# Density Experiment

## Density Experiment

Carleton University
Laboratory Report
Course #:PHYS 1007Experiment #: 1

MEASUREMENT OF DENSITY
Name:
Student #:
Date Performed: 22nd September 2014
Date Submitted: 6th October 2014
Lab Period:
Partner:
Station #: 13
TA:
PURPOSE:
The purpose of this lab is to find the density of a solid cylinder using two methods; 1) A direct application of the density formula and 2) Using the Archimedes’ principle. We would also like to estimate the errors during the experiment and compare them to accepted values.
THEORY:
Direct method:
In the first part of the experiment, the direct method was applied in order to calculate the density. The density of a substance is defined by its mass per unit volume. It has the symbol ρ and can be written as ρ=MV. Where M is the mass of the object and V is its volume. In this experiment, the density of a metal cylinder was determined in terms of its mass (M), length (l) and diameter (d).
For a cross section of a cylinder where A denotes the surface area, the density is:
ρ=4Mπld2 (1)
The error to this value of density can be given by σp=σmM2+σll2+2²(σdd)² (2)
Archimedes’ Principle:
In the second part of this experiment, the Archimedes’ principle was used to find the density. In theory, the density found in the first part should be the same as the one calculated here.
Archimedes’ principle states that when an object is either partially or fully immersed in a fluid, an upward buoyant force is exerted on the body. This force is equal to the weight of the fluid that is displaced by the body:
F = ma = ρf Vf g (3)
In the above equation, 𝑔 is the acceleration due to gravity, 𝜌f the density of the fluid and 𝑉f, the volume of fluid displaced.
The weight of the object in water is given by:...