Archimedes' Law Demo

P115/P116 Laboratory Demonstration #17

* Immerse aluminum block in water and measure displaced volume.
* Measure apparent weight of immersed block.
* Calculate the density, using water density as reference.

Further information on Theory, Apparatus, and Procedure is available. The equipment for this demo is stored in Rockefeller rooms 302 and 302B.

The purpose is to demonstrate Archimedes' Law by calculating the density of aluminum and then comparing the result with known textbook values. In a complete version of the experiment, one immerses the block in a vessel which is itself placed in initial equilibrium on a pan balance. The measured weight reduction of the aluminum after immersion should very closely equal the added apparent weight of the vessel.

Theory

A body submerged in a fluid experiences a buoyant force equal to the weight of the displaced fluid. Let WA be the weight of the aluminum in air, WW be the weight of the aluminum when submerged, and w be the weight of an equal volume of water.The ratio of the density (D) of the aluminum to the density (d) of the water is equal to the weight (W) of the aluminum divided by the weight (w) of the water displaced. One measures w by measuring WA-WW and INVOKING the principle, or by measuring the displaced volume of water, using the known density of water, and PROVING the principle. The density of the aluminum is then given by:

D = d[WA/(WA-WW)]

Apparatus

The equipment needed for this demo is:

* a piece of aluminum with wire support
* a spring scale, and a large beaker full of water
* a sample setup with a 1000 ml beaker is available in 302-Cabinet D
* the 500 cc mass weighs 1.35 Kg in air and 0.850 Kg in water. Unfortunately, both the beaker and the aluminum block often are pressed into service for other purposes, so check for availability ahead of time!


A more complete demonstration is provided by placing the beaker on a pan balance, and noting that the upward force of the water on the aluminum (i.e. the reduction in apparent weight) that shows up as an apparent increase in weight of the beaker full of water. Suitable pan balances can be borrowed from room 403. The above picture from "Physics Demonstrations Experiments" by H. F. Meiners shows how to do it with two conventional balances, but a spring balance is a better choice to suspend the aluminum block unless very high accuracy is desired.

Procedure

Weigh the aluminum in air, then in water. Measure the volume of water displaced, either using the calibration marks on the beaker or measuring the beaker diameter and the rise in water level. Calculate the value for the density and compare to the accepted textbook value. A spring balance is the easiest type to use for weighing the block. For purists, we have some which read in Newtons, but they have a minimum detectable mass of about 0.5 kg, so you will probably be stuck with a spring balance which reads in grams, unless you have a big piece of Al.

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