Archimedes� Principle

Purpose

To illustrate Archimedes� Principle by determining the density of various materials

Apparatus

Introduction

The density of a material is defined as its mass per unit volume. The most straightforward way to determine density is by calculating the volume of a given sample from its dimensions and then dividing this into the mass, which an quickly be found with a beam balance. However, it is difficult to use this technique for an irregularly shaped sample, e.g. a rock. In such cases Archimedes� principle provides an accurate means of determining the density.

Archimedes� Principle:
A body immersed in fluid is buoyed up by a force equal to the weight of the fluid displaced.

(1)  F_b = (r_f V)g

where r_f is the density of the fluid, V is the volume of the object, and g is the gravitational acceleration constant. We can determine the density of an abject from this principle in the following way: If we measure the weight of the object when immersed in a fluid W_i and the weight outside in air W_o the difference in these forces equals the buoyant force.

(2)  W_o - W_i = F_b

Archimedes

Combining ideas (1) and (2), the volume of he object can be found.

(3)

Since the weight of the object in air W_o is just the product of its mass m and the acceleration constant g, we can find the unknown density of the object in terms of the measured weights and the known density of the fluid r_f.

(4)

When an object (x) floats in a fluid, this indicates that the density of the fluid is greater than the density of the object.  In this case, the buoyant force is equal to the weight of the object.

(5)

1.   Examine the beam balance and note the platform on which the beaker or water can be placed.

2.   Find the weight of the copper sample in air, then in water.

3.   Determine its density and compare this with the accepted value.

4.   Now that you have determined the density of copper, perform the experiment again using an unknown fluid instead of water.  Use the accepted value for the density of copper to calculate the density of the unknown fluid.  Compare this density to a table to determine the type of fluid.

5.   The Copper sample readily sinks in the water because it is more dense, but the wood block is less dense and will not sink on its own.  Being careful not to exert a vertical force on the wood block, balance it so that it floats in the water, then remove the block and measure the height of the water mark.  Using equation (5), explain why the density of the wood is equal to the height of the water mark divided by the total height.  Compare this density to a table to determine the type of wood.