laboratory manual physics 1401 - al akhawayn universityphysics_lab/labman/phy1401_lab... ·...
Post on 27-Mar-2020
2 Views
Preview:
TRANSCRIPT
1
School of School of School of School of Science &Science &Science &Science & Engineering Engineering Engineering Engineering
LABORATORY MANUAL
PHYSICS 1401
Cours : Phy 1401
Semester : Fall 2008
By : Dr.Khalid Loudyi
2
Table of Content
INFORMATIONS AND INSTRUCTIONS FOR GENERAL PHYSICS LABORATORIES....3 PHYSICS LABORATORY RULES ......................................................................................................... 4 LABORATORY SUPPLIES & EQUIPMENT ........................................................................5
The experiments:
GRAPHS AND GRAPHICAL ANALYSIS .............................................................................6 THE MEASUREMENT OF MASS, LENGTH AND TIME ...................................................11 VECTORS AND EQUILIBRIUM.........................................................................................19 ONE DIMENSIONAL MOTION ..........................................................................................25 ATWOOD'S PULLEY.........................................................................................................32 WORK AND ENERGY IN THE SIMPLE PENDULUM .......................................................38 ELASTIC PROPERTIES OF DEFORMABLE BODIES......................................................43 ROTATIONAL INERTIA, ANGULAR MOTION ..................................................................48 THE SIMPLE PENDULUM ................................................................................................54 BUOYANT FORCES..........................................................................................................61 LINEAR EXPANSION OF A SOLID MATERIAL ................................................................66 GAS LAWS ( BOYLE’S AND GAY-LUSSAC’S LAW) ........................................................71
3
INFORMATIONS AND INSTRUCTIONS FOR GENERAL PHYSICS LABORATORIES
In science, no idea is accepted, no theory is believed, until they have been tested, then tested
again. Only then can the truth of the theory emerge. The ultimate test of any physical theory is by
experiment. This reliance on experiment differentiates science form other important human activities.
Unfortunately the beginning student often misses the importance of experiment to physics. Years or
centuries after the crucial experiments have been done, the student finds scientific truth by studying a
textbook. To show the student the importance of experiment in establishing "truth", we provide the
Physics Laboratory as part of your General Physics Course. The physical laws make predictions. We
do experiments to see if these predictions hold true, and, if they do, then, and only then, can we have
confidence in the truth of the laws.
The goal of any science is to arrive at a simple and universal explanation of natural events.
These explanations start out as theories, and they become physical laws if they are shown to be true by
comparing their predictions with the results of many experiments. Your experience in the physics
laboratory will, in a way, be similar to that of scientists in research laboratories around the world.
However, our laboratory differs form the research laboratories of professional scientists in that we
already know what theory will be applied to explain the experimental results. This means that you will
probably not discover any new physical laws this semester in the physics lab. However, you will learn
some of the methods of experimental physics used by scientists at the forefront of physics research.
While taking a physics laboratory; you will learn how to make scientific measurements and
how to present and understand these measurements by means of graphs and tables. You will also learn
the inherent limitations of measurements by discussing error analysis. These techniques can be applied
to problems in a large number of fields, other than physics such as the social, behavioural, and life
sciences.
Finally, we want you to enjoy yourself in the physics laboratory. Those of you who plan to
make a career of science will find it immensely satisfying to verify the predictions of a scientific
theory. We also hope that those of you who do not go on to become practicing scientists take with you
the excitement of "doing" physics.
4
PHYSICS LABORATORY RULES
The following suggestions will help you do your work in the physics laboratory:
1. Report to the laboratory promptly, ready to work. Expect to remain for the full lab period.
2. Your laboratory station should have everything you need to complete the lab assignment. If you
encounter a shortage (or damaged equipment), notify your instructor immediately. Never borrow
any apparatus from another station even though it may not be in use. At the end of the lab period,
check your station and leave it in good order. Again, call attention of the instructor to any
equipment problems you may have encountered. Space at the lab station is limited. You should
have only the laboratory manual and one or two sheets of clean scratch paper at your workstation.
Books, coats, hats, large purses, etc. should be stored elsewhere.
3. No food, drink, or tobacco in any form is permitted in the laboratory.
4. Each student working on his own conducts laboratory work.
5. The laboratory is a working area. Feel free to get up and stretch or go out for a drink of water. Talk
with your fellow students or your instructor. Consult your instructor when you have a question
about your work.
6. Do not waist time. Report to your work area, review the previous week's work and return it to the
instructor (5 minutes), and then get involved in the experiment activity. Do not wait for the
instructor to tell you what to do.
7. Be prepared before you come to the lab. Read the experiment as well as any helpful information
provided in the introductory portion of the laboratory manual before you attend lab. Failure to be
prepared will cause delays and you may not be able to complete the experiment in the allotted time.
8. Always keep your emphasis on quality of work and completeness of understanding. Do not set a
high priority on the amount of work accomplished in a laboratory period.
5
LABORATORY SUPPLIES & EQUIPMENT
This laboratory manual contains write-ups of experiments to be performed during the semester,
as well as materials explaining laboratory policies and generally accepted laboratory practices.
In addition to the laboratory manual, every student should bring the following supplies to
each lab session:
• One or two pencils (We prefer that you use pencil instead of pen in the laboratory.)
• A good eraser
• A combination straightedge and protractor.
• Bring your own calculator and DO NOT plan to borrow one from your laboratory partner
NOTE: We do not allow students to fail to buy these materials and then borrow them
from other students during the lab. There will be no need to carry your physics textbook to the
laboratory. The current experiment should be read before coming to each lab period.
6
EXPERIMENT 1
GRAPHS AND GRAPHICAL ANALYSIS
INTRODUCTION
In the physics laboratories the student is often asked to make a graph of the data he has gathered, and
usually the graph is the technique by which the data is analysed. It is therefore important for the student to have a good idea of how to go about plotting a graph, and how a graph may be used to analyse (particularly, non-linear) data.
In this experiment you will: (a) learn to quickly, and accurately plot a graph. (b) Learn using graphical techniques to analyse laboratory data.
THEORY
1. What is to be plotted?
When the student is told to plot, say, S versus (vrs) t, it is accepted that this means: 1) S is the dependent variable, plotted on the "y" or vertical axis; and, 2) t is the independent variable, to be plotted on the "x" or horizontal axis. This is a convention (agreement) which should be memorised.
2. Choice of Scale.
The scale of a graph is the number of (usually) centimetres of length of graph paper allotted to a unit
of the variable being plotted. For example, 1 cm for each 10 seconds of time. In general the scales for the x and y axes may be different. There are two criteria for choosing the scale of a graph, range of the variable, and convenience in
plotting:
a) range of the variable: Suppose the range of values of S is from 5 cm to 125 cm. We then need a scale for S that allows us to plot values from 0 to values somewhat greater than 125 cm. Notice that (unless told to do so by the instructor) we do not choose to suppress the zero of the graph and start the S scale from 5 cm. The reason is that we may later need to use the graph to find values extrapolated (continued) to the zero.
Also we usually try to allow space on the graph for values somewhat greater than the largest value (in this example, 125 cm) because we may take a little more data in the experiment, with larger values, or we might want to extrapolate the graph to larger values.
Finally the scale should be chosen to most nearly use the whole of the graph paper. Just because a choice of, say, l cm to represent 1 sec of time makes the graph easy to plot, we should not do this if it makes the graph only occupy a small part of the whole paper and be hard to read and use. b) Convenience in Plotting: It turns out (as we shall see in an exercise in this lab) that scales of 1, 2, 5, and 10 (and multiples of 10 of these) per centimetre are easiest to use; a scale of 4 per centimetre is somewhat more difficult, but can be used; but scales of 3, 6, 7 , 9, etc.. per centimeter are very difficult and should be avoided. In choosing scales it sometimes helps to turn the paper so that the "x-axis" is either the long or short dimension of the paper.
3. Label the Axes and put a title to the graph
The vertical and horizontal axes of the paper should carry labels of the quantities to be plotted, with units. In our previous example the label on the y-axis would be: S(cm). The graph itself should have a title. In our example the title is: Plot of S vrs t.
7
4. Circle your Data Points
Each data point should have a neat circle drawn around it. If more than one experimental trial is used one can use circles, triangles, squares, with a legend to distinguish these.
5. Put a Smooth Solid Curve through the Data Points
This can be done "by hand" or with a plotting aid. Ignore any points that fall far outside the curve
(after checking that they are plotted correctly). A dashed line should indicate extrapolations to larger or
smaller values, outside of the range of data taken.
6.Graphical Analysis
Often we have data (x, y) which we believe follows the theoretical relation y = rnx + b; we can verify
this relation if we obtain a straight line when we plot y vrs x. Also, the plot obtained allows us to find the
values of m and b as follows: b = y-intercept of graph (value of y when x = 0) m = slope of graph = ∆y/∆x = (Y2-Y1)/(X2-X1 )
Other times we have data that we believe follows a non-linear theoretical relation. For example consider S = (1/2)at². We can verify this relation by plotting S vrs t². If this relationship holds then the graph will be a straight line with intercept zero. The slope of the graph then gives the constant a/2. remarks: The points chosen to determine the slope should be relatively far apart. Points corresponding to data points should not be chosen, even if they appear to lie on the line.
EXPERIMENTAL PROCEDURE
Exercise 1.
Consider the following data:
S (m) 0.27 1.08 2.43 4.32 6.75 9.72
t(sec) 0.10 0.20 0.30 0.40 0.50 0.60
• On a sheet of graph paper draw 5 lines parallel to the y-axis, each separated by a few centimetres. Plot
the values of S on the 5 lines to the following scales (with some scales you may not be able to plot all points):
a) 1 m equivalent to l cm.
b) 1 m equivalent to 2cm.
c) 1 m equivalent to 3cm.
d) 1 m equivalent to 5cm.
e) 1 m equivalent to 7 cm.
• Which scales are easy to plot?
• Which scales are difficult? Explain why.
Y (units)
X (units)
(x1, y1)
(x2, y2)
∆x
∆y
y-intercept y = mx + b
8
Exercise 2.
• Plot a graph of S Vs t.
• Does this plot give a straight line?
Exercise 3.
• On the same graph paper as for exercise 2, plot a graph of S vrs. t². This should give a straight-line plot.
• What is the y-intercept of this graph?
• What is the slope of the straight line? (Include units.)
Conclusion:
Conclusions are a necessary part of every experiment. The main purpose of the conclusions is to
summarise the following:
• What was investigated? i.e. relate to how the purpose was confirmed or contradicted. What was found?
i.e. outcome of graphs and main qualitative/quantitative results • What can be interpreted? i.e. significance of graphs/results and correlation to theory • Lastly, you would discuss reasons for any serious discrepancy and any major problems encountered in
the experiment (and perhaps suggestions for improvement). When comparing experimental results to expected values, it is important to quote the result together with its associated uncertainty (error). If the difference between experimental and expected values is greater than the expected uncertainty, you should note the disagreement and give possible reasons for the discrepancy (sources of errors). If the experiment deviates from theory, then you can try to explain the deviation, or perhaps, modify the theory to account for the behaviour. For example, theory often assumes idealised conditions, but in the actual experiment these ideal conditions may not be true.
EXPERIMENT 1
GRAPHS AND GRAPHICAL ANALYSIS
NAME: . DATE: .
SECTION: .
THIS ¨PAGE NEEDS TO BE DONE AT HOME BEFORE COMING TO THE LAB. SESSION
1. EXPERIMENTAL PURPOSE:
State the purpose of the experiment.( 5 points )
2. Answer Pre Lab Question (5 points)
:
PHY 1401 LABORATORY REPORT
10
3. RESULTS AND ANALYSIS
Exercise 1:
Graphs of S with different scales in attached graph paper: (15 points)
Questions (15 points)
Exercise 2 : Graph of S vrs. t in attached graph paper: (20 points)
Questions (5 points)
Exercise 3:
Graph of S vrs. t² in attached graph paper: (15 points)
Questions (10 points)
Conclusions: (10 points)
11
EXPERIMENT 2
THE MEASUREMENT OF MASS, LENGTH AND TIME
INTRODUCTION: The purpose of this experiment is to familiarise you with the basic measurement necessary to make physical observations. The procedures outlined illustrate the difference between basic physical quantities(e.g. mass, length and time) and derived quantities (e.g. volume, area and density). The units used to describe these quantities are also introduced, and appreciation of the
methods and accuracy by which these quantities can be measured. BACKGROUND: Physics is fundamental an observational science. All “laws”, ”theories”, ”principles”, ...etc. are based upon experimental observation. We observe nature, and then devise laws and theories, ...etc. to explain our observations. We then test our theories by using them to predict what will happen given a certain set of conditions. We set up those conditions in experiments and in this way make further observations that either support or deny our original theory. It becomes clear then that a fundamental aspect of physics is the ability to make accurate observations. The observations themselves usually consist of detailed measurements. Often, our theories stand or fall based on the accuracy with which we can make these measurements. The quantities length , mass and time are the so-called base quantities in mechanics; their corresponding units are called the base units. The word base refers to the fact that they cannot be defined in terms of any other quantities or units; they are fundamental “building blocks” of all other quantities. That is all other quantities can be defined in terms of mass, length and time. These latter quantities are called derived quantities and the corresponding units are derived units. As a simple example, the derived quantity density is defined in terms of the base quantities mass and length, thus:
Density = Mass/Volume or, similarly, speed is derived thus:
Speed = Distance/Time
Thus, the accuracy with which density (for example) can be measured depends upon the accuracy with which length and mass can be measured.
THE EXPERIMENT: 1- Experimental Apparatus:
The apparatus for this experiment consists of: plastic ruler, meter stick, electronic balance, Ohaus balance, pair of callipers, micrometer gauge, graduated cylinder, stopwatch, and a variety of objects for measurement. 2- Experimental Procedure:
A. Measurements of Regular Shaped Objects
a) Steel cylinder measurements using meter stick and pan balance:
12
• Measure the length and diameter of the steel cylinder using the meter stick record the result in the data table in your laboratory report. You should make the measurement several times and then compare results - this is one of the best way to avoid careless results in the laboratory work.
• Measure the mass of the cylinder using the pan (Ohaus) balance.
• Calculate the volume of the steel cylinder. The volume of a cylinder is the product of its height (h) and its cross-sectional area, namely:
V h r= π 2
where r is the cylinder’s radius.
• Calculate the density of the steel cylinder in the space provided and record your answer in the table. SHOW YOUR WORK, showing the correct use of units and significant figures. The density of the cylinder is then its mass (M) divided by its volume:
ρ =M
V
b) Steel cylinder measurements using vernier calliper and electronic balance:
Another useful instrument for measuring length is the vernier calliper, shown schematically in Fig 1
FIGURE 1: A vernier calliper,
• Take several readings of the length and diameter of the cylinder with the vernier calliper. When you are satisfied with your answer, record the data in the second row of the table.
• Now use the electronic balance to measure the mass of the cylinder.
• Recalculate the volume and density and show your work in the appropriate section of your laboratory report.
c) Steel sphere measurements using vernier calliper and electronic balance:
13
• Measure the diameter of the sphere with the vernier calliper. When you are satisfied with your answer, record the data in the third row of the table.
• Measure the mass of the sphere by using the electronic balance.
• Calculate the density of the steel sphere. Note that the volume of a sphere is given by:
V r=4
3
3π
where r is the radius of the sphere. d) Steel sphere measurements using micrometer and electronic balance: The micrometer calliper is an instrument used for the accurate measurement of short lengths (see Figure 2).
FIGURE 2: A micrometer calliper
• Measure the diameter of the steel ball using the micrometer and record it on the fourth row of Table I.
• Calculate the density of the steel ball.
• Compare this measurement with those that you’ve made earlier. B. Measurements of Irregular Shaped Objects The above measurements were straightforward because of the regular shape of the objects concerned. The volumes of these objects were easy to calculate using prescribed formulae. However, what about irregular shaped objects, such as the rock provided in this experiment? To calculate the volume of such objects is difficult, if not impossible. To determine the density thus requires a separate measurement (i.e. not a calculation) of the volume. To do this proceed by:
• Measuring the mass of the rock using the electronic balance.
• Fill the graduated cylinder about half-full of water and note the level to which the water rises in the cylinder. Fully immerse the rock fragment in the water, and note the new water level. Subtraction of two readings gives the volume of the rock..
• Calculate the rock’s density. Show all your data and your calculations in the space provided in the laboratory report.
C. Time Measurements
• Familiarise yourself with the operation of the stopwatch. Experiment to determine the shortest time interval that you can measure.
14
• Construct a ramp by taping one end of the plastic ruler and elevating one end by about 1/4 of an inch. -use a pencil or a thin notebook.
• Let the steel ball roll down the ramp and on to the table, and determine the time taken for the ball to roll over a distance of 1 m on the table. Record your results in the data table.
• Repeat the measurement three times and determine the average time value.
• From this calculate the average speed of the ball The average speed, defined as:
average speed = length traveled
time taken
D. Percent Difference and Errors a) If you have measured the same quantity more than one-way, one can calculate the percent difference between the two results. This is defined as:
100tsmeasuremen twoof average
tsmeasuremen twobetween differencedifference% x=
• Calculate the percent difference in the two values you obtained for the density of the steel cylinder, the values obtained in row 1 and row 2 of the data table I.
b) If a “true” or reference value is known for the measured quantity, one calculate a percent error for the experimental result, thus:
100 valuereference
valuereferencevalue alexperimenterror% ×
−=
• Calculate the percent error in your experimental value for this quantity (use the value obtained in row 4 of the data table I). Assume the reference value for the density of steel as 7.8 g/cm3.
• List reasons (other than measurement errors) why your measured value for the density of steel may differ from the accepted value.
c) The smallest sub-division marked on a measuring instrument is sometimes called the least measure of the instrument.
• List the measuring instruments used in this experiment and note their least measure. d) When making experimental measurements one can also expect error due to imprecision in the measurement. Thus one defines:
100measured quantity theof magnitude
instrument the of measureleast error expected ×=
• Calculate the expected errors for the diameter of the steel cylinder using the meter stick, and using the vernier callipers. Also calculate the expected error in the measurement of the diameter of the steel sphere using the micrometer gauge.
15
EXPERIMENT 2
THE MEASUREMENT OF MASS, LENGTH AND TIME
NAME . DATE: . SECTION: . THIS ¨PAGE NEEDS TO BE DONE AT HOME BEFORE COMING TO THE LAB. SESSION
1. EXPERIMENTAL PURPOSE: State the purpose of the experiment.( 5 points ) 2. EXPERIMENTAL PROCEDURES AND APPARATUS: (5 points ) Briefly outline the apparatus General procedures adopted.
PHY 1401 LABORATORY REPORT
16
3. RESULTS AND ANALYSIS A. Measurements for Regular Shaped Objects
Data (15 points )
Data Table I: Density of Selected Solids
Object Measured
Measuring Instrument
Length (cm)
Diameter (cm)
Mass (g)
Volume (cm3)
Density (g/cm3)
Steel Cylinder Meter Stick
Steel Cylinder Vernier Calliper
Steel Sphere Vernier Calliper
Steel Sphere Micrometer
Calculations Show your work Volume of cylinder (using meter stick) (5 points) Density of cylinder (using meter stick ) (5 points) Volumes of cylinder and steel ball (using vernier-callipers ) ( 5 points ) Densities of cylinder and steel ball (using vernier-callipers ) ( 5 points ) Volumes and Densities of steel ball (using micrometer ) ( 5 points )
17
B. Measurements for Irregular Shaped Objects: Rock (10 points) Volume of water (before rock immersed): Volume of water (after rock immersed): Volume of rock: Mass of rock: Density of rock: C. Time measurements
Table 3 (5 points )
Average speed calculations: (5 points)
18
D. Percent Difference and Error a) Density of steel; percent difference (5 points) b) Density of steel; percent Error (5 points) Reasons for percent difference and percent error (5 points) c) Least Measures (5 points )
d) Expected Errors (5 points)
19
EXPERIMENT 3
VECTORS AND EQUILIBRIUM
INTRODUCTION:
The purpose of this experiment is to confirm the laws of vector addition, and to study the
equilibrium of force vectors at a point.
BACKGROUND:
A scalar is a quantity that has magnitude only; examples are temperature, mass, and density. A
vector is a quantity that has both magnitude and direction; examples are velocity, acceleration, and force.
A vector may be represented by a straight line in the direction of the vector, with the length of the
line proportional to its magnitude. Placing an arrowhead at the end of the line indicates the direction of the vector.
Vectors may be added. The sum or resultant of two or more vectors is defined as the single vector
that produces the same effect. Figure 1 shows the resultant of two forces A and B.
The resultant is defined as the force equal and opposite to the resultant as shown in Figure 1. If the
resultant is added to the sum of A and B the sum of the forces equals zero, and the system of forces is in
equilibrium.
Vector addition may be accomplished graphically or analytically. Using the graphical method for
more than two forces we have the polygon method of vector addition: the vectors to be added are placed so
that the tail of the second is on the head of the first vector, maintaining their original directions. The tail of
the third vector is placed on the head of the second vector, etc. when all the vectors are in place, the side which closes the polygon is the resultant of the vectors. This is shown in figure 2, for the addition of vectors
A, B, C, and D. If the polygon closes by itself, the resultant is equal to zero and the vectors, if representing
forces, are in equilibrium.
Then addition of the two vectors is most conveniently carried out by the parallelogram method shown
in figure 4.
Equilibrant
Resulant
A
B
A
B R
Figure.3: Polygon method for addition of two vectors A, B
Fig. 4. The Parallelogram method to add two vectors
A, B
180
270
90
0
Resultant
A
B
Figure 1: The resultant and
equilibrant of two forces A, B.
A
B
C
D
R
Figure 2: Polygon method to
add four vectors A, B, C, D.
20
Vectors may also be added analytically, and this is preferred to the graphical method since one does
not have to make precise drawings. The method is illustrated in figure 5 for the addition of two vectors A
and B. The vectors are broken down into components:
then R = Rx i + Ry j where Rx = Ax + Bx, and Ry = Ay + By
The magnitude of R is then
R = (Rx² + Ry²)1/2 = [(Ax + Bx)² + (Ay + By)²]
1/2
while the angle that R make with the x-axis is given by
θ = tan-1(Ry/Rx) = tan
-1[(Ay + By) / (Ax + Bx)]
This method may be extended easily to the sum of any number of vectors A, B, C, etc. by just replacing the
appropriate quantities in equations (1) and (2) by sums of all the x and y components.
THE EXPERIMENT:
1- Experimental Apparatus:
Vectors and the equilibrium of forces may be most easily studied in the lab by means of the force table
shown in figure 6. The apparatus consists of: force table, weight hanger, slotted weights, ring attached to
strings, and pulleys.
2- Experimental Procedure:
θθθθA
R
A
B
θθθθB
θθθθ
iAx Ax Bx
Ay
By
y
x
Figure 5. Analytic addition of two vectors A, B
A = Ax i + Ay j B = Bx i + By j where
Ax = A cos θA Ay = A sin θA
Bx = B cos θB By = B sin θB
(1)
(2)
Figure 6: Force Table
21
Part A
• Mount a pulley on the 30° mark and suspend a total of 200 g over it. By means of a vector diagram
drawn to scale (choose your own scale) find the magnitude of the components along the 0° and 90°
directions.
• Set up on the force table 0° and 90° forces you found from the diagram. These forces are equivalent to
the original force. Test this statement by replacing the initial force at 30° by an equal force at 180° away from the initial direction, and check for equilibrium.
• Have your instructor check the equilibrium
Part B
• Mount a pulley on the 20° mark on the force table and suspend a total (including the mass holder) of
100g over it. Mount a second pulley on the 120° mark and suspend a total of 200 g over it.
• Draw a vector diagram to scale, using a scale of 20 g per centimetre, and determine graphically the
direction and magnitude of the resultant using the parallelogram method.
• Check your results so far by setting up the resultant on the force table. Putting a pulley 180° from the
calculated direction of the resultant, and suspending weights equal to the magnitude of the resultant does
this.
• Have your instructor check the equilibrium
Part C
• Mount the first two pulleys as in Part B, with the same weights as before.
• Mount a third pulley on the 220° mark and suspend a total of 150 g over it.
• Draw a vector diagram to scale and determine graphically the direction and magnitude of the resultant,
(Hint: This may be done by adding the third vector to the sum of the first two, which was obtained in
Part A.) Now set up the resultant on the force table and test it as before.
ANALYSIS:
1. Calculate analytically the magnitude and direction of the resultant in part B and compare to the graphical determination.
22
EXPERIMENT 3
VECTORS AND EQUILIBRIUM
NAME: . . DATE: . .
SECTION: . .
THIS PAGE NEEDS TO BE DONE AT HOME BEFORE COMING TO THE LAB. SESSION
1. EXPERIMENTAL PURPOSE:
State the purpose of the experiment.( 5 points )
2. EXPERIMENTAL PROCEDURES AND APPARATUS:
Briefly outline the apparatus used and the general procedures adopted. (5 points )
PHY 1401 LABORATORY REPORT
23
3. DATA and ANALYSIS:
Part A (20 points)
Attach the graphs and the analysis
Part B (25 points)
Attach the graphs and the analysis
Part C (25 points)
Attach the graphs and the analysis
24
QUESTIONS: (20 points)
25
EXPERIMENT 4
ONE DIMENSIONAL MOTION
INTRODUCTION
This experiment explores the meaning of displacement; velocity, acceleration and the relationship that
exist between them. An understanding of these concepts is essential to a later study of more complex motion
and the relationship between force and motion. The experiment allows you to record graphically the changes
in displacement, velocity and acceleration that occur when constant forces are applied to objects, using the
computer as a data acquisition and analysis tool.
THEORETICAL BACKGROUND
Displacement (distance), velocity (speed) and acceleration are three necessary concepts to be understood before one can undertake a study of the physics of motion called “kinematics”. To describe the
motion of an object we must be able to define the direction in which the motion is occurring, the speed with
which the motion occurs; and details regarding how the speed of the object changes as the motion takes place. You will have learned form your class-work that this information is contained in three vector
quantities of displacement, velocity and acceleration.
In this experiment we will be dealing only with motion in a straight line (i.e. in one dimension). In
one dimensional movement if the distance travelled by an object is ∆x and the time taken is ∆t, then the average speed of the object is simply:
t
s,speed average
∆
∆=v
The limiting value of the average velocity as the time interval ∆t approaches zero gives the instantaneous velocity,
dt
sd
t
svv
tt
vrr
=∆
∆==
→∆→∆ 00limlim
One can define the average acceleration and instantaneous acceleration in a similar way to that
already discussed. Thus we have:
t
va
∆
∆=,onaccelerati average
and
dt
sd
dt
vd
t
vaa
tt
rrrr
2
00limlim ==
∆
∆==
→∆→∆
For the special case of constant acceleration a set of equations can be derived which relate the displacements and velocities at various times to the acceleration. The derivation of these equations is given
in your textbook as,
)x(xa2vv
2
attvxx
2
t)v(vxx
avv
0
22
2
00
00
0
0−+=
+=−
+=−
+= t
26
In these equations, v0 is the original speed of the object at time, t = 0; v is the speed of the object at time t; (x
-x0) is the distance travelled in time t and a is the (constant) acceleration during this period.
Finally, we note that three quantities x, v, a can be displayed graphically as functions of time. The
figures shown below give the displacement as a function of time for two different objects. The first (object A; Figure 1) is travelling at a constant velocity such that its displacement-versus-time graph is a straight line.
The slope of the displacement-versus-time graph at any time gives the velocity at that time. Since the graph
is a straight line, the velocity must be constant and thus the instantaneous velocity must always equal the average velocity. In these circumstances, the acceleration is zero since the velocity does not change.
For object B (Figure 1) we have an example of an object undergoing constant acceleration. The
displacement versus time graph is an upward curve. This means that the object is travelling further in equal
time intervals as the motion progress -i.e. its velocity is increasing. Here the instantaneous velocity does not
equal the average velocity. The instantaneous velocity is given by the value of dx/dt -i.e. by the slope of the
tangent to the line at any point. Clearly this slope increases as time increases - in other works the object is
accelerating. To obtain the acceleration we would have to construct a velocity-versus-time curve, extracted
from the above curve, by calculating the slope of the tangent at every point. This is done in Figure 2(b) where it can be seen that the velocity-versus-time graph is a straight line.
Figure 1: Position, velocity, and acceleration as functions of time for objects A and B.
27
THE EXPERIMENT:
This experiment uses a variety of options for collecting information for the physical phenomena
described above.
1- Experimental Apparatus:
The apparatus consists of a microcomputer connected to Lab Pro Lab Interface box, an Ultrasonic
Motion Detector, a Logger program for Windows, a clamp, rods, a pulley, a wooden block, a metal cart, and
weights.
2- Experimental Procedure:
• Clamp the pulley to the edge of the table using the clamps provided.
• Fasten one end of the provided string to the metal cart and put a nut to hold the mass hanger on the other
end of the string.
• Set the provided masses on the metal cart.
• Plug the Ultrasonic Motion Detector into DIG/SONIC 1 of the LabPro interface.
• Place this motion detector on the same side as the pulley at about 50-cm distance from the metal cart.
• Make sure that the image of the cart is seen on the golden coloured plate of the motion detector.
• Pass the mass hanger over the pulley and make sure that the stretched string is parallel to the table.
• Switch on the computer, and monitor.
• Open Logger Pro using the icon on the desktop.
• From the Menu Bar, choose the File menu to open the MOTION file in Physics_Experiments folder
• Click on the Collect button of the toolbar in order to start the action of the Motion Detector (MD).
While operating the motion detector emits short bursts of 40 kHz ultrasonic sound waves from the gold
foil of the transducer. These waves fill a cone-shaped area about 15 to 20° of the axis of the centerline of
beam. The MD then “listens” for the echo of these ultrasonic waves returning to it. By timing how long
it takes for the ultrasonic waves to make the trip from the MD to an object and back; distance is
determined. The MD will report the distance to the closest object that produces a sufficiently strong
echo. Objects such as chairs and tables in the cone of ultrasound can be picked-up the MD.
• Select the Data menu from the Menu Bar, then Delete data set.
• Select an experiment length of 5 seconds, using the Timing button in the toolbar or by choosing the
Timing option from the Experiment menu.
• Have the metal cart with its added weight at about 50-cm distance from the MD, then let the weight
hanger slide over the pulley as soon as you click on the Start button of the toolbar.
• When the collection of data is finished (the collect button turns green and the MD stops its clicking
28
sound), and once your are satisfied with the collected data, save the data file in D or USB Drive: under
the name: met_cart.exp.xmbl
ANALYSIS OF RESULTS: On the LoggerPro Program Menu Bar, the Analysis menu provides access to various options for data
review and analysis. You can turn on an examination cursor and tangent lines. You can zoom in and out on
the data, auto-scale the graph, or try to fit a function to the data. If you select a region of a graph (this is
accomplished by pressing on the left mouse key and dragging the mouse over the desired region then
releasing the left mouse key) you can get the statistics, the regression line, the integral, or try a curve fit on
just that region.
• Open the experiment file met_cart.xmbl and select a regular region of the distance-versus-time curve.
• To this region try to fit a Quadratic function by choosing the Automatic Curve Fit from the Analysis
menu. Once the fit is finished keep it.
• Select the corresponding region of the velocity-versus-time curve and try to fit a Linear mathematical
function to the data by choosing Automatic Curve Fit from the Analysis menu. Once the fit is finished; keep it and report the values of M and B to Table 2 of your laboratory report.
• For the acceleration-versus-time curve, select the same region and choose Statistics for the analysis
menu in order to determine the average acceleration of the metal cart and report the value in the data
table, then get a print out of your computer graphs corresponding to met_cart.xmbl.
4. DATA ANALYSIS
• From your computer-generated graphs calculate the followings:
a- Average velocity from the initial time(ti) to the final time(tf). Show your work.
b- Average acceleration from initial time to the final time. Show your work.
• Since the slope of a velocity-versus-time graph is acceleration, the value of M for this graph should be
close to the value of the average acceleration from the statistics of the acceleration vrs. time graph..
Examine the appropriate quantities in Table 2 and calculate percent differences.
5. CONCLUSIONS What conclusions regarding the relationships between displacement; velocity and acceleration have you arrived at as a result of this experiment? In particular, do your data agree with the predicted
relationships for acceleration given in equations (1) - (4)?
Wooden Block Motion Detector
Pulley
Weights and mass hanger Table
EXPERIMENTAL SET-UP FOR THE MOVING CART
29
EXPERIMENT 4
ONE DIMENSIONAL MOTION
NAME: . . DATE: . .
SECTION: . .
THIS PAGE NEEDS TO BE DONE AT HOME BEFORE COMING TO THE LAB. SESSION
1. EXPERIMENTAL PURPOSE:
State the purpose of the experiment.( 5 points )
2. EXPERIMENTAL PROCEDURES AND APPARATUS: (5 points )
Briefly outline the apparatus
General procedures adopted.
PHY 1401 LABORATORY REPORT
30
3. RESULTS AND ANALYSIS Do a sketch of the graphs obtained in your computer (30 points)
Summary of computer generated graphs . (15 points)
Table 2: (10 points)
Graph M B AVERAGE
Velocity
Acceleration
4. DATA ANALYSIS (15 points)
31
5. CONCLUSIONS (10 points)
32
EXPERIMENT 5
ATWOOD'S PULLEY
INTRODUCTION:
Newton's second law is expressed as amFrr
=∑ , where the acceleration a may vary as the force
varies. Up to now, you have been assuming that this formula is true. This experiment will allow you to
explore the validity of this assumption by testing Newton's second law for the Atwood pulley system shown
in Figure 1.
THEORETICAL BACKGROUND
The law governing the operation of the Atwood Pulley is
just Newton's second law:
amFrr
=∑
where F = net force on the system, m = total mass of the
system, and a = acceleration of the system. Suppose that
the pulley is massless and frictionless. Considering
Figure 2, we see that each mass feels the downward force
of gravity and the common upward string tension. The
heavier mass m1 accelerates downwards with an
acceleration a while the fixed length of the string forces
the lighter mass m2 to move upwards at the same rate of
acceleration. Applying Newton's second law to each of
the masses gives:
(1) T- m1g = m1(-a) and T –m2g = m2 a
Subtracting the two equations to eliminate the string
tension T, yields:
(2) (m1 -m2) g = (m1 + m2) a.
In this equation (2) mJ - m2 is simply the total mass m, which is accelerating under the force of gravity.
(3) Fnet = (ml – m2)g.
The linear acceleration of the system is determined using the equation for uniformly accelerated motion
h = ½(at²)
where t is the time it takes the masses to move a distance h from rest.
THE EXPERIMENT:
Figure 2: Forces acting on the
systme
33
1- Experimental Apparatus:
The apparatus for this experiment consists of meter stick, electronic balance, stopwatch, mass hangers,
slotted masses, pulley, rods, and stands.
2- Experimental Procedure:
Newton’s second law F = ma involves three quantities: the net force F, the total mass m and the
resulting acceleration a. In order to test this relationship, one of the three quantities must be held constant. In
this experiment the total mass m is kept constant. The force on the system F net is varied and the resulting
accelerating a is measured.
• Start the experiment with 500 plus 25 g of the slotted masses placed on one side and 500 grams on the
other side (mass of the 50-g holders included). The mass of the heavier side is m1 while the mass of the
lighter side is m2.
• Release the mass m1 from a height h (around 1.0 m) above the floor as shown in Figure 1, and record the
time of fall to the floor.
• Calculate the system acceleration a using equation (4) and the unbalanced force acting on the system Fnet
using equation (3). Take the value of g to be 9.81 m/s². Organise all your data and results on the data
table of the laboratory report.
• Decrease the force Fnet by transferring a 1-gram slot from m1 to m2. This changes the values of m1 and m2
and also Fnet while keeping the total mass (m1 + m2) constant. Since the string may stretch, the height
should be measured prior to each run.
• Release the mass m1 from a height h (around 1.0 m) above the floor, and record the time of fall to the
floor.
• Continue decreasing Fnet by successively transferring 1 gram at a time from m1 to m2, and record times of
fall through the height h. Perform the experiment for 10 different pairs of ml and m2
ANALYSIS OF RESULTS:
• Plot a graph of Fnet versus a.
• Determine the slope and the intercept of the best-fit line. The scatter of the points about the best-fit line
is an indication of the random error in the measurement of time.
• If equation (2) is the correct theoretical equation to explain the motion of Atwood's Pulley, what values
do you predict for the theoretical slope and theoretical intercept of your graph?
• Test the agreement of theory and experiment by comparing the experimental slope and intercept to the
theoretically predicted values?
• If the intercept of the graph does not agree within error of the theoretically predicted value, calculate the
mass difference necessary to produce a force equal to the intercept. Does the mass seem reasonable? If
time permits, return to the equipment and determine the mass necessary to overcome the static friction in
the pulley.
CONCLUSIONS
• What conclusions can be made from this experiment on the basis of your graphs and results?
• If experiment and theory do not agree within error, what explanation can you give to account for the
discrepancy?
Questions
34
1. Equation (2) is arranged in the format of a straight line y = mx + b. Following the suggested procedure
identify the variables and constants then show which quantities correspond to the variables y, x and the
constants m, b respectively.
2. From equation (2), the theoretical acceleration a is given by
a == g (m1 - m2)/( m1 + m2)
Calculate the theoretical acceleration a using the experimental values of m1 and m2 from your first trial.
Do the calculated and experimental values agree within error?
3. What is the tension T in the string when m1 = 525 grams and m2= 500 grams?
35
EXPERIMENT 5
ATWOOD'S PULLEY
NAME: . . DATE: . .
SECTION: . .
THIS PAGE NEEDS TO BE DONE AT HOME BEFORE COMING TO THE LAB. SESSION
1. EXPERIMENTAL PURPOSE:
State the purpose of the experiment.( 5 points )
2. EXPERIMENTAL PROCEDURES AND APPARATUS: (5 points)
Briefly outline the apparatus
General procedures adopted.
PHY 1401 LABORATORY REPORT
36
3. RESULTS AND ANALYSIS Table 1: (30 points)
Heavier
mass, m1
Lighter
mass, m2
(m1-m2) Height of
fall, h
Time of
fall, t
Acceleration,
a
Net force,
Fnet
GRAPH (attach graph paper. 25 points)
ANALYSIS OF GRAPH (15 points)
37
4. CONCLUSIONS (10 points)
5. QUESTIONS (10 points)
38
EXPERIMENT 6
WORK AND ENERGY IN THE SIMPLE PENDULUM
INTRODUCTION: Conservation laws play a fundamental role in modern physical theory. A conservation law is a
statement that there is some property of a system, such as energy, that does not change as we study the
system in a specified way. In this experiment, we seek to verify the law of conservation of energy for a
particular, simple system.
THEORY:
When a constant force, F, acts on an object, O, and results in a
displacement, x, the work done (W) is defined as the product of force
and displacement. Since both force and displacement are vectors, the product must be found by using not F but rather the component of the
force in the direction of the displacement; i.e., Fx in the direction of x
(x being the displacement).
W = (Fx)(x)
When an object of mass m is raised a vertical distance h=hf - hi (hf
being the final height and hi being the initial height of the object) in
the earth’s gravitational potential field, the gravitational potential energy of the object changes by an amount
GPE = mg (hf - hi )
where g is the acceleration due to gravity.
An object moving with speed, v, has kinetic energy (KE) associated with it given by the relation:
KE = mv²/2
We would also like to introduce the concept of the work-energy theorem which states that when
forces act on a body while it undergoes a displacement, the total work Wtot done on the object by all the
forces equals the change in the particle’s kinetic Energy, namely
Wtot = KE2 - KE1
Finally, the work done on an object in a uniform gravitational field can be represented in terms of a
potential energy (GPE) as: Wgrav = mgy1 - mgy2 = GPE1 - GPE2
THE EXPERIMENT:
1. EXPERIMENTAL APPARATUS:
The apparatus used in this experiment is a pendulum with a spherical
bob. A string is fastened to the pendulum bob and passes over a pulley to a
weight hanger so that a known horizontal force can be applied to displace the
pendulum. A timing device (photo-gate timer), to be explained later, allows
you to measure the speed of the pendulum as it passes through the rest position. The units of work in the SI system are (force)(displacement) =
(Newtons)(meters) = joules
x0 x1
F
Fx
x
hf
hi
Bob
Pulley
Load hi
hf
xi
xf
39
2. EXPERIMENTAL PROCEDURE:
A. Measurement of the Work Done in Displacing the pendulum:
• Measure and record the mass of the pendulum bob.
• Construct a pendulum from the provided bob and strings. Allow the pendulum to hang vertically and
place the meter stick on the table with one end directly under the pendulum bob. The meter stick should
lie along the direction of the string be used to displace the pendulum. This string should go over the
pulley placed on the lab-table edge.
• Record hi, the initial height above the table of the string fastened to the pendulum bob (measure to the
center of the bob).
• Add the weight hanger to as a load to displace the pendulum bob. The string which displaces the
pendulum should be kept horizontal (parallel to the lab-table) by adjusting the height of the pulley
• Record the horizontal displacement of the pendulum bob form its initial position in the data table of your
lab-report.
• Add 10-gram mass to the weight hanger, make sure the string is horizontal by adjusting the height of the
pulley, and record (in the data table of your lab-report ) both the load (in Newtons) and the horizontal
displacement of the bob form its initial position.
• Repeat for a series of at least 10 different loads on the weight hanger (not to exceed 150 grams for the
final load), and record both the load and the horizontal displacement of the bob form its initial position.
• For the largest load only, record the final height hf of the string attached to the pendulum bob.
• Draw a graph of Fx versus x.
• Find the work done on the pendulum by measuring the area under the curve of Fx versus x.
B. Measurement of Gravitational Potential Energy of the Pendulum:
• Calculate the increased gravitational potential energy of the pendulum bob in the elevated position (refer
to the Figure for further clarifications). Show your work.
C. Measurement of the Kinetic Energy of the Pendulum:
• Position the U-shaped arm of the photo-gate timer such that the pendulum bob hangs directly in its
center when the pendulum is at rest. During subsequent motion, the cylinder must interrupt the light
beam between the U-shaped arms to activate the timer.
• With the pendulum held at an elevated position hf turn on the timer (use the “gate” setting), and release
the mass of the pendulum from this elevated position, it will pass through the rest hi position (i.e.,
equilibrium) with a kinetic energy of mv²/2. CAUTION: The attached string can also trip the timer as it falls through the beam, consider only the time for the pendulum itself to pass through the beam.
• In your lab-report record the beam-interruption time, which corresponds to the time for the diameter of
the bob to cross the photo-gate timer.
• Repeat the measurement as necessary to insure accuracy of the time (at least four measurements).
• Measure the diameter of the pendulum bob (sphere).
• Using this mass and the average photo-gate time calculate the velocity at the lowest point of the
pendulum swing.
• Calculated the maximum kinetic energy. Report your results in the lab-manual.
• In a brief paragraph, summarise the results of your experimental work.
• Calculate percent differences (between KE and W, KE and GPE, GPE and W). What does this tell you
about the meaning of work done by the variable force? How does this demonstrate conservation of
energy? Try to account for any significant difference between your results and what you would expect to
occur.
40
EXPERIMENT 6
WORK AND ENERGY IN THE SIMPLE PENDULUM
NAME: . . DATE: . .
SECTION: . .
THIS PAGE NEEDS TO BE DONE AT HOME BEFORE COMING TO THE LAB. SESSION
1. EXPERIMENTAL PURPOSE:
State the purpose of the experiment.( 5 points )
2. EXPERIMENTAL PROCEDURES AND APPARATUS:
Briefly outline the apparatus used and the general procedures adopted. (5 points )
PHY 1401 LABORATORY REPORT
41
3. DATA and ANALYSIS: (10 points)
Mass of pendulum bob =
Initial height of string =
Final height of string =
TABLE 1: (20 points)
Attach graph of Fx versus x (20 points)
3. CALCULATIONS:
A.Work: (5 pints)
B. GPE: (5 points)
C. KE: (10 points)
42
4. SUMMARY OF RESULTS: (5 points)
Percent differences: (5 points)
%difference (Work and KE)
%difference (Work and PE)
%difference (PE and KE)
5. CONCLUSION: (10 points)
43
EXPERIMENT 7
ELASTIC PROPERTIES OF DEFORMABLE BODIES
INTRODUCTION:
In this experiment we have two goals. Firstly, we examine a rubber strap and a steel spring to see if
Hook’s law is obeyed and, if so, determine the constant of proportionality in the law. This constant is
frequently referred to as the “spring constant” or as the “force constant”. Secondly, we investigate the
energy transformation which occur when a mass is suspended from an elastic spring and set into vertical
oscillation.
THEORY
In 1678, Robert Hook announced his theory of elastic bodies.
Now known as “Hook’s law”, the theory states that the stretch (∆y) in a wire or spring supporting a load (∆F) is directly proportional to the load, or ∆F= k(∆y) where k is a proportionality constant
Elasticity:
Elasticity is the property of an object determining the extent to
which it tries to return to its original shape and size after removal of a
deformable force. In general the deformation of an object increases as the applied force increases. If the deformation is directly proportional
to the applied force, we say the object obeys Hook’s law. For the case
of a linear stretching of an elastic material, we may write Hook’s law
in the form:
F = kY, where F is the deforming force, Y is the deformation of the
material from its original size, and the proportionality constant k is
called the force constant. The graph of this equation (F vrs. y) is a straight line and the slope is the force constant, k.
Elastic Potential Energy: The force-displacement curve for a body that obeys Hook’s
law is a straight-line, as shown. When the body has been stretched by
an amount y1 the force is ky1. In an earlier experiment, you learned
that the area under the F(y) curve represented the work done. In this
case,
ELASTIC ENERGY IN SPRING = KY²/2 (2)
THE EXPERIMENT: 1. EXPERIMENTAL APPARATUS:
To carry this experiment you lab station should have the following items: spring, rubber band, mass
hanger, slotted weights, meter stick, ruler.
2. EXPERIMENTAL PROCEDURE:
• Support the spring and meter stick as shown in Figure 3.
• Record Po (the location of the bottom of the spring when no load is applied).
y1
F
y
Work
Figure 2
44
• Add a weight hanger and record the new equilibrium
position.
• Fill up the cells of Table 1 in your laboratory report with
the data corresponding to mass increments of 20 g for the
spring.
• Change the spring with the rubber band and follow the
same procedure for recording the bottom of the band when no load is applied, when the mass hanger is added, and
when new mass in increments of 200 g is added.
• Record the data in the corresponding cells of Table 1 of
your laboratory report.
• Now, support the spring and meter stick as shown in Figure
3 again, and record P0.
• Add a weight of 150 grams (weight hanger + 100 g) to the
spring and record the new equilibrium position, P2.
• Raise the mass until the lower end of the spring is now at
an intermediate position, P1, between Po and P2.
• Release the mass and observe the lowest position to which
it descends. Repeat this last observation as necessary until
P1 and P3 are measured as accurately as possible and record
the final data to your lab-report.
ANALYSIS OF RESULTS:
• From the data collected in Table 1, plot a graph of the load-versus-displacement for the spring and
the rubber band. The graph paper is provided on the worksheet. Use the same sheet for both
graphs. Use the combination of right/lower axis for the spring data and the left/upper axis for the
rubber data.
• From the plotted data determine whether or not the steel spring and the rubber tube at your lab
station obey Hook’s law as expressed in equation (1).
• Determine the force constant, if it is appropriate. Briefly summarise the results of your work.
• From the P1, P2, and P3 measurements, you should be able to fill in the data cells of Table 2 on
your laboratory report. Use the point P3 as the reference level for the GPE = mgh. The elastic
potential energy (EPE = ½ k∆y²). Take the reference point for this energy as point P2. The total
energy (TE) possessed by the spring-mass system is the sum of the kinetic energy and the two
potential energies, that is: TE = KE + GPE + EPE
QUESTIONS:
1. What kinds of errors appear in your calculations of the energies in this experiment as a result of not
considering the mass of the spring? Think carefully and answer as specifically as you can. Can you estimate the magnitude of these errors and determine whether or not they are really significant?
2. Consider Figure 2. What would it mean if the straight line had an intercept on the F axis other than
zero (0)? How might this affect your computation? 3. Will all springs made of the same steel wire have the same force constant, k? Explain.
KEY FOR FIGURE 3
P0 : no mass position .
P1: highest point of oscillation
P2: rest position with mass.
P3: lowest point of oscillation.
45
EXPERIMENT 7
ELASTIC PROPERTIES OF DEFORMABLE BODIES
NAME: . . DATE: . .
SECTION: . .
THIS PAGE NEEDS TO BE DONE AT HOME BEFORE COMING TO THE LAB. SESSION
1. EXPERIMENTAL PURPOSE:
State the purpose of the experiment.(5 points)
2. EXPERIMENTAL PROCEDURES AND APPARATUS:
Briefly outline the apparatus used and the general procedures adopted. (5 points)
PHY 1401 LABORATORY REPORT
46
3. DATA and ANALYSIS:
TABLE 1: (10 points)
SPRING RUBBER
ADDED MASS POSITION ADDED MASS EQUILIBRIUM
GRAPH: Attach the graph(20 points)
Summary of graph: (10 points)
Suspended mass: (5 points)
p0 = ; p1 = ; p2 = ; p3 = (10 points)
Calculations of energies: GPE = mgh, EPE = ky²/2, TE = GPE + EPE + KE: (10 points)
47
Table 2: (10 points)
EPE GPE KE TE
P1
P2
P3
4. CONCLUSIONS: (10 points)
5. QUESTIONS: (5 points)
48
EXPERIMENT 8
ROTATIONAL INERTIA, ANGULAR MOTION
INTRODUCTION:
The aim behind this experiment is the study of angular motion, and the concept of rotational inertia.
In particular, to determine the effect of a constant torque upon a disk free to rotate, to measure the resulting
angular velocity, and to determine the moment of inertia of a body about an axis.
THEORY
The angular speed of a body is defined as its time rate of change of angular displacement, or the ratio
of the angular displacement, of the ratio of the angular distance which it has traversed to the time required to
travel that distance. If ∆θ is the small increment of angular distance traversed and ∆t the time required for
the body to travel that distance. Instantaneous angular speed ω is the limit of the ratio of the angular displacement over the time,
tt ∆
∆=
→∆
θω lim
0
If ∆ω is the small increment of angular velocity in the time interval ∆t, than the instantaneous angular
acceleration α is defined as,
tt ∆
∆=
→∆
ωα lim
0
The relation between the angular velocity (ω) and the tangential speed (v) of an object on the rotating body
at a distance r form its center is given by:
v = rω
The tangential acceleration of the same point as above on the rotating body is defined as:
a = α r
A rotating object has rotational kinetic energy given by:
(K.E.)rot. = ½ Iω²
where I is the moment of inertia of the rotating object. Now if the rotating object has translational motion
with velocity v as well as rotational motion if kinetic energy is the sum of the two kinetic energies,
K.E. = ½ mv² + ½ Iω²
A ball of radius R rolling about an axis through its center has a moment of inertia of I=2/5 MR², will have
through any point of its motion down the inclined ramp a total mechanical energy of:
T.E. = mgh+½ mv² + ½ Iω²
Angular momentum (L) is the analogue of linear momentum of a particle. For a particle with a constant
mass m, velocity v, linear momentum p = mv, and position vector r relative to the origin O of an inertial frame, the angular momentum L is defined as
vmrprLrrrrr
×=×=
Eq. 1
Eq. 2
Eq. 3
Eq. 4
Eq. 5
Eq. 6
Eq. 7
Eq. 8
49
For a rigid body with a moment of inertia, I, that is rotating around a symmetry axis with angular velocity ω
its angular momentum is given by:
vmrprLrrrrr
×=×=
When the net external torque acting on a system is zero, the total angular momentum of the system is
constant (conserved).
THE EXPERIMENT:
1. EXPERIMENTAL APPARATUS:
On you work station you will be provided with an angular momentum apparatus which consists of:
25 cm wheel that revolves on a low-friction bearing, an acceleration timer, a 40 cm metal arm with 3 cups,
metal balls, and an adjustable launching chute. You will also find a photo-gate timer, a D.C power supply, a
vernier calliper, and a ruler.
2. EXPERIMENTAL PROCEDURE:
A. Measurements of the Ball Velocity:
• Place the photo-gate timer at the base of the
inclined ramp, in a position to detect the metal
ball as it leaves the launching ramp.
• Set the photo-gate timer in the GATE mode.
• Record the height (H), the start-up point in the
launching inclined ramp of the rolling ball, in
your laboratory report.
• Record the height (h), the point at which the
ball leaves the launching inclined ramp, in your laboratory report.
• Place the metal ball on the top of the launching
inclined ramp at height (H), and release it.
• Measure the time that the ball diameter took to cross the photo-gate timer
• Repeat the same measurement for at least three times (make sure that the ball is released from the
same starting point, H).
• Report the data in your laboratory report write-up.
B. Measurements of the angular momentum:
• Tape a waxed recording tape on the rim of the
rotating disc.
• Make sure that the timing motor’s chain makes
contact with the rotating disc rim.
• Release the ball from the same initial height (H)
as in part A.
• As the ball gets inside the outside cup in the metal arm, press on the red button of the timer. As the
disc rotates, there will be marks on the waxed recording tape.
• Record the time for on revolution of the disc.
• Remove the waxed recording tape from the rim the disc
• Measure the distance between the successive points and record the values in table II of your
laboratory report.
Rim of rotating disc
Rotational velocity, ω
Metal arm with ball inside one of the 3 cups
Ball rolling down an incline
H
h
v
ω
Photo-gate timer
Start-up point of the rolling ball
Eq. 9
50
DATA ANALYSIS:
A. Measurements of the Ball Velocity:
• From the data obtained in part A of the experiment calculate the linear speed of the ball as it leaves the
ramp by using the conservation of the mechanical energy given by equation 7 in the theoretical
background section.
• Compare this calculated velocity to the measured velocity obtained from the data recorded in table I (that
is find the percent difference between the two velocity values).
• Explain the reasons for any difference between the two velocities.
B. Measurements of the angular momentum:
• Calculate the circumference of the rotating disc (C=2πr) and divide it by the distance between two
waxed tape marked points, this will give you the number of points marked on the waxed tape during a complete disc revolution.
• Divide the time for one complete disc revolution by the number of points marked on the waxed tape
during a complete disc revolution to obtain the time between successive data points.
• In a graph paper plot distance obtained from data table II versus the time. Calculate the disc’s rotational
speed.
• Using equation 8 for the system of the ball and metal arm on the disc; calculate the angular momentum
just before impact.
• Assuming that no external torque act on the system of the ball and metal arm on the disc, use the
conservation of angular momentum to find the moment of inertia of the system.
• Calculate the moment of inertia of the system.
51
EXPERIMENT 8
ROTATIONAL INERTIA, ANGULAR MOTION
NAME: . DATE: .
SECTION: .
THIS PAGE NEEDS TO BE DONE AT HOME BEFORE COMING TO THE LAB. SESSION
1. EXPERIMENTAL PURPOSE:
State the purpose of the experiment.( 5 points )
2. EXPERIMENTAL PROCEDURES AND APPARATUS: (5 points)
Briefly outline the apparatus
General procedures adopted.
PHY 1401 LABORATORY REPORT
52
3. DATA and ANALYSIS:
A. Measurements of the Ball Velocity: (15 points)
The initial height of the ball as it starts at the top of the ramp (H):_________________
The height of the ball as it leaves the ramp (h):_____________________
The moment of inertia of the ball (I=2/5 MR²):_________________________
Velocity of the ball as obtained by the conservation of mechanical energy: (show your work)
TABLE I: (10 points)
Ball Diameter (cm) Time (s) Velocity (m/s)
First Trial
Second Trial
Third Trial
% Difference between measured velocity (from table I) and calculated velocity: (5 points)
B. Measurements of the angular momentum:
TABLE II. (15 points)
TIME INTERVAL MEASURED DISTANCE (cm)
Graph: (15 points)
53
.
4. CALCULATIONS:
Time between successive data points (show your work): (5 points)
Angular velocity of the rotating disc: (5 points)
Angular momentum before impact (show calculations): (5 points)
Moment of Inertia of the system: (10 points)
5. CONCLUSION: (5 points)
54
EXPERIMENT 9
THE SIMPLE PENDULUM
INTRODUCTION The simple pendulum offers a method of measuring the constant acceleration due to gravity very
precisely. The object of this experiment is to study simple harmonic motion of the simple pendulum and to
measure the acceleration of gravity g.
THEORETICAL BACKGROUND
A simple pendulum is defined, ideally, as a particle suspended by a weightless string. Practically it
consists of a small body, usually a sphere, suspended by a string whose mass is negligible in comparison
with that of the sphere and whose length is very much grater than the radius of the sphere. Under these conditions, the mass of the system may be considered as concentrated at a point -namely, the center of the
sphere- and the problem may be handled by considering the transitional motion of the suspended body,
commonly called “bob,” along a circular arc.
Figure 1: Diagram Analysis of the Simple Pendulum.
Consider the diagram of a simple pendulum shown in Figure 1. In its equilibrium position the bob is at the point A vertically below the point of support O. In this position the downward pull of gravity w is
counteracted by the upward pull p of the cord. When the bob is displaced to some point B, the weight w=mg
may be resolved into two components. One n normal to the arc AB which is counteracted by the pull p of the
string, and a force f tangent to the arc that tends to restore the pendulum to its equilibrium position. The
greater the displacement, the greater is this component f and the less the force p in the string, as can be seen
by comparing positions B and C. Thus the bob is subjected to a translational force f which increases with the
displacement and always tends to reduce the displacement. When the pendulum is released from a given displacement, it moves with increasing velocity toward
its equilibrium position, acquiring thereby momentum that carries it through the neutral position and
produces a negative displacement. It should be noted here that the choice of positive and negative directions is purely arbitrary. It is convenient, although not necessary, to call displacements to the right positive and
those to the left negative. Neglecting the effect of friction, the maximum negative displacement will be
equal exactly to the initial positive displacement. When the point B’ is reached, the restoring force causes a
reversal of the motion and the bob returns to B. This to-and-fro motion of a pendulum is called “vibratory”,
or “oscillatory”, motion.
The translational force f is equal to mg sin θ, as apparent from the vector diagram in Figure 1, where
θ is the angle the string makes with the vertical at the instant shown. Note that if angle θ is small, sin θ is
55
very nearly equal to the displacement, arc length x, divided by the string length l, sinθ = x/l.
fmg
lx= − ( Eq. 1)
Thus, if the amplitude of vibration is small; the resultant force on the ball is at all times proportional
to the displacement x as required for simple harmonic motion. Now, from Newton’s second law of motion,
we know that:
f ma md x
d t
mg
lx= = = −
²
² (Eq. 2)
A solution of Equation (2) requires that the second derivative of x be proportional to the negative to
x. Either the sine or cosine of some function of time will satisfy this requirement, we choose a solution of the form:
x A t= sinω (Eq. 3)
where
fmg
lx=− (Eq. 4)
is the angular velocity. The period of vibration is the time required for it to go through one cycle (i.e., the
time for pendulum to move from any point on its path back to the same point with motion in the same
direction), and is related to ω by the relation T = 2π/ω.
Tl
g= 2π (Eq. 5)
Note finally that the constant A in Equation (3) is the amplitude of the motion which measures how
far the bob swings away from the vertical -the maximum value of the displacement. This is conveniently expressed as an angle in degrees.
THE EXPERIMENT:
After you read the preceding material, you may notice that among the factors that might affect the period of a simple pendulum are the mass of the pendulum, the length of the pendulum, and the amplitude of
its swing. We shall confine our attention to these as they are easy to control experimentally.
If we are to investigate the effect of any one of these variables on the period of the pendulum, the remaining variables must be controlled (i.e., they must not be allowed to change during the experiment).
Suppose we start with an investigation of the effect of length upon the period. This means that we choose a
pendulum of fixed mass, allow it to swing always through angles of the same amplitude, and observe
changes in the period due to changes in the length of the pendulum.
1. EXPERIMENTAL APPARATUS:
The experimental apparatus consists of rods, clamps, pendulum bobs, string, metric ruler, stop watch, protector, electronic balance, computer, the LabPro interface, LoggerPro program and the Motion Detector.
2. EXPERIMENTAL PROCEDURE:
A. Effect of changing length on the pendulum period: • Prepare a pendulum about 1 m long.
• Position the Ultrasonic Motion Detector so that it monitors the motion of the pendulum. Remember
that the pendulum must be placed at more than 0.5 m distance away from the motion detector.
56
Use the computer to measure the position of the ball versus time. To do this make sure the motion sensor is plugged into the Lab Pro device and the Lab Pro’s USB cable is plugged into the computer. Open Logger Pro using the icon on the desktop. Logger Pro should automatically recognize the sensors, if it doesn’t:
Click on LabPro icon, a window will open with a picture of the LabPro. Select the Dig/Sonic 1 box in the
upper right hand corner and choose the Motion Detector You can close the LabPro window now.
• Give the mass a small displacement from equilibrium (around 5 degrees), let it swing within the range of the motion detector, and click the Collect button to start the data collection. Make sure that the time period for data collection is long enough to accommodate at least ten periods (use the timer icon) of the pendulum swing.
• Repeat this step until you obtain a good data set.
• While you are taking these computerized data acquisitions, you should use the provided stop-watch to measure the time for the ten periods of the pendulum oscillations. This period can be determined with greater accuracy if the time to make a large number of cycles (say 10) is noted and the period calculated by dividing the total time by the number of cycles.
• Record the mass, amplitude, length, and period of the pendulum in Data Table 1.
• Decrease the length of the pendulum by about 15 cm and determine the period in the same manner, and record the results in data Table I.
• Repeat the measurement for total 5 lengths of the pendulum, the last length should be about 20 cm, and record the results in data Table I.
Remember that both the mass and the amplitude must remain the same throughout this series of
observations.
B. Effect of changing mass on the pendulum period:
• Prepare a pendulum about 75 cm length.
• Change the mass while holding the length and the amplitude constant. Displace the mass at a small
angle (around 5 degrees).
• Use the stop-watch to measure the time for the ten periods of the pendulum oscillations.
• Record the period of oscillation in data table II.
• Repeat the same procedure for three different masses, and report the results in data table II.
C. Effect of changing amplitude on the pendulum period:
• Prepare a pendulum about 75 cm length.
• Change the amplitude while holding the length and the mass constant. To start displace the mass at a
small angle (around 5 degrees).
• Use the stop-watch to measure the time for the ten periods of the pendulum oscillations.
• Record the period of oscillation in data table III.
DATA ANALYSIS:
• Using the data collected in Table I, prepare a graph of the period versus the length of the pendulum.
• What does this graph tell you about the relationship between length and the period.
• On the same sheet of graph paper, plot a graph of T² versus L (This required a different vertical scale
since a different quantity is being plotted). To avoid the confusion, place the new scale along the right
margin of the graph paper.
• What is the form of this graph? Explain the relationship between the length and the period.
• Summarise the results of your three experiments. Examine your data and graphs carefully before
writing.
• Using graphs of T² vrs. L, calculate the experimental value of g by comparing the slope of the graph with
equation 5.
57
• Show your calculation on the worksheet. Compare your calculated g value to the theoretical value of 9.8
m/s².
• Equation (3) describes the motion of the bob for a simple pendulum undergoing simple harmonic motion
(vibrating with small amplitude). From the plotter graph windows describe the motion of the pendulum
bob, and explain if you happen to see the effect of friction on this motion.
QUESTIONS:
1- Identify variables other than those investigate in this experiment which might affect the period of
pendulum.
2- Many clocks are regulated by the swinging of o pendulum. Most materials expand when heated. Would
this cause a pendulum clock to run fast or slow on a hot summer day? Explain your reasoning?
58
EXPERIMENT 9
THE SIMPLE PENDULUM
NAME: . DATE: _____________________ .
SECTION: .
THIS PAGE NEEDS TO BE DONE AT HOME BEFORE COMING TO THE LAB. SESSION
1. EXPERIMENTAL PURPOSE:
State the purpose of the experiment (5 points )
2. EXPERIMENTAL PROCEDURES AND APPARATUS: (5 points )
Briefly outline the apparatus
General procedures adopted.
PHY 1401 LABORATORY REPORT
59
3. DATA and ANALYSIS:
TABLE 1: (10 points)
Length, L Time for 10 cycles Period, T T²
LoggerPro Stop watch LoggerPro Stop watch LoggerPro Stop watch
TABLE 2: (10 points) TABLE (10 points):
Discussion of first graph: (5 points)
Summary of second graph: (5 points)
Summary of three experiments: (10 points)
Description of the pendulum bob movement using the data graph windows: (5 points)
60
Calculations of “g”: (5 points)
Comparison between theoretical value and experimental result of “g”, Percent error: (5 point)
Attach MPLI plotter graph windows and analysis(10 points).
CONCLUSIONS: (10 points)
QUESTIONS: (5 points)
61
EXPERIMENT 10
BUOYANT FORCES
INTRODUCTION:
The purpose of this experiment is to determine buoyant forces on submerged solid objects, and to investigate the dependence of buoyant forces on volumes and masses of submerged objects
BACKGROUND:
When a solid objects submerged in a fluid (gas or liquid), an upward force is exerted by the fluid on
the object. This force is called the buoyant force (B). The magnitude of the buoyant force always equals the
weight of the fluid displaced by the object (Archimede’s Principle). In other words,
B = ρf Vg
where,
ρf = Density of fluids (mass/unit volume of fluid)
V = Volume of the solid object g = Gravitational acceleration (9.81 m/sec²)
Let us examine the external forces acting on an object submerged in a fluid (see figure 1). The
object is supported by a string attached to a balance. Assuming the system is in equilibrium, then:
B = mg - T1
where T1 = Tension in the string (weight of the object when submerged).
If the same object is weighed in air and assuming no buoyant force due to air:
mg = T2
From equation 2 and 3 one can find that,
B = T2 - T1 = (weight of the object in air) - (weight of the object in fluid)
Figure 1: Set-up and Analysis of Buoyant Forces
The apparatus shown in figure 1 will be used for this experiment. The spring balance provided has a
special hook attached to the bottom. Masses to be measured should be attached to this hook, and their
weight should be read from the spring balance scale.
THE EXPERIMENT:
1- Experimental Apparatus:
(1)
(Eq. 2)
(Eq. 3)
(Eq. 4)
mg
T2
mg
T1
B
- - - -
Spring balance
Container filled with liquid
Suspended sphere
62
The apparatus for this experiment consists of:
Spring balance, masses to be measured, and beaker, Vernier-calliper
2- Experimental Procedure:
A. Measurements for Different Spheres With the Same Volume:
Spheres of different masses but of equal volumes are provided for the purpose of this study. Prepare
a table to record your results as you proceed.
• Measure the dimensions of these spheres and be sure that their volumes are almost the same. Use a
vernier for these measurements.
• Attach one of the spheres to the spring balance.
• Measure the mass of the sphere in air.
• Continue to measure the masses of other spheres in air.
• Submerge one sphere in liquid measure its mass while in the liquid.
• Do the same for other spheres and find their masses while in liquid.
• Use equation # 4 to determine the buoyant force in each case.
• Record your results and include units.
B. Measurements with Different Masses:
Another set of spheres of different volumes and masses are provided for the purpose of this part of
the experiment. Again, prepare another table to record the results of this part and proceed as follows:
• Use a vernier to measure the dimensions of all masses ( except those that were used in part A).
• Find the volume of each mass.
• Measure the masses of the spheres in air.
• Submerge one sphere in liquid measure its mass while in the liquid.
• Do the same for other spheres and find their masses while in liquid.
• Use equation # 4 to determine the buoyant force in each case.
• Record your results and include units.
• Use graph paper to plot buoyant force versus volume of submerged object for each liquid.
DATA ANALYSIS:
Now with all these data at hand, you should be able to answer the following questions:
• What conclusion could by reach on the basis of the results of part A
• Do you think that the above conclusion would be reached if you use another liquid? Explain.
• Using the results of part B (slope of the graph), determine the density of water.
63
EXPERIMENT 10
BUOYANT FORCES
NAME: . DATE: .
SECTION: .
THIS PAGE NEEDS TO BE DONE AT HOME BEFORE COMING TO THE LAB. SESSION
1. EXPERIMENTAL PURPOSE:
State the purpose of the experiment.( 5 points )
2. EXPERIMENTAL PROCEDURES AND APPARATUS:
Briefly outline the apparatus used and the general procedures adopted. (5 points )
PHY 1401 LABORATORY REPORT
64
3. RESULTS AND ANALYSIS
A. Measurements for Different Spheres With the Same Volume:
Data (25 points )
Data Table I:
Object
Measured
Length
(cm)
radius
(cm)
Volume
(cm3)
Mass in
air (g)
Mass in
fluid (g)
Buoyant force
(N)
Calculations Show your work for one of the objects measured (5 points)
65
B. Measurements with Different Masses:
Data (25 points )
Data Table II:
Mass
Measured
Length
(cm)
radius
(cm)
Volume
(cm3)
Mass in
air (g)
Mass in
fluid (g)
Buoyant
force (N)
Calculations Show your work for one of the objects measured (5 points)
RAPH (15 points)
QUESTIONS (15 points)
66
EXPERIMENT 11
LINEAR EXPANSION OF A SOLID MATERIAL
INTRODUCTION:
Earlier this semester, we saw that the length of the pendulum effects the period. Many practical
devices, such as the mercury thermometer, work on the principle of thermal expansion. It is important for
engineers to take thermal expansion into account when designing structures. Bridges; for example, often
have joints in the roadway to allow for thermal expansion without damage.
It is found that change in length of a solid is proportional to the original length and to the change in
temperature. The constant of proportionality, which is called the coefficient of linear expansion, depends on the material of which the solid is made. It is the purpose of this experiment to determine the coefficient of
linear expansion of several metals.
THEORY:
Most solids expand when they are heated, except for those rare cases where the molecular structure
simultaneously changes to a more dense form. Ice, for example, shrinks upon melting and alloy Inver
gradually changes crystal form to a more compact structure upon heating. These few exceptions to the
general rule extend over a range of only a few degrees.
When you heat an iron rod, its molecules vibrate more violently. They shove one another away
causing the rod to expand. When the rod cools again its molecules vibrate less violently and it contracts.
It is interesting to note that each solid has a characteristic rate of expansion unique to that solid. The
rate of expansion is determined by heating a measured length of the solid through a definite temperature change and then measuring the change in length.
The coefficient of linear expansion, α, is a number which indicates the change in length per unit
length per degree of temperature change. It is a characteristic property of the material and can be calculated
as follows:
α =×
∆
∆
L
L T0
where,
∆
∆
T T T
L L L
H
H
= −
= −
0
0
TH is the hot temperature at which the new length is LH, and T0 is the initial temperature of the rod when its
length is L0.
THE EXPERIMENT:
1. EXPERIMENTAL APPARATUS:
In this experiment you will use a steam generator (boiler), heating plate, aluminium rod, brass rod,
copper rod, heating jacket, laboratory fingers, thermometer, power supply, lamp, and electrical cables.
67
Figure 1: Experimental Apparatus.
2. EXPERIMENTAL PROCEDURE:
The thermal expansion of three materials will be investigated -aluminium, brass, and copper. To
operate simply
• Insert the desired rod in to the heating jacket.
• Place the heating jacket onto the base so that the water in-take valve is at the end nearest to the electrical
terminals. The thermometer should be facing up, and should be inserted in the stop-cock at the jacket
center. The water outlet valve that is near the micrometer should be placed near a laboratory sink.
• The length of the rod is found by adjusting the micrometer dial until electrical contact is established (see
Figure 1). To establish electrical contact between the rod and the lamp follow part (b) of Figure 1.
When electrical contact is established the lamp should light up.
• The micrometer screw should initially not be touching the rod. If there is contact, turn the dial until a
small gap exists between the rod and the screw.
• Fill the thermal expansion apparatus jacket with tab water and record the length of the Aluminium rod
and the water bath temperature.
• Turn the micrometer dial counter-clockwise for two complete turns so that there’s no electrical contact
(the light is off).
• Heat-up water contained in the steam generator to a particular temperature about 35 °C; and then pour it
in the heating jacket through the intake hose. You should use the laboratory fingers to pour the hot
water, gently, from the flask into the apparatus’ jacket. HANDLE WITH EXTREME CARE. DON’T
BURN YOURSELF!!.
• Once the jacket is filled with the hot water, allow at least 30 seconds for the rod temperature to reach
equilibrium with the water temperature, and turn the micrometer dial until the screw just makes contact with the rod, then record the micrometer’s reading for the final length, LH.
• Repeat this procedure (i.e. heating water, pouring it in the heating jacket, and measuring new length of
the rod) for four different hot water temperatures (about 50 °, 60°, 70°, and 85°).
• Record all the data in data Table 1.
For the Copper, and brass rods it is only necessary to measure ∆L obtained from the tab water bath
and at another hot water temperature. Record this data in data Table 2.
ANALYSIS OF RESULTS:
For the aluminium rod (data table 1):
68
• Construct a graph of ∆L versus ∆T.
• Calculate the slope and compare the value obtained for α with the given theoretical value.
• Discuss your graph.
From Table 2:
• Compare results.
Summarise all of your results and calculate percent errors for all α‘s.
TABLE: Linear Expansion Constants for Common Materials:
Solid αααα (Per °C)
Aluminium
Brass
Copper
Glass
Glass (Pyrex)
Invar (nickel/iron alloy)
Iron
Platinum
Quartz
Steel
Tungsten
0.000022
0.000019
0.000017
0.000007
0.000032
0.000007
0.000012
0.000009
0.000004
0.000013
0.000044
QUESTIONS:
What would happen to the coefficient of thermal expansion if the rod is not made of a pure metal?
For an Aluminium rod that is twice as long as the one used in our experiment, estimate the expected linear
expansion of this rod at the same highest temperature used in our experiment.
69
EXPERIMENT 11
LINEAR EXPANSION OF A SOLID MATERIAL
NAME: . DATE: .
SECTION: .
THIS PAGE NEEDS TO BE DONE AT HOME BEFORE COMING TO THE LAB. SESSION
1. EXPERIMENTAL PURPOSE:
State the purpose of the experiment.( 5 points )
2. EXPERIMENTAL PROCEDURES AND APPARATUS: (5 points )
Briefly outline the apparatus
General procedures adopted.
PHY 1401 LABORATORY REPORT
70
3. DATA and ANALYSIS:
TABLE 1: (25 points)
T0 TH ∆T L0 LH ∆L
GRAPH: (30 points)
Slope of Graph and ααααAl calculation: (10 points)
Discussion of Graph: (5 points)
Percent errors: (10 points)
4. CONCLUSIONS: (5 points)
5. QUESTION (5 points)
71
EXPERIMENT 12
GAS LAWS ( BOYLE’S AND GAY-LUSSAC’S LAW)
INTRODUCTION:
In order to specify fully the condition of a gas it is necessary to know its pressure, volume, and
temperature. This quantities are interrelated, being connected by the general gas law, so that if any two of
them are known, the third is determined by the mathematical relation between them.
One of the important properties of a gas is that it always tends to expand until it completely fills the
vessel in which it is placed, and thus the pressure it exerts depends on the volume it occupies. To describe
fully the condition of a gas it is necessary to give not only the volume but also the temperature and pressure,
because they are all interrelated.
The purpose of this experiment is to study two of the gas laws; that is, to develop the relation
between the volume and the total pressure of a given mass of gas when the temperature is kept constant; and to investigate the variation of the pressure, of a given mass, of gas with changes in its temperature, when the
volume is kept constant.
the volume to the pressure, and the pressure to the temperature.
THEORY
In studying the behaviour of a gas under different conditions of pressure, temperature, and volume, it
is convenient to keep one of these constant and to vary the other two. Thus, if the temperature is kept
constant, one obtains the relation between the pressure and the volume; if the volume is kept constant, one gets the relation between the temperature and the pressure.
Boyl’s law: if the temperature is kept constant, the volume of a given mass of gas varies inversely as
the pressure. This means that for a constant temperature, the product of the volume and the pressure of a given amount of gas is constant. Thus
PV = constant (Eq. 1)
or P1V1 = P2V2, where V1 is the volume of a given mass of gas at pressure P1, and V2 is the volume at
pressure P2.
The experimental test of Boyl’s law consists in observing a series of different volumes, measuring
the corresponding pressures, and observing how nearly constant the product of the two remains.
GAY-LUSSAC LAW: if the volume remains constant, the pressure of a container of a gas is directly
proportional to its absolute temperature.
THE EXPERIMENT:
1. EXPERIMENTAL APPARATUS:
To demonstrate the concept of BOYL’S LAW (pressure vs. volume) and GAY-LUSSAC’S LAW
(pressure vs. absolute temperature) you will use the Pressure Sensor and the temperature Probe with the
Vernier Logger Pro Software and its Interface (Lab Pro). You will also find your laboratory station equipped with an Erlenmeyer flask, beaker, and heating plate.
3. EXPERIMENTAL PROCEDURE:
The white stem on the end of the Gas Pressure Sensor Box has a small threaded end called a luer lock.
With a gentle half turn, you may attach the plastic tubing to this stem using one of the connectors already
mounted on both ends of the tubing. The Luer connector at the other end of the plastic tubing can then be
connected to one of the stems on the rubber stoppers that are supplied, as shown in figure 1.
72
Figure 1 Figure 2 Figure 3
Preparing Logger Pro for Measurements
A. Boyl’s law experiment:
• Connect the Pressure Sensor into the LabPro interface's Ch.1; Open the LoggerPro application from the
desktop.
• Set the syringe to 20 cc volume.
• Connect the 20mL plastic syringe directly to the stem, as shown in figure 3, to secure the connection
twist the syringe with a gentle 1/2 turn. The pressure inside the syringe is now equal to atmospheric
pressure at the selected volume.
• Open Boyle’s Law file from Physics_Experiments folder
• Click the Collect button and monitor the pressure in the data table. Make sure that the pressure on the
syringe keeps the volume at 20 cc while your are collecting the data.
• When this pressure has stabilized, read the volume on the syringe and click Keep button. A data
entry box will appear allowing you to enter the volume of air in the syringe; in this box you should
record the syringe volume in cc (i.e. 20).
• Decrease the volume to 15 cc and take a new pressure measurement. Again let the pressure stabilise
before you click the Keep button.
• Collect the pressure for the volumes of 12 cc, 10 cc, and 7 cc by following the same procedure outlined
in the previous steps.
• Click Stop once you have taken all the readings
• Save this data in D drive or USB drive: under a filename that consists of six characters. The first three
characters should correspond to the first three letters in your last name and the last three characters
should be Boy. Example Rac_Boy for Rachid.
B. Gay-Lussac’s law:
• Plug the temperature probe in Channel 1, and the pressure sensor in Channel 2.
• Connect the white valve stems to one end of the long piece of plastic tubing.
• Connect the other end of the plastic tubing to one of the stems on the rubber stoppers (figure 2). This
rubber stopper should, in turn, be inserted into the Erlenmeyer flask to provide a constant-volume gas
sample.
Note: the 2nd valve on the rubber stopper is shown in a closed position. (Check this?!).
• Insert the Erlenmeyer flask in a cold water bath of the beaker (make sure that the beaker is not too full of
water, so that no water splash over).
• Open the GAY-LUSSAC file from the File menu.
• Set the experimental time to 10 minutes.
• Place the water baths on top of the heating plate, and immersed in the water you should have Erlenmeyer
flask and the Temperature Probe. Make sure that the temperature probe is not touching the walls of
the water bath.
73
• Set the heater at 3/4 of its full scale, and then turn it on.
• Click the Collect button to have the computer collect data for the change in pressure as a function of
temperature for the period of 10 minutes.
• Save this data in drive E or USB drive: under a filename that consists of six characters. The first three
characters should correspond to the first three letters in your last name and the last three characters
should be Gls, Example Rac_Gls for Rachid.
ANALYSIS OF RESULTS: A. Boyl’s law experiment:
• In a new column of the data table from the saved Boyle’s experiment file have the computer calculate the
product PV for each pressure.(Data����new calculated column)
• Leave the Graph and the Data windows on your screen and close the text window. Call the laboratory
instructor to check your results.
• Plot a second curve using the values of the pressure as the dependent variable and the corresponding
values of 1/V as the independent variable. You can easily graph pressure vs. the reciprocal of the volume by clicking on the "volume" label on the x-axis of the graph, and from the list of columns that will
appear; select "1/V" then click on the "autoscale button ".
• Using the curve fitting options in the Analyze menu, show how your results and curves verify Boyle’s
law. Explain the shape of the curves.
B. Gay-Lussac’s law:
• From the saved data file for the Gay-Lussac experiment, using the curve fitting option in the Analyze
menu, and show how your results verify the Gay-lussac’s law.
• Explain what the slope of the curve represents.
QUESTIONS:
1- Explain what effect a change in temperature will have on the Boyle’s law experiment.
2- What is the barometric pressure in Ifrane? Would you expect this value to be different than the barometric pressure in Rabat? Explain your reasoning.
74
EXPERIMENT 12
GAS LAWS (BOYLE’S AND GAY-LUSSAC’S LAW)
NAME: DATE: .
SECTION: .
THIS PAGE NEEDS TO BE DONE AT HOME BEFORE COMING TO THE LAB. SESSION
1. EXPERIMENTAL PURPOSE:
State the purpose of the experiment.( 5 points )
2. EXPERIMENTAL PROCEDURES AND APPARATUS: (5 points )
Briefly outline the apparatus
General procedures adopted.
PHY 1401 LABORATORY REPORT
75
3. DATA and ANALYSIS:
Attach computer printouts from the Logger Pro Program with the Table window showing PV
column, and the Pressure-versus-Volume graph: (15 points)
Attach computer printouts from the Logger Pro Program with the plot of P-versus-1/V graph with
the corresponding automatic curve fit: (15 points)
Comparison of the graphs with Boyle’s law: (5 points)
Explain the shape of the curves: (10 points)
Attach computer printouts from the LoggerPro Program with the Pressure-versus-Temperature
graph and the corresponding automatic curve fit: (15 points)
Comparison of the graph results with the Gay-lussac’s law: (5 points)
Slope of Pressure-versus-Temperature graph and its physical significance: (10 points)
76
CONCLUSIONS: (10 points)
QUESTIONS: (5 points)
top related