ARCHIMEDES' PRINCIPLE
Experiment No. ___1____
1
OBJECTIVE:
To study Archimedes' Principle and to measure the density and specific gravity of solids
and liquids by immersion method.
APPARATUS:
Beam balance, 400 ml. beaker, light wooden block, metal cylinder, light and heavy
hydrometers, hydrometer jars, alcohol and salt solution, and Mohr-Westphal balance (if
available).
FOREWORD:
Density of a specimen is defined as the ratio of its mass to its volume. It is expressed in
grams per-cubic centimeter, kilograms per cubic meter and slugs per cubic foot.
Weight density of a specimen is defined as the ratio of its weight to its volume. It is expressed
in dynes per cubic centimeter, newtons per cubic meter and pounds cubic foot.
d = m/V; D = w/V; hence, D = dg.
(1)
where d is the mass density and D is the weight density of the specimen. The specific gravity of the
specimen is the ratio of the density of the specimen to that of water. In symbols,
density of the specimen
Specific Gravity = ----------------------------density of water
(2)
Archimede's Principle states that an object immersed in a fluid is buoyed up by a force equal to
the weight of the displaced fluid. The volume of the specimen, no matter how irregular it is, is always
equal to the volume of the fluid displaced. By knowing the buoyant force exerted by the fluid on the
immersed object and the density of the displaced fluid, one can then determine the volume of the
submerged object and hence its density. For solids denser than water, the specific gravity is given by
the equation:
weight in air
Sp. Gr. = ---------------------------------apparent loss of weight in water
or
weight in air
Sp. Gr. = ---------------------------------weight in air - weight in water
(3)
For solids lighter than water, a sinker is used.
weight in air
Sp. Gr. = --------------------------------------------wt. of specimen in air _ wt. of specimen and sinker
and sinker in water
both in water
(4)
In getting the specific gravity and density of the liquids, immersion method is applied with the
use of a sinker immersed in the liquid to which its specific gravity is to be measured.
wt. of sinker in air - wt. of sinker in liquid
Sp. Gr. = ---------------------------------------------------apparent loss of weight in water
(5)
2
or
wt. of sinker in air - wt. of sinker in liquid
Sp. Gr. = ---------------------------------------------------wt. of sinker in air - wt. of sinker in water
(6)
Once the specific gravity of a specimen is obtained, its density can easily be obtained by using
the equation that
density = specific gravity X density of water
Hydrometer is an instrument used for direct measurement of the specific gravity of liquids. It
consists of a closed graduated glass tube with a weighted bulb at the lower end. The specific gravity of
the liquid in which it floats is read directly on the calibrated scale that lies on the liquid level (lower
miniscus).
PROCEDURE:
1.
Weigh the metal cylinder in air, then in water, in salt solution, and in alcohol. In weighing the cylinder
in the liquid specimens, the metal cylinder must be fully immersed but must not touch the beaker.
2.
Weigh the wooden block in air. Then attach the metal cylinder to the wooden block by means of a light
string and weigh the system with the wooden block in air and the metal cylinder in water. Then weigh
them again when both are immersed in water.
3.
Study the scales of hydrometer. Then let them float in the liquid specimen in the jars. Observe and
record the readings of the scales at the liquid levels. These readings are the densities of the liquids in
the metric system.
4.
If available: Set up the Mohr-Westphal balance on the table. Adjust its height so that the plummet may
be fully immersed in the liquid specimen in the small jar. Hang the plummet at the end of the beam
and adjust the screw at the base of the instrument so that the pointers of the beam and the frame are in
line. This is done with the plummet in the air. Immerse the plummet now in salt solution and restore
the balance condition by placing and adjusting riders on the beam. The riders must be placed on the
notches of the beam. If two riders are required to be placed at the same position, hang the smaller rider
from the hook of the bigger rider. Record the riders used and their respective positions. Repeat with
the plummet immersed in alcohol.
3
TABULATIONS:
Table 1.
Weight of metal cylinder in air
Weight of metal cylinder in water
Weight of metal cylinder in salt solution
Weight of metal cylinder in alcohol
Specific gravity of metal solution
Experimental density of a metal cylinder
Specific gravity of salt solution
Experimental density of salt solution
Specific gravity of alcohol
Experimental density of alcohol
Standard density of metal cylinder
Standard density of salt solution
Standard density of alcohol
Percentage error of metal cylinder
Percentage error of salt solution
Percentage error of alcohol
Table 2.
Weight of paraffin in air
Weight of paraffin in air and cylinder in water
Weight of paraffin and cylinder both in water
Specific gravity of paraffin
Experimental density of paraffin
Standard density of paraffin
Percentage error
Table 3.
Specific gravity of salt solution
Specific gravity of alcohol
Experimental density of salt solution
Experimental density of alcohol
Percentage error for salt solution
Percentage error for alcohol
Table 4. Mohr-Westphal Balance
For salt solution
For alcohol
Riders
1
2
3
1
2
3
Position
COMPUTATIONS:
4
1.
From the data of step 1, compute the density and specific gravity of the metal cylinder, salt solution and
alcohol. Compare the density of the material with the value in the Physics Handbook.
2.
From step 2, compute the density and specific gravity of paraffin and compare it with the value of the
hydrometer.
3.
Compare the density of salt solution and alcohol obtained in computation 1 with the readings of the
hydrometers.
4.
From the data obtained in step 4, compute the specific gravity of each liquid and compare the value
from those obtained by using the hydrometers.
The three riders have relative weights of 1, 0.1, and 0.01. Each kind of rider comes in pairs. The
plummet and its components area so constructed that, when it is immersed in water, the state of balance
can be restored by hanging the first rider in the hook, same position as the plummet. We can say then,
that the buoyant force of water on the plummet is equal to 1.
The specific gravity of other liquids can, therefore, be determined by knowing the riders being
used and their positions. The first rider takes two positions in the value of specific gravity, namely, the
whole number and the first decimal place. The second and the third riders take the second and the third
decimal places respectively. For instance, if the first rider is present in the hook and also in the third
notch, while the second rider is on the fifth notch and the third rider is on the second notch, then, the
specific gravity of the liquid that is being tested is 1.352.
Questions and Problems
1. Ice cubes float in glass of water filled to the brim. As the ice melts, will the glass overflow?
2. Why do we float easier in salt water than in fresh water?
3. A 2-kg aluminum block has an apparent mass of 1.7 kg in a certain liquid. Find the density of the liquid.
4. A ring that is made of an alloy of silver and gold is made to have a density of 13 g/cc. and a mass of 52
grams. What mass of gold was used?