The laboratory exercises are not just about getting the right result, but about recognizing that fundamental physics principles shape your everyday experiences and underlie many of the devices that you will use in their personal and professional life.

Please do not treat them as cookbook exercises.  Permit yourself to think!  Thoughtful answers to the questions in blue will give you most of the laboratory credit.

Experiment 1:  Archimedes' Principle

An object partially or wholly immersed in a gas or liquid is acted upon by an upward buoyant force B equal to the weight w of the gas or liquid it displaces.  In this experiment you will verify this by measuring the apparent loss of weight of several submerged objects and by finding the weight of the displaced fluid.  You will also determine the density of the objects.  The PASCO Force Sensor together with the Science Workshop interface and the Data Studio software is used to measure the weights.

#### Equipment:

 Force Sensor Two containers, one with and one without overflow spout Various solid objects

#### Procedure:

Part I
Verify Archimedes' principle.  From the data below:

(a)  Determine the weight Wc of the empty container with the handle.  When the container is suspended from the force sensor, the force sensor measures the force of gravity (weight) acting on the object, and the program displays the magnitude of this force (in N) on the computer screen.
(b)  Determine the weight of an object Wo when it is suspended above the container with the overflow spout.  This container is completely filled with water, and the container with the handle standing below the spout is empty.
(c)  Determine the apparent weight of the object Wow after it has been lowered into the water.  As the object is lowered into the water, water pours out of the overflow spout.  The container with the handle has collected this water.
(d)  Determine the weight Wcw of the container with the handle holding the collected water.
Determine these weights for four different objects and record the weights in a spreadsheet as shown below
 Wc Wo Wow Wcw Ww Fb (Fb-Ww)/Fb Object 1 Object 2 Object 3 Object 4

#### Data:

Click on a small picture if you want to see an enlarged picture.

 (a) (b) (c) (d) Object 1: Object 2: Object 3: Object 4:

For each of the objects:

 Calculate the weight of the water that was displaced.  Ww = Wcw- Wc.  Record it in the spreadsheet. Calculate the difference between the weight of the object in air and its apparent weight in water.  This difference yields the buoyant force Fb.  Fb  =  Wo - Wow.  Record Fb in the spreadsheet. Compare Fb and Ww.  Calculate the percent difference = 100%(Fb - Ww)/Fb and record it in the spreadsheet.

Part II
Determine the density of the objects used in part I.

Set up labels as shown below.
 mo mw Vw ρo material Object 1 Object 2 Object 3 Object 4
Determine the mass mo of each objects by dividing its weight by the acceleration due to gravity and record it in the spreadsheet.
From the weight of the water displaced by the object calculate its mass mw and record it in the spreadsheet.
Use the density of water, 1000 kg/m3, and the mass of the displaced water, to calculate the volume Vw of the displaced water.  Record this volume in the spreadsheet.
The volume of the displaced water is the same as the volume of the object.  Calculate the density ρo of the object  (ρ = m/V) and record it in the spreadsheet.
Compare the density you found with the density of the materials ρt given in the table below.  Try to identify the material each object is made of.  If you cannot identify the material based on the density alone, also consider the appearance of the material.  (Brass and steel have a different color.)

 Material Density (kg/m3) Aluminum 2.7*103 Brass 8.7*103 Lead 11.3*103 Steel 7.9*103 Water 1.0*103

Open a Microsoft Word document and address al points highlighted in blue.

In one or two sentences state the goal of this experiment.

 According to Archimedes' principle, the buoyant force is equal to the weight of the displaced fluid.  Do your experimental results verify Archimedes' principle?  Comment on your results. Do your experimentally determined densities of the various materials agree with the densities given in the table?  Comment on your results.

Exercise 1:  Ideal Fluids

 Ideal fluids are incompressible and flow steadily without friction.  The flow is laminar and can be represented graphically by streamlines.  In a straight section of pipe with constant cross sectional area all fluid particles move with the same velocity. Real fluids have viscosity.  They flow with friction.   For viscous fluids with laminar flow, the speed of the fluid increases with distance from the walls of the pipe.  Water is a low viscosity fluid.
 Conservation of mass leads to the equation of continuity for ideal fluids.  Consider the flow of an ideal fluid through a pipe with varying cross sectional area A.  For the pipe we write the equation of continuity as A1v1 = A2v2, or Q = Av = constant.  Q is called the volume flow rate.  For a viscous, incompressible fluid with laminar flow through the pipe, we write the equation of continuity as Q = Avavg = constant.  If the density of a compressible the fluid with laminar flow is approximately constant, the equation of continuity still holds approximately.  For example, when air is flowing over an airplane wing, the equation of continuity still holds approximately. Conservation of ordered energy together with conservation of mass leads to Bernoulli’s equation for ideal fluids. P + ρgh + ½ρv2 = constant. For viscous fluids with laminar flow ordered energy is converted to thermal energy, so Bernoulli's equation cannot be strictly valid.  However, for a fluid at rest there is no frictional energy loss, and therefore Pbottom = Ptop + ρg(htop - hbottom) still holds.