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 the laboratories as cookbook exercises. Permit yourself to think! Thoughtful answers to the questions in blue will give you most of the laboratory credit.
In this you will determine the density of a metal block by applying Archimedes' principle. You will also explore some of the consequences of the equation of continuity and Bernoulli's equation.
Open a Microsoft Word document to keep a log of your experimental procedures and your results. This log will form the basis of your lab report. Address the points highlighted in blue. Answer all questions.
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. A PASCO Force Sensor is used to measure the weights.
Part I
Verify Archimedes' principle. From the data below:
(a) Determine the weight W_{c} 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 W_{o} 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 W_{ow} 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 W_{cw} 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
W_{c} | W_{o} | W_{ow} | W_{cw} | W_{w} | F_{b} | (F_{b}-W_{w})/F_{b} | |
---|---|---|---|---|---|---|---|
Object 1 | |||||||
Object 2 | |||||||
Object 3 | |||||||
Object 4 |
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:
Part II
Determine the density of the objects used in part I.
Extend your Excel spreadsheet. Set up labels as shown below.
m_{o} | m_{w} | V_{w} | ρ_{o} | material | |
---|---|---|---|---|---|
Object 1 | |||||
Object 2 | |||||
Object 3 | |||||
Object 4 |
Material | Density (kg/m^{3}) |
---|---|
Aluminum | 2.7*10^{3} |
Brass | 8.7*10^{3} |
Lead | 11.3*10^{3} |
Steel | 7.9*10^{3} |
Water | 1.0*10^{3} |
Log entries:
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 A_{1}v_{1} = A_{2}v_{2}, 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 = Av_{avg} = 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 + ½ρv^{2 }= 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
P_{bottom} = P_{top} + ρg(h_{top}
- h_{bottom}) still holds.
Do the following exercises and add answers to the questions in blue to your Word document.
(a) Lay your hands on the table in front of you and locate a bulging
vein. Slowly raise your hand until it is well above your head while
constantly watching that vein. What happens? What
height above your shoulders do you first notice a change? Describe your
observations.
Slowly lower your hand while still watching the vein.
Repeat the process. Do you have an explanation for your observations?
(b) Lay two thick books about 10 cm apart. Place a sheet of paper on the books so that it bridges the gap between them. Try to blow the paper off the books by blowing underneath it. Describe what happens. Do you have an explanation for your observations?
(c) Hold two sheets of paper vertically about 5 cm apart. Blow the sheets apart by blowing hard between them. Describe what happens. Do you have an explanation for your observations?
(d) Cut a drinking straw into roughly two equal length pieces. Hold one piece upright in a glass of water so that the top projects over the top of the glass. Place the second piece perpendicular to the first so that the end of the second piece is almost touching the opening of the first, but is not blocking it. Blow hard through the second piece. Describe what happens. Do you have an explanation for your observations?
Convert your log into a lab report.
Name:
E-mail address:
Laboratory 1 Report
Save your Word document (your name_lab1.docx), go to Canvas, Assignments, Lab 1, and submit your document.