Archimedes’ Principle
Goal: To design and carry out a measurement of specific gravity using
Archimedes’ principle and Hooke’s law with a limited set of measuring tools.
Lab Preparation
Read through the following material. Knowing how to do problems using
Archimedes’ principle would also be very helpful for this lab.
Specific gravity. The specific gravity of a material is the ratio of its density to the
density of water. Since the density of water is 1.00 g/cm3, the specific gravity
also corresponds to the numerical value of the density of the object when density
is measured in g/cm3.
!
Specific gravity = ! !
!
Here, 𝜌x is equal to the density of the object and 𝜌w is the density of water.
Hooke’s law. Hooke’s law states that the amount of stretch (or compression) of a
spring is directly proportional to the applied force. The ratio of force to stretch is
called the spring constant. Hooke’s law is often written in the form
F = kx
where F is the magnitude of the force, k is the spring constant, and x is the
amount of stretch (which is the magnitude of the displacement from equilibrium
position).
Archimedes’ principle. Archimedes’ principles states the following:
An immersed object is buoyed up by a force equal to the weight of the fluid it displaces.
If we let FB represent the buoyant force and Wdis represent the weight of the fluid
displaced then Archimedes principle can be written in equation form as
FB = Wdis.
Equipment
For this lab you are provide with water, a spring, a beaker, some string, a ruler,
and an irregularly shaped object whose specific gravity you are to determine.
1 Procedure
I. Specific gravity of a solid
Consider the diagrams below that show an object X that you are to find the
specific gravity of. The diagrams show the object suspended by a spring in air
and in a fluid. Also indicated at the end of the spring is a brass weight. Here,
the brass weight attached to the end of the spring is there merely to ensure that
the spring is always slightly extended and will then follow Hooke’s law. Thus
consider the equilibrium length of the spring to be the length when just the brass
weight is attached.
brass weight X
X
A. Draw diagrams that illustrate the system (a) without the object; (b) with
the object hanging in air; (c) with object hanging, but immersed in water.
B.
For both cases (b) and (c) above draw the freebody diagram for the object
with vectors showing all forces acting on the object.
C. Apply Newton’s 2nd law (ΣF = ma) to each freebody diagram. Use
Hooke’s law to express some forces in terms of distances that can be
measured (these should be indicated in your first 3 sketches drawn
previously). Use symbols, not numbers, throughout. Find a way to
eliminate everything except measurable distances and the ratio of
!
densities ! ! and arrive at an expression for the specific gravity of the
!
object.
D. Using only the equipment provided invent and execute a method to
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measure ! ! for the sample provided. Your lab team should discuss
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options and possible methods and settle on a single satisfactory approach.
Make revisions to your method as necessary after trying it. Clearly
present your measurements and show your calculations to find the
specific gravity of your object.
2 II. Specific gravity of a liquid
Incorporate your previous results from part I, and develop an equation to
determine the specific gravity
!!
!!
of the additional liquid provided.
*Please return the liquid to the proper container when finished and make sure
your lab station is cleaned up.
Homework
1. How many significant figures are there in your measurements with your
solid sample?
2. How many significant figures are warranted in your final result from part I?
3. Comment on how reasonable your results were from parts I and II of the lab.
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