid cylinder by putting the cylinder in air and water respectively. The density of the solid cylinder should be consistent with each other. Therefore, we estimate the experimental errors on these measurements, and find the average value to compare.

Theory

The density, ρ (rho), represent the mass of an object per unit volume. In this experiment, the density of cylinder determined by Mass, Volume, and the length(l),and the diameter (d ),the surface area (A), the V=Al, and A= πd2/4.

ρ = 4M/ πld2 (Eq.1)

The error on the density:

σρ = ρ √( σM/M)2 + (σl /l)2 +22 (σd /d)2 (Eq.2)

In the second part, we use Archimedes’ principle to find the density of the same object (ρA). The Archimedes’ principle states that an object, wholly or particularly immersed in a fluid, the force pointing vertically up(F), equal in magnitude to the weight of the displaced fluid,

F= Ma= ρf Vf g (Eq.3)

We can find the density of cylinder is :

ρ A = ρw (Mair /Mair -Mwater ) (Eq.4)

The error on density is :

σ PA = ρW√ (MwaterσMair / Mair -Mwater )2 +( Mair σMwater /( Mair -Mwater) 2 )2

(Eq.5)

The final value is :

ρD =( density+ error)g/cm3 (Eq.6)

Apparatus:

For the first part, we use the Vernier Caliper to measure the diameter, the precision of Vernier is 0.05mm.Then using the 0.01mm of precision to measure length....