0−1

PHYSICS 124

LAB MANUAL

Fall 2019

Revised by Pengqian Wang

Department of Physics

Western Illinois University

0−2

Table of Contents

Note to the Students

Instruction on Writing a Lab Report

Lab 1 – Introduction to Linear Motion

Lab 2 – Free Falling Objects and Graphical Analysis

Lab 3 – Force Table and the Addition of Vectors

Lab 4 – Force Sensor and Newton’s Second Law

Lab 5 – Work and Energy

Lab 6 – Impulse and Momentum

Lab 7 – Torque, Equilibrium, and Center of Gravity

Lab 8 – Archimedes’ Principle and Buoyancy

Lab 9 – Thermal Expansion

Lab 10 – Spring Force and Simple Harmonic Oscillator

0−3

Note to the Students

Welcome to Physics 124 laboratory! It is my great pleasure to explore the wonders of physics

with you, my students, in the lab.

Please retain this lab manual and put it in a binder or folder. You will need to bring the manual

to the lab, or at least bring the sheets for each particular lab, since every experiment will involve

filling in data on these lab manual sheets. In addition, please bring some blank paper to work out

some of the calculations. You will turn in the material for grading, along with additional sheets

with your calculations (if called for), graphs or drawings, and any computer printouts. These

reports will be graded and returned to you.

In order to make this brief, this lab manual does not include detailed discussions on theory, so

you will need to study the textbook before coming to the lab. Please preview the materials in the

lab manual prior to the lab. The labs will be easier to understand if you do the readings in the

textbook before the lab.

In this course, the exams and the homework are competitive activities, meaning that you should

do your own work and not copy from others. The labs, on the other hand, are intended to be

cooperative activities, so you should be taking the data as a group, sharing ideas, and discussing

the answers to any questions that come up. The report from each person in the group will probably

look similar to others in that group, which is acceptable. We would like each person in the group

to understand what is going on, and contribute to the lab activity. One reason for each person to

turn in his or her own report is to keep you involved in the experiment, as you tend to think a bit

harder when you have to write something down. Another reason is so that you will have a copy of

the lab to study after it is returned. The lab is not just an isolated activity, but should be the basis

for many classroom discussions. The ideas you learn in the lab might appear in an exam.

Finally, please ask me if you have any questions on the lab. I wish you all have a successful

semester.

0−4

Instruction on Writing a Lab Report

You are required to submit a lab report for each lab. It is recommended that you use software

like Microsoft Word to type you lab report and submit a printed copy, while a handwritten legible

lab report is also acceptable. Each lab report is due in the next meeting time of the lab. Your lab

grade will be based mostly on the scores of your lab reports. However, your attendance to the lab

and your active involvement in lab activities will earn you extra bonus.

Each lab consists of a number of experiments. In the lab you will make observations and

measurements, and you will try to understand and analyze what you have observed. It is suggested

that you use a lab notebook to keep a record of what you have done and what you have seen in the

lab, as well as to summarize your observations, measurements, analysis and conclusions. This

notebook will be a great help in writing the lab report.

Each lab report should be organized in the following way:

0) Title page. Place your name in the upper right-hand corner of this page, along with the date of

the experiment, your lab section number, and your lab instructor’s name. (This makes it easier to

hand back the reports after we grade them.) In the center of this page, write the title of the

experiment.

1) Introduction. Describe the objectives of the lab and the important concepts to be studied.

2) Apparatus. Describe the instruments and equipment you use. If necessary, you can include

hand drawing sketches. The sketches should be supplemented with legible notes.

3) Procedure. Describe the procedure you follow to get the experimental data.

4) Data, graphs, and answers to questions. This is the most essential part of your lab report.

Please include the lab manual pages that show your data tables and answers to the questions. When

asked by the lab manual, please include the graphs you print in the lab, and any additional data

tables and graphs you make after the lab. Data tables should have a title and headings for each

column, including the units of physical quantities. Graphs should have a title, clearly marked axes

and a scale with units.

5) Discussion: Do your data agree with the accepted values? Are they self-consistent? Discuss

how your results demonstrate basic principles of physics.

6) Conclusion: Provide a summary of what you have seen and what you have learned through the

lab exercises.

Each lab report has a potential value of 20 points, and the credit breakdown is as follows:

Lab report writing: 8 points

Data and analysis: 8 points

Answering questions: 4 points

1−1

Name: ____________________________________

Physics 124 Lab 1: Introduction to Linear Motion

Goal:

Your mission is to learn how to use a computer to observe motion in one dimension with a

motion detector and to learn how to analyze one-dimensional motion graphically.

Setup:

In this lab you will use a device called a “motion detector” to observe motion in one

dimension. The motion detector does exactly what its name implies: it detects motion. It is not

necessary for you to understand how this device works for you to complete this lab, but for

curious minds here is a brief description. The motion detector is capable of measuring the

distance to an object, at which it is pointed, by sending and receiving ultrasonic pulses that are

reflected from the object and travel back to the detector. Because the sound waves travel at high

speeds, the motion detector can tell how far away the object is, even as the object moves.

However, because of the finite time duration of the sound pulses that the motion detector uses, it

cannot detect the distance smaller than about 0.4 m. This device will be plugged into a computer

and used in a series of instructive exercises to get you thinking about motion in a critical manner.

Log on into the computer using your ECOM account. Wait for the computer to start. Then

double click the Logger Pro icon on the desktop of the computer.

You now need to open an experiment file. From the drop-down menu along the top, use the

mouse to select File > Open > _Physics with Vernier > 01a Graph Matching.cmbl. Once you

click on that experiment file, a single position vs. time graph should appear.

You should notice that the window is in the form of a graph with two axes. The horizontal

axis is for time in seconds, and the vertical axis is for distance from the motion detector in

meters. The motion detector will tell you the distance to an object at which it is pointing by

plotting points in rapid succession. The time between successive points is so small that it will

look like a line.

The motion detector will start collecting data after you click the COLLECT button. It is often

necessary to manually rescale your graph, so that only the interested data range is displayed. This

is done by clicking on the lowest or highest numbers on the horizontal or vertical axis, and type

in your desired numbers. You can change the length of the experiment time by using the menu

Experiment > Data Collection > Duration, then enter the time duration, e.g., 10 seconds.

1−2

Procedure:

Using a flat object such as a book or a notepad, perform the following set of activities using

the motion detector and the Lab Pro system. Make sketches of the resulting graphs as they

appear on the computer screen, and thoroughly answer any questions in the space provided.

I. Constant position

a. Perform the "motion" that produces a constant "50 cm" position.

b. Perform the "motion" that produces a constant "150 cm" position.

c. Sketch the results for both a & b on the graph below, as appearing on the computer screen.

This is much quicker than printing the graph using the printer.

d. Describe the “motion” you performed to obtain these two curves.

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

II. Changing position

a. Perform the motion that produces an increasing position.

b. Perform the motion that produces a decreasing position.

c. Perform the motion that produces an increasing, then decreasing position.

d. Plot the three curves in the graphs below (a & b in one graph, c in the other).

1−3

e. Describe the motion that you performed to obtain the graph in each part.

Part a: ________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

Part b: ________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

Part c: ________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

f. A displacement is the difference between the final and initial positions during a time

interval. What would you have to do to get a displacement of 2.5 meter over the 10-second time

interval?

______________________________________________________________________________

______________________________________________________________________________

g. If you start at a position of 1.0 m, and then increase your position by 2 m, is the

displacement 1, 2, or 3 meter?

______________________________________________________________________________

III. Constant velocity

a. Walk away from the detector slowly and steadily.

b. Walk away from the detector quickly and steadily.

1−4

c. Walk toward the detector slowly and steadily.

d. Walk toward the detector quickly and steadily.

e. Plot the four curves in the graphs below (a & b in one graph, c & d in the other).

f. Describe the difference between the graphs obtained in parts a and b.

______________________________________________________________________________

______________________________________________________________________________

g. Describe the difference between the graphs obtained in parts c and d.

______________________________________________________________________________

______________________________________________________________________________

h. Describe the difference between the graphs obtained in parts a and c.

______________________________________________________________________________

______________________________________________________________________________

IV. Changing velocity

A person starts at 0.5 m, walks away from the detector slowly and steadily for 5 seconds,

stops for 3 seconds, and then walks toward the detector quickly and steadily for the last 2

seconds. First, make a prediction by sketching the expected distance vs. time plot on the blank

graph below to the left. Then have your lab partner perform the actual motion and sketch what

appears on the screen on the blank graph to the right. Be sure to discuss your prediction with

your lab partners.

1−5

a. For this activity, is your prediction the same as what appears on the computer screen?

______________________________________________________________________________

b. If not describe how you would move to make a graph that looks like your prediction.

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

For activities 5-6, you will use the motion detector to observe a velocity vs. time graph.

Click on the word “Position” on the graph and a Y-axis selection box appears. Select “Velocity”.

Change the vertical scale by clicking on the highest number and enter 1.0. Then click on the

lowest number and enter -1.0. Change the Time axis to run from 0 to 5 seconds. The Logger Pro

software produces the velocity vs. time graph by calculating the average velocity over the time

interval between two successive position measurements.

V. Constant velocity

a. Perform the motion that produces a constant zero velocity.

b. Perform the motion that produces a constant, but small positive velocity.

c. Perform the motion that produces a constant, but larger positive velocity.

d. Perform the motion that produces a constant, but small negative velocity.

e. Perform the motion that produces a constant, but larger negative velocity.

f. Plot the curves in the graphs below.

1−6

g. Describe the motion that was performed to obtain the graphs for each part of a, b, and c:

Part a: ________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

Part b: ________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

Part c: ________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

h. What is the most important difference between the graphs made in

Part b and c? ___________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

Part d and e? ___________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

Part b and d? ___________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

VI. Changing velocity

1−7

A person starts at 0.5 m, walks away from the detector slowly and steadily for 5 seconds,

stops for 3 seconds, and then walks toward the detector quickly and steadily for the last 2

seconds. First, make a prediction by sketching the expected velocity vs. time plot on the blank

graph below to the left. Keep in mind that you are given information regarding initial position

and time, and you must predict what will happen in the velocity graph. Then have your lab

partner perform the actual motion and sketch what appears on the screen on the blank graph to

the right. Be sure to discuss your prediction with your lab partners. Note that the time range is

now changed to 10 seconds.

a. For this activity, is your prediction the same as what appears on the computer screen?

______________________________________________________________________________

b. If not describe how you would move to make a graph that looks like your prediction.

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

VII. Graph matching

In this exercise you will let the graph tell you how to move, and compare your measured

motion with the prescribed motion. Please follow the menu File > Open > _Physics with Vernier,

then select the experiment file “01b Graph Matching.cmbl” for the distance vs. time graph

matching. You need to place your motion detector on an edge of the lab table so that you have

about 3 meters of room to move toward or away from the detector.

What motion must be performed to duplicate this graph? Describe for each portion of the

graph what motion should be performed.

______________________________________________________________________________

______________________________________________________________________________

1−8

______________________________________________________________________________

______________________________________________________________________________

Now please try to match the fixed graph with the graph of your motion. Let us see who does

the best in your group. After you are satisfied with the match, please confirm with the instructor.

Please print a copy of the graph using the printer and attach it in your lab report.

VIII. Additional questions

You do not need to do this part in the lab. Please study the following three distance vs. time

graphs and answer the questions below in your lab report.

a. Describe how you can move to produce each of the distance vs. time graphs.

Graph 1: ______________________________________________________________________

______________________________________________________________________________

Graph 2: ______________________________________________________________________

______________________________________________________________________________

Graph 3: ______________________________________________________________________

______________________________________________________________________________

b. What is the general difference between motions that result in a straight distance vs. time

graph and that result in a curved distance vs. time graph?

______________________________________________________________________________

______________________________________________________________________________

2-1

Name: ____________________________________

Physics 124 Lab 2: Free Falling Objects and Graphical Analysis

Goal:

Your mission is to use the motion detector to observe the free falling motion of an object

dropped from rest. You will analyze the distance vs. time and the velocity vs. time graphs for the

free falling object and practice fitting theoretical curves to the experimental data. You will also

experimentally determine a value for the acceleration due to gravity near the surface of the earth.

Setup:

The data collection will be very similar to the measurements you made during the previous

lab exercise. Using a set of clamps and aluminum rods, set up your table according to the

schematic picture below. We suggest that the horizontal bar be placed somewhat above the level

of your head. Please secure the motion detector safely with a clamp before proceeding to the

experiment.

Procedure:

1. Once everything is hooked up according to the schematic diagram, double click the

Logger Pro icon to launch the program. Follow the menu File > Open > Physics with Vernier >

06 Ball Toss.cmbl to load the experiment file. You should now have a position vs. time graph

2-2

and a velocity vs. time graph on the computer screen. For this exercise, you should set the

maximum on the Position axis to 2 m.

2. Make sure the basketball is bouncy. Hold the basketball about 0.5 meters below the

motion detector. Have your lab partner say the word “ready” at the instant the motion detector is

started. Wait until you hear the clicking noise from the detector, and only then release the ball.

Care must be taken in dropping the ball. You may recall from your previous experience with the

motion detector that at times it is confused about what it is observing. If your hands or any other

part of your body makes a significant movements while the ball is falling, your body’s motion

could be observed instead of the ball. This, of course, is undesirable. Once you release the ball,

concentrate on keeping your entire body motionless during the entire four seconds for which the

experiment time is set. Take your time and make a few practice runs until you get it done.

3. When you are convinced that you have not interfered with the ball’s motion, examine the

resulting graphs. You will notice several features on each of the two graphs that correspond to

the motion the detector observed. At this point, each of the members of your group should

endeavor to understand exactly what motion each of the features corresponds to. Do this for both

graphs. Record in the space below a detailed description of what was happening during the time

segment associated with each feature on the graphs. For example, you might describe something

like, “…between 0 and roughly 1.2 seconds the ball was falling downward away from the motion

detector, and this downward motion corresponds to the upward curving feature observed. The

ball then bounces, and the feature corresponding to the first bounce is the first ‘peak’ on the

position vs. time graph…”. Before you move on to the next step, make sure each member of your

group understands and can describe all the features that appear in both position vs. time and

velocity vs. time graphs.

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

2-3

4. To answer the following questions, concentrate on the time interval that corresponds to

the motion occurred between the first and second bounces of the ball, when the ball is not in

contact with the ground and is entirely subject to a free fall. Identify the correct time interval for

this time interval on both position vs. time and velocity vs. time graphs.

i) What are the start and end time for the time interval between the first and second bounces

of the ball? Based on the ideas presented to you in class, do you expect the acceleration of the

ball to be constant in this time interval? Why?

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

ii) Is there a way for you to predict what the position vs. time and velocity vs. time graphs for

the free falling ball should look like? Based on your answer to this, is the shape of the curve in

each graph what you expect?

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

iii) Which one-dimensional kinematic equation does each curve correspond to?

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

iv) What are the mathematical names for these two curves?

______________________________________________________________________________

______________________________________________________________________________

5. Now we analyze the “between the bounces” data in more detail. On the position vs. time

graph, highlight the “between the bounces” part of the curve by holding down the mouse button

while dragging it across the appropriate time interval you have determined. A grey area will

appear as you do this, marking the extent of the curve over the time interval between the first two

2-4

bounces. Now choose “Curve Fit” from the “Analyze” menu. A curve fit dialog box will appear.

Choose a mathematical curve with which the computer will fit the experimental data. Consider

the shape you expect and click on the corresponding curve in the list of functions in the lower

left corner of the dialog box. After selecting the name of the mathematical function you have

chosen, click the “Try Fit” button to the right of the list of functions, then click the “OK” button

to close the curve-fitting window. An information box will now appear on the Graph window

with the equation of the fitting curve and the fitting parameters that the computer used to create

the best fit to the data.

i) Which mathematical curve did you choose to fit the position vs. time data? Did it assume

the same shape as the data? (If it does not have the same shape as the data, you probably chose

the wrong function or selected too long a region of data points.)

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

ii) The information box provides the fitted curve equation and values for the parameters.

Which of these parameters is related to the acceleration due to gravity, g? What is the relation?

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

iii) Use the relation you indicated above to calculate a value for g. Show the calculation

below. How close is it to the expected value?

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

6. Now concentrate on the velocity vs. time graph. You may need to adjust the vertical

range. Follow the above directions to fit a curve to the velocity vs. time data. You will need to

drag the cursor over a range where the velocity “curve” is a straight line, in the interval of time

between the bounces.

i) Which mathematical curve did you choose to fit the velocity vs. time data, and did it

assume the same shape as the data? (If it does not have the same shape as the data, you probably

chose the wrong function or selected too long a region of data points.)

2-5

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

ii) The information box provides the fitted curve equation and values for the parameters.

Which of these parameters is related to the acceleration due to gravity, g? What is the relation?

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

iii) Use the relation you indicated above to calculate the value for g. Show the calculation

below. How close is it to the expected value?

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

iv) Please try to understand why your experimental value for g tends to be less than expected.

Describe it below.

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

Please print the entire screen and include it in your lab report.

3-1

Name: ____________________________________

Physics 124 Lab 3: Force Table and the Addition of Vectors

Goal:

This lab gives the student some practice in the addition of vectors by the geometric method,

the analytic method, and the experimental method using forces in strings due to hanging weights.

Setup:

The force table uses a hoop with three or four strings attached, tied to weights at various

angles. The instructor will briefly describe this simple setup. Force is calculated using the

equation for the weight of an object near the surface of the earth: F = mg, where F is the force in

newtons (N), m is the mass in kilograms (kg), and g is the acceleration due to gravity; g = 9.8

m/s2 = 9.8 N/kg. You have to use the mass in kg, but the weights are marked in grams.

Procedure:

As the first case, consider two masses, each is 200 g. The weight of each mass is w = mg, so

the force in each string has a magnitude of F = 0.2 kg×9.8 m/s2 = 1.96 N. If we have these strings

pointing in different directions, the two forces are each of the same magnitude, 1.96 N, but the

vector forces are set in different directions, e.g., at 30º and 120º as marked on the force table.

For each of the three cases in this lab, you should draw the force vectors on a graph with all

of the vectors placed so that their tails are at the origin. This represents the actual physical

situation with 3 or 4 forces pulling on the ring. These vector forces add up to zero net force on

the ring.

Your drawing will literally match the placement of the strings if you pull out the center pin

and place your drawing underneath the strings, assuming that they are balanced.

To practice the addition of vectors we will find the vector sum of these two forces by three

methods:

A. Experimental method of vector addition. Using the force table, arrange two pulleys at

the angles of 30º and 120º, then put two of the strings over the pulleys and add enough weights

to give a total mass of 200 g on each string. Remember that a hanger itself has a mass of 50 g.

Then experiment with the position and weight needed on the third string and pulley to get a

balance. This will happen when the ring is centered on the center pin and not touching it. This

3-2

will give you the magnitude and direction of the equilibrant force, which when added to the sum

F1 + F2 will result in a total force of zero. In other words, the equilibrant force is the negative of

the sum of F1 + F2; it has the magnitude of F1 + F2 and is in the opposite direction, and results in

an equilibrium situation with no motion. You may to finely adjust the position and weight on the

third string to reach this equilibrium state.

Repeat this procedure for two more cases shown in the table below and record your results of

the sum of the two vectors using the experimental, the analytical and the graphical method. You

need to include your calculations and graphs on separate sheets of paper in the lab report.

Case Masses and directions Equilibrant force (magnitude F and direction θ )

Experimental Analytical Graphical

1 m1 = 200 g θ1 = 30º

m2 = 200 g θ2 = 120º

F =

θ =

F =

θ =

F =

θ =

2 m1 = 200 g θ1 = 0º

m2 = 150 g θ2 = 90º

F =

θ =

F =

θ =

F =

θ =

3 m1 = 200 g θ1= 20º

m2 = 150 g θ2 = 80º

F =

θ =

F =

θ =

F =

θ =

B. Graphical method of vector addition. Make a drawing, as mentioned above, for each of

the three cases, which has the force vectors placed with their tails at the origin. Compare with the

placement of the strings to see that you got the angles correct. The scale has to be chosen so that

the vectors stay on the paper. For example, you might choose a distance of 5 cm on the paper to

represent a force of 1 N.

Then for each of the three cases, use a separate sheet of paper to graph the parallelogram

method or the triangular method (described in your book) to add the two given vectors. You need

to use rulers and protractors. Compare the result with the third vector obtained from the

experimental method.

3-3

C. Analytical method of vector addition: Using the component method, compute the

magnitude (F) and direction (θ, angle from the x-axis) of the resultant force. The relevant

equations are listed below:

1 1 2 2

1 1 2 2

2 2

1

c o s c o s

s in s in

ta n

x

y

x y

y

x

F F F

F F F

F F F

F

F

θ θ

θ θ

θ−

= +

= +

= +

=

When calculating the angle using the arctangent function, pay attention to the quadrant of the

(Fx, Fy) vector.

In your lab report please discuss on how well the results of the three methods of vector

addition agree with each other. Please do not forget to include your calculations and graphs on

separate sheets of paper.

4-1

Name: ____________________________________

Physics 124 Lab 4: Force Sensor and Newton’s Second Law

Procedure:

I. Calibrating the dual-range force sensor

A force sensor, as shown in the figure, measures force. When the movable arm of the force

sensor is pushed or pulled, it sends a signal to the computer in the form of a voltage. The harder

the push, the higher the voltage produced. The combination of the force sensor and the computer

can be used to measure force if it is calibrated; that is, if you instruct the computer how to

convert the measured voltage to a force. Follow these steps to set up the force sensor:

i) Connect the force sensor to CH 1 of the Lab Pro. Set the switch on the force sensor to the

±10 N setting. Connect the motion detector to the DIG/SONIC 1 port.

ii) Start the Logger Pro program. The computer will automatically detect the force sensor. If

it works properly, you should see a Force vs. Time graph, above the position and velocity graphs.

Try clicking on the Collect button and you will see a line appear. Push or pull on the sensor

“arm” to see the effect of a force. You also see “meter” windows with the numerical values of

the force and position.

iii) These force sensors should already be calibrated, but they will not give precise results

unless we make a small adjustment, called “zeroing the sensor”. Place the sensor on the table,

with the movable arm pointing horizontal. Then click on “Experiment” > “Zero…” and be sure

to uncheck the motion detector box, so that only the force sensor is zeroed. After a short delay,

the sensor is ready to measure forces.

iv) To check that the sensor is measuring force accurately, suspend a 500 g weight and a 50 g

weight hanger from the hook on the force sensor. Hold the sensor as still as possible. Once you

have suspended the weight and hanger from the force sensor you will notice that the force is

4-2

indicated on the screen, indicating that something is indeed pulling down on the force sensor.

The value of the force (i.e., the weight of the 550 g mass) should be 5.39 N.

II. Observing and measuring forces

At this point, it will be good for you to push and pull on the sensor with your fingers to get an

idea of how thing works, and to get a feel for what a force of one newton is. To observe the value

of the force exerted on the sensor as a function of time, click the “Collect” button at the top. You

can also change the Force and Time scales as needed to better observe the data. Each individual

in your group should take a moment to try the following:

* With your thumb, exert a constant +10 Newton force for 5 seconds.

* With your thumb, exert a constant –10 Newton force for 5 seconds.

* Apply a varying force with your thumb.

* Try to observe the effects of gravity on the force sensor by rotating it by 180º with no extra

weight added. First point it up, and then point it down. You may have to change the scales on the

Force vs. Time graph to observe this effect. Is there a noticeable difference between the two

cases?

______________________________________________________________________________

______________________________________________________________________________

* Put the sensor on its side on the table and check for a zero force again.

III. Measuring force and acceleration of a fan cart

Next, you will make use of the PASCO track and the cart with the little fan on it. When the

fan motor is switched ON, you will notice that, when released, the fan causes the cart to

accelerate down the track. Therefore, the fan must effectively be exerting a net force on the cart.

The fan can be rotated to face any direction (it is best to hold the fan near its base to do this).

This allows us to vary the component of force along the direction of motion of the cart.

Newton’s second law (F = ma) tells us that a net force exerted on a massive object should

cause an acceleration of the object which is directly proportional to the exerted force and

inversely proportional to the object’s mass. We will now check the validity of this assertion by

measuring the net force exerted on the cart and the acceleration of the cart when the fan is set at

different angles.

Before you make any measurements, observe qualitatively the effect that different fan

settings have on the motion of the cart. “Qualitatively” means to observe the effect of different

4-3

settings without estimating any actual values of the force. Also, for a given angle, observe the

effect of different fan speeds by running the fan on “high” and then on “medium” modes.

To quantitatively measure (i.e., get an actual number for) the net force exerted on the fan and

the acceleration of the fan cart associated with the different settings, follow this procedure for

each fan setting and enter the measured force and acceleration in Table 1.

i) Set the force sensor on the track so that the movable arm is facing along the track. Place

the fan cart directly in front of the force sensor so that the fan will push the cart up against the

sensor. The sensor may record this as a negative force, but you can ignore the negative sign. Set

the time for observation to 10 second, and set the vertical scale of the graph from –1.0 to 1.0

newtons (you may have to use a different scale to suit your particular fan). With the fan set at the

angle of interest (see Table 1), switch the fan to the desired speed so that it pushes against the

arm of the force sensor. Wait for two or three seconds, then click on the “Collect” button and

observe the measured force for the 10-second interval. You will notice that a jaggedness,

characteristic of any measurement device, appears. This jaggedness is commonly referred to as

“noise” and is an example of random error associated with the operation of the instrument.

ii) A good way to estimate the value of the force is to find the average of a number of

measurements of the force. Using the mouse, select most of the set of data by holding the mouse

button and dragging the cursor (a + symbol) across the horizontal extent of the Force vs. Time

graph (it is OK if you leave out a few of the data points at the beginning and the end). From the

“Analyze” menu, choose “Statistics” and a box will appear indicating statistical information

about the set of data that you selected. (There is also a shortcut STAT button on the main menu.)

The important quantity in this box is the “Mean” value, which is the average for all the data

points you selected.

iii) You have measured the force exerted on the cart when the fan is set at High 0º. Now for

this setting, we will measure the associated acceleration of the cart. To do this, use the motion

detector. Here is a procedure to follow in order to determine the acceleration of the fan cart.

iv) Position the motion detector at the end of the track. The motion detector must be able to

detect the fan cart as it is accelerating down the track away from the detector. There should be a

bumper at the other end to stop the fan cart, or someone should catch the cart.

v) Put your finger in front of the fan cart, with the cart at least 50 cm away from the detector.

Once the fan is switched on and is up to speed, click the Collect button, wait for the sound of the

motion detector, and then pull your finger away so the cart can accelerate away from the motion

detector. Someone should catch the cart. You may have to play with the position of the motion

detector to ensure that you are actually detecting the fan cart.

4-4

vi) Measure the acceleration for the fan setting High 0º and record this in Table 1. You

should remember how to obtain acceleration by curve-fitting a Distance vs. Time or a Velocity

vs. Time graph.

vii) Follow this procedure and measure force and acceleration for each fan setting indicated

in Table 1, and record them. It is better to use angles on one side or the other, but remember

which side you used.

Table 1

Fan setting Measured force F (N) Measured acceleration a (m/s2)

High 0°

High 30°

High 60°

Medium 0°

Medium 30°

Medium 60°

IV. Validating Newton’s second law of motion

With Table 1 completed, you have sufficient data to make a validity test of Newton’s second

law of motion.

Describe below how you propose to use this data to test the validity of Newton’s second law.

Hint: Notice that F = ma is similar to y = mx so you will need to do a linear fit to a graph of F vs.

a using the values of F and a from the columns of Table 1. Which variable, F or a, goes on the

horizontal axis and which on the vertical axis?

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

What do you expect your proposed graph to look like? Why?

4-5

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

Now use Excel to make the plot you propose in the above description. Enter your data in

Table 1 into a worksheet in Excel. Make sure a is entered into the column corresponding to the

x-axis, and F the y-axis. To get these to plot correctly, you may need to order the pairs of data

points in order of increasing a. Select all the data points and plot a scattered line. To find the

linear fit equation for the line, use the trendline feature in Excel, and display the equation of the

fitted line on the graph.

What do you expect the slope of this graph to be equal to? Is the actual slope equal to the

expected value (the mass of the fan cart)? You can weigh the fan cart on a pan balance in the lab

to get its mass. When you weigh the fan cart, tilt it on its side to keep it from rolling off the pan.

Different fan carts may have slightly different masses since they may have different types of

batteries in them. If the slope is significantly different from what you expect or predict to be,

how can you account for the difference?

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

How will you know if you have indeed validated Newton’s second law?

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

In your lab report please include a printed copy of the graph you made by Excel.

5-1

Name: ____________________________________

Physics 124 lab 5: Work and Energy

Goal:

By the time you start this experiment, you should be well acquainted with the motion

detector and the force sensor. In this experiment, you will be measuring work and kinetic energy.

In addition, you should begin to see the relationship that these quantities have with each other.

When a force acts through a distance, work is performed, as long as a component of the force

is in the direction of motion. Work can also be thought of as the transfer of energy from one

system to another. The amount of energy transferred into or out of a simple mechanical system,

such as the system you will look at in this laboratory, can be quantified through the work-energy

theorem, which you are familiar with by the time you read this lab.

Setup:

Set up your workstation so that both the force sensor and the motion detector are connected,

with the force sensor plugged in CH1 and the motion detector in DIG/SONIC 1. Once everything

is properly connected, start the Logger Pro program. You should see three windows: Force vs.

Time, Distance vs. Time, and Velocity vs. Time. Your workstation should now be ready to use

both the motion detector and force sensor to make measurements. We should also set the

sampling rate, by starting with the “Experiment” menu, choose “Data Collection” then in the

Sampling Rate data entry box, type in 50, and click “Done”. Make sure that both sensors are

working properly, and zero the force sensor.

Procedure:

I. Measuring the frictional force

In this section we will measure the frictional force exerted by the track on the cart. To do this

we actually measure the acceleration of the cart when there is only the frictional force, and no

other forces are acting in the direction of motion of the cart. You can relate the acceleration of

the cart to the frictional force, which we are seeking for, using newton’s law. Explain (in the

space below) the relationship between the frictional force and acceleration.

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

5-2

It then seems that we need the mass of the fan cart. Let us measure it using a balance and

write down the result below.

______________________________________________________________________________

Set the fan cart on the PASCO track with the motion detector on the end of the track, and a

bumper on the other end of the track, to allow the detector to measure the fan cart for the entire

track length. Check that the fan is off. Place the cart at the end of the track closer to the motion

detector. Give the fan a gentle push and measure its motion as it slows down.

We are going to measure the acceleration of the fan cart. We have learned this in previous

labs. Which graph should we use to measure acceleration (e.g., distance vs. time, velocity vs.

time)? What kind of curve fit do we apply?

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

i) What is the acceleration of the cart you measured?

______________________________________________________________________________

ii) What is the frictional force on the cart?

______________________________________________________________________________

______________________________________________________________________________

This frictional force should be about the same for other experiments. Remember, the work

done by this force will be different if different distances of travel by the fan cart are considered.

iii) For practice, pick an interval of the motion and calculate the work done in joules by

friction. Please clearly indicate the magnitude of the displacement of the fan cart you used to

calculate these values. (This is an arbitrary distance and will not be used in the following

sections. We will calculate the frictional work again for the different distance used in the motion

in the following section.) Is this work positive or negative?

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

In your lab report please include a printed copy of the graph you are now using in measuring

the frictional force.

5-3

II. Relationship between work and energy

Now that you know how to calculate the work done by friction, we can look at a more

complicated system where an applied force is accelerating the cart.

i) Place the fan cart on the track and set it up against the force sensor to measure the force

that the fan exerts on the cart. Flip the switch to "high" mode and set the angle of the fan at 0º

tilt. Record the value of the force below.

______________________________________________________________________________

______________________________________________________________________________

ii) With the fan cart in "high" mode, release the cart and measure the velocity and the

position of the cart as a function of time as it travels all the way down the track. Remember to

start the cart at least 50 cm away from the motion detector.

iii) Pick a proper region on the graph (i.e., without incalculable forces, such as exerted by

your hand to stop the cart) to calculate the work done by the "fan force". You could include the

motion from just after releasing the cart, until just before it was caught at the end of the track. Do

this calculation below. You should use the force measured by the force sensor in the last

question. Keep the graph up on the screen to obtain the needed information.

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

iv) For the same region of the graph, calculate the work done by friction, assuming the

frictional force is the same as previously found in part I.

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

v) Calculate the work done by gravity for this motion (or is it zero?).

______________________________________________________________________________

______________________________________________________________________________

vi) Calculate the change of kinetic energy (∆K) during this same interval using the initial and

final velocities at the beginning and the end of the interval. (Remember that the difference in

kinetic energy is the difference between two values of ½ mv2, one at the end of the interval, and

5-4

the other at the beginning of the interval.) It might be useful to draw an appropriate curve fit on

the v curve to best estimate the velocities. If this is done, be sure it shows on the velocity graph.

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

vii) Finally, calculate the net work done on the cart, Wnet, and compare it to the change in

kinetic energy of the cart, ∆K. Show these calculations and the comparison below. Should they

be the same? Why or why not? If your values are not the same do your best to account for the

reason.

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

In your lab report please include a printed copy of the velocity vs. time graph you are using

in doing the above calculations.

6-1

Name: ____________________________________

Physics 124 Lab 6: Impulse and Momentum

Goal:

In this lab exercise your mission is to use the laboratory apparatus, including the force sensor

and the motion detector, to study the impulse-momentum theorem and the principle of

conservation of momentum. In the following procedure, it is assumed that you remember how to

use the apparatus to make the measurements required. You may at times have to refer back to the

descriptions of previous lab exercises for a quick review.

You will be asked to answer in detail many questions regarding how the quantities you have

measured relate to the physical ideas. Make sure that you discuss the questions with your group,

with other groups, and with your lab instructor or lab assistant as is necessary to achieve a full

understanding of each one. Write a thorough answer to each question before moving on.

Procedure:

I . Measuring impulse

1. Plug a force sensor into the CH1 input and connect a motion detector into the DIG/SONIC

1 input of the Lab Pro interface, and start the Logger Pro program on your computer. Zero the

force sensor (which should be placed horizontal on the table) using Experiment > Zero and then

uncheck the DIG1: Motion Detector box because we only want to zero the Force Sensor, and

then click OK.

2. Set the sampling rate for the force sensor to 1000 samples/second (use Experiment > Data

Collection and enter 1000 in the sampling rate box). Put the force sensor on the PASCO track

and use a thumb and finger with a squeezing force to keep it from moving during the following

collision. You will roll one of the carts toward the force probe and cause a collision with the

movable arm of the sensor, which can be observed on a force vs. time plot. Make sure that the

time axis is set for a sufficient amount of time to observe the collision event. You may have to

play with different cart speeds to observe a reasonably well behaved force vs. time curve. You

should use the end of the cart with the spring-loaded plunger to produce a "longer" collision. At

the same time, you should have the motion detector behind the cart in order to measure its speed

before and after the collision.

3. Rescale the time axis so that the collision takes up most of the plot. You should include a

region of the motion both before and after the collision, so that you can fit a line to the position

curve before the collision to get the initial velocity before the collision, and, similarly, fit another

line to an interval on the position curve to get the final velocity after the collision.

6-2

4. So far you have measured a time-dependent force. In other words, the force vs. time plot is

not a straight, horizontal line. In class, we have concentrated only on calculating an impulse by

using an average value of the force for the time interval over which it acts. To analyze your force

vs. time data, highlight the force curve by dragging the mouse from the initial time of the

impulse to the final time of the impulse, and select “Statistics” from the Analyze menu (or click

on the STAT button on the main menu). The computer will provide you with the average (mean)

value of force. Record the value of Fave below.

______________________________________________________________________________

5. Write down from your force vs. time plot the values of ti and tf , the times when the force

was first applied and when the force ceased to be applied, respectively.

______________________________________________________________________________

______________________________________________________________________________

6. From the measurements made in the previous two steps, calculate in the space below the

impulse delivered to the cart during the collision. (You could also try the “Analyze” …

“Integral” sequence to see how the computer shades the area in red and calculates the impulse.)

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

7. Keeping in mind the impulse-momentum theorem, what is the expected effect of this

impulse on the cart?

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

8. Measure the mass, the initial velocity and the final velocity of the cart. Record your results

below.

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

9. Calculate the initial momentum, the final momentum, and the change of the momentum of

the cart. Are your measurements consistent with the impulse-momentum theorem?

______________________________________________________________________________

6-3

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

II. Collisions and conservation of momentum

Now that you have observed the relationship between impulse and momentum, we will look

at elastic collisions between two carts. Place on the track two carts with magnets embedded in

the ends so that the magnets will repel each other when the carts approach each other at close

distances. This configuration of the carts will result in an essentially elastic collision if the carts

do not actually touch when they collide. For the following, refer to the elastic 1D collision

equations from your text (where we will use v20 = 0). You should exit the Logger Pro program,

disconnect the force sensor, and then plug in the motion detector to the DIG/SONIC 1 port.

Then start the Logger Pro program again before making the velocity measurements below. You

should position the motion detector so that it observes the motion of cart 1 that is initially

moving.

When cart 1 of mass m1 moving with a velocity V10 collides elastically with cart 2 of mass m2

(stationary, V20 = 0), the resulting final velocities of each cart in terms of the initial velocity V10

of the moving cart are

1 2 1 1 1 2 2 11 10 2 10

1 2 1 2 10 1 2 10 1 2

2 2, , or , .

m m m V m m V mV V V V

m m m m V m m V m m

− −= = = =

+ + + +

This equation can be obtained from Eq. 6.14-15 on Page 200 of our textbook. It is derived

from the principles of momentum conservation and kinetic energy conservation. Now consider

two carts with equal mass. Push the first cart into the second cart, which is at rest (stationary

cart) in the middle of the track, and observe what happens and measure the final velocity V1 of

the first cart that was initially moving with velocity V10. Record the velocities V10 and V1 in the

data sheet below. Compare with the predicted value. Now take one of the black metal 500g

blocks and place it in the stationary cart. This should approximately double the mass, but you

may want to weigh the cart to be sure. Again, push the cart 1 at a reasonable speed into the

6-4

second cart, and measure the initial velocity V10 and final velocity V1 of the cart that was initially

moving. Does the ratio of the final velocity over the initial velocity (V1/V1o) agree with the

prediction? Continue the process of adding 500-gram masses on cart 2 and record your results in

the data table below. Compare the measured V1 / V10 with the predicted value for each case until

3 black metal blocks have been added to the initially stationary cart. What do you observe? Is

there a trend in the resulting final velocities?

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

Mass

Measured

V10

Measured

V1

Measured

1

10

V

V

Predicted

1 1 2

10 1 2

V m m

V m m

−=

+

m2 = m1

m2 = 2m1

m2 = 3m1

m2 = 4m1

What should happen as the stationary mass m2 becomes infinitely massive? Why?

______________________________________________________________________________

______________________________________________________________________________

Now redo the variable mass experiment by placing additional mass on the cart 1, which is

initially moving and by keeping the initially stationary cart 2 empty. Add mass to the moving

cart 1 in 500 gram increments. For each case, make the same measurements and observations as

you did in the steps above, and record your results in the data table below. How does adding

mass to the moving cart affect the final velocities? Is there a trend? What is it? What is the major

difference in the motion of the carts after a collision when adding the mass to the moving cart as

opposed to the stationary cart?

6-5

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

Mass

Measured

V10

Measured

V1

Measured

1

10

V

V

Predicted

1 1 2

10 1 2

V m m

V m m

−=

+

m1 = m2

m1 = 2m2

m1= 3m2

m1 = 4m2

7-1

Physics 124 Lab 7: Torque, Equilibrium, and Center of Gravity

Goal:

In this lab exercise, your goal is to understand the mechanical equilibrium of a simple object

and how to apply the ideas of torque to this problem. You should also be able to explain how a

laboratory balance works.

Procedure:

The setup consists of a meter stick, support clamp, loops of string, weight hangers, and

weights. String and small bits of masking tape may be useful to hold the loops in place if they are

near the end of the meter stick. Determine the mass of the meter stick by weighing it on a

laboratory balance. Record the result on the data table. Place the support on the lab jack, which

can be lowered so that the meter stick does not tilt too much (otherwise the loops will slide off

the meter stick).

The knife-edge clamp is used to support the meter stick, and should be placed near the center

of the meter stick. Orient the meter stick so that you can read the metric side correctly and so that

the scale will go from 0 to 100 cm from left to right. Place these on the support (without any

other clamps or weights) and move the clamp until you find a position that balances. To get a

stable equilibrium, the center of mass of the meter stick must be below the pivot points,

otherwise you will need to pull the clamp off and put it back on the other way. It is usually not

exactly at 50 cm. Record the position of the pointer, which indicates the center of gravity of the

meter stick.

I. Two known masses

With the knife-edge clamp firmly clamped on the meter stick at the center of gravity, the

meter stick should be balanced. Now add a mass of 150 g (remember that the weight of the

hanger is 50 g) using a loop of string, so that it hangs from the meter stick at a fixed position of

15 cm (as indicated by the scale on the meter stick). Now hang 200 g from a point on the other

side of the meter stick to get a balance. Record the various values in the data table, and calculate

the torques due to the two hanging masses. Remember to use the lever arm, which is the distance

from the point of support to the point where the loop is hanging. Calculate the difference of the

two torques; divide by the smaller of the torques, and multiply by 100% to get the percent

difference (a few percent at most).

II. Three known masses

7-2

a) Starting with the balanced meter stick, suspend a mass of 100 g at position x1 = 30 cm,

then a mass of 200 g at x2 = 70 cm, and then find the position where a third mass of 50 g will

produce a “balanced beam”. Record the data values, and calculate the torques and differences.

This time you will need to add two of the torques to find the total torque in one of the two senses

(clockwise or counterclockwise).

b) In this part we will study the same situation of three hanging masses, but let’s predict the

correct position before we hang the third mass on the beam.

Use these values: m1 = 100 g, m2 = 200 g, m3 = 50 g, x1 = 20 cm, x2 = 60 cm, and then

calculate the location x3 before you hang the third mass on the beam. After calculating the

position x3, hang the masses on the beam at the fixed position x1 and x2, but now vary x3

experimentally and record the result for the experimental value of x3 (and r3).

III. An unknown mass

Obtain an “unknown” mass (painted) and hang it at a position of 10 cm. Then hang a known

mass of 300 g (called the “counter mass”) so that you get a balance. If you cannot get a balance,

you may need to use a larger weight. By calculation, using your measured lever arms and a

calculation of torques, find the unknown mass, record the value, and then take the unknown mass

off the beam and weigh it using a laboratory balance to get a “known” value of the mass. Record

your data and compare your experimentally determined value with the “known” value.

Next we will study two cases where the meter stick is not balanced. This means that we

cannot ignore the mass of the meter stick in the torque calculations.

IV. Meter stick with one mass

Suspend a 100 g mass from one end of the meter stick (or very close to the end, using

masking tape). Move the knife-edge support so that the entire system of meter stick and mass is

balanced. Record the positions of the knife-edge support and the mass. Calculate the torque due

to the meter stick, using the center of gravity of the meter stick as the position x2 of the entire

mass of the meter stick for the calculation of the lever arm due to the weight of the meter stick.

Use the usual method of calculating the lever arm of the hanging mass (but remember that you

have to measure from the new position x0' of the knife-edge). Show your work on a separate

sheet and record your results.

V. Center of gravity

With the knife edge position at the same position as in part IV, balance the system using one

weight (given in the table) on the left side and two weights on the right side (use your own

values for weights and distances).

7-3

Physics 124 Data and results for Lab 7 Name: _____________________________

Mass of meter stick: ____________________

Balancing position of meter stick (center of gravity): _________________________

Case Mass Position Lever arm Results

I

m1 _________

m2 _________

x1 = 15 cm

x2 _________

r1 _________

r2 _________

τccw _________

τcw _________

% diff ________

II(a)

m1 _________

m2 _________

m3 _________

x1 = 30 cm

x2 = 70 cm

x3 _________

r1 _________

r2 _________

r3 _________

τccw __________

τcw __________

% diff ________

II(b)

m1 _________

m2 _________

m3 _________

x1 = 20 cm

x2 = 60 cm

x3 _________

r1 _________

r2 _________

r3 ____________

(calculated)

r3 ____________

(measured)

III m2 _________

(known)

x1 = 10 cm

x2 _________

(from experiment)

r1 _________

r2 _________

m1 _________

(calculated)

m1 _________

(measured)

7-4

Case Mass Position Lever arm Results

IV

m1 _________

m2 _________

(meter stick)

x1 = 0 cm

x2 = ______

x0' ________

(knife edge)

r1 _________

r2 _________

τccw _________

τcw _________

% diff ________

V

m1 = 300 g

m2 _________

m3 _________

m4 _________

(meter stick)

x1 = _____

x2 = _____

x3 = _____

C.G. = _____

r1 _________

r2 _________

r3 _________

r4 _________

τccw _________

τcw _________

% diff ________

8-1

Physics 124 Lab 8: Archimedes’ Principle and Buoyancy

Goal:

In this lab exercise, your goal is to validate Archimedes’ Principle and to measure the density

and specific gravity of solid and liquid samples.

Procedures:

I. Demonstration of Archimedes’ Principle

The setup consists of a pan balance from which a string can be attached, so that the mass may

be immersed in an “overflow can”. The water that overflows is caught in a beaker and can be

weighed to determine its volume, or the volume can be directly read from the graduations on the

beaker. The weight of the mass can be measured while it hangs in air or immersed in water.

a) Determine the mass of the metal sample by weighing it on a laboratory balance. Record

the result in the data table. Weigh the empty beaker also.

b) Fill the overflow can with water until it overflows. Catch any overflow water in a beaker

and dump it down the drain. Now suspend the mass in the water and catch the overflow in the

beaker in order to determine the volume of water displaced. Record this volume. You should also

weigh the beaker with this water in order to determine the mass of water displaced, and in order

to compare with your estimate of the volume of the water as measured by the graduated marks.

Here you need to know that 1.0 gram of water has a volume of 1.0 cubic centimeter.

c) The metal sample should also be weighed while it is under water, in order to determine the

buoyant force. This can be done separately from capturing the overflow water. You just need to

make sure that you are measuring the force in the string, and that this is due to the weight of the

mass, minus the buoyant force. In order for this to be true, you must ensure that the mass is not

touching the sides or bottom of the beaker. (Think of how the free-body diagram for the mass

would change if it were partly supported by the bottom of the beaker; you wouldn’t be able to

measure that contact force and would therefore be unsure of the size of the force in the string.)

By looking at the free-body diagram for the mass suspended in water, you can see that this

buoyant force is the difference between the object’s true weight and submerged weight, Fb = m0g

– m0'g, as Archimedes’ principle says that this buoyant force is equal to the weight of the

displaced water (which was the water that overflowed), Fb = ww = mwg. You should compute the

(measured) buoyant force to the weight of the displaced water, and find the percentage

difference.

d) Finally, compute the specific gravity of the metal sample and compare to the accepted

value (Al – 2.7, Brass – 8.4, steel – 7.9, lead – 11.3).

8-2

II. Density of a light object

Determine the density of a wooden block by using a heavy metal object as a sinker. There are

several ways to do this, and your instructor will show one method. First weigh the wooden block

while it is still dry.

One way is to hang the sinker below the wooden block so that 1 or 2 cm of string separates

the two, then immerse the sinker but leave the wooden block above the surface. Record the

apparent mass of the two objects, as measured by the balance. Then raise the container of water

so that both the sinker and block are immersed, and record the apparent mass of the two. The

difference between these two measurements is that the block is immersed or not, and so the

difference in the apparent masses is related to the buoyant force created when you immerse the

wooden block. Therefore, you can just take the difference in apparent masses, write it in grams,

and immediately conclude that this is the mass of the water displaced (by Archimedes’

principle). Therefore, the volume of water displaced is equal to this number (of cubic

centimeters) and you do not need to measure the actual water displaced. Now that you know the

volume of water displaced by the block, you deduce that it is also the volume of the block. Then,

knowing the mass and volume of the block, you calculate the density of the wooden block by

using the recorded dry mass of the block and its deduced volume, and applying the definition of

density ρ = m/V.

III. Density of a liquid

The density of a liquid will be determined directly by using a container with an accurate

volume of liquid and simply weighing the volumetric flask with and without the liquid to

determine the mass of the liquid. Therefore, the calculation of density is immediate. This will be

done with a “mystery” liquid that will be available in the laboratory. This liquid is harmless

unless you drink a moderate amount of it. Start by weighing the empty flask (with its glass plug).

Fill the flask to slightly overflowing with the unknown liquid, and then put the plug in (gently,

do not push too hard or it might get jammed). Wipe off excess liquid and weigh the full flask.

Please recycle the liquid to the Erlenmeyer flask (conical flask) after weighing the full

volumetric flask. You can read the volume of the flask off the side and directly calculate the

density of the fluid from the mass of liquid and its exact volume. Compare your calculated

density to the known density of some possible fluids.

8-3

Physics 124 Data and results for Lab 8 Name: _____________________________

I. Demonstration of Archimedes’ Principle

a) Type of metal ______________

Mass of metal m0 in air ___________________

Mass of beaker mb ____________

b) Mass of beaker and displaced water (mb + mw) _________________

Mass of displaced water ___________

Volume of displaced water (cm3) ____________

How does this relate to the mass of water? ________________________________________

c) Apparent mass of metal m0' when suspended in water ________________

Difference between true mass and apparent mass under water (m0 – m0') ______________

Buoyant force (in newtons) Fb = (m0 – m0') g = ___________________

Weight of displaced water (in newtons) _______________________

Percent difference of these two forces ____________

d) Density of metal sample _________________

Specific gravity of metal sample ________

Show calculations here:

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

II. Density of a light object

Mass of dry wooden block in air _________________

Apparent mass of block and sinker with only the sinker submerged __________________

Apparent mass of block and sinker with both submerged __________________

Difference in measured apparent masses ______________________

Deduced volume of displaced water (hence volume of block) _________________

Density of wooden block ______________________

8-4

III. Density of a liquid

Mass of empty volumetric flask _____________________

Mass of full flask ______________________

Mass of liquid (difference between above masses) ___________________

Density (divide by 50 ml volume of flask) __________________

Question: The accepted value of specific gravity for pure isopropanol is 0.786. For rubbing

alcohol it is 0.79. For methanol it is 0.81. For water it is 1.00. Which liquid do you think it is?

Is your value a little high? If so, what contamination might be there in the liquid? Is the sample

actually a mixture of liquids?

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

9-1

Physics 124 Lab 9: Thermal Expansion

Goal:

In this lab exercise, your goal is to measure the coefficient of linear thermal expansion for

three different metal rods.

Procedure:

The setup consists of a metal rod supported on one end by pins and on the other end by a

simple support so that it can expand. Steam can be generated and passed through the rod in order

to heat it. The temperature of the rod is measured by measuring the resistance of a temperature-

dependent resistor in a small clip attached to the rod. The instructor will show how this is set up.

The temperature of the rod can then be determined by looking up a value in a table attached to

the apparatus. The apparatus should be set up so that condensed steam (water) drains out of the

rods into a small beaker or pan. Blocks of wood are useful in order to prop up the apparatus so

that it drains properly. Gloves or paper towels are needed to handle the hot rods after measuring

their expansion.

a) Determine the length of each rod by using the meter stick. Leave the rods on the table

away from the apparatus so that they remain cool, at room temperature. Room temperature can

also be determined from the electronic thermometers on your lab table.

b) One by one, you will measure the expansion of the three rods, so the procedure will be

the same for each one. Start by putting the rod on the apparatus, with the pin in the proper slot.

Notice how the micrometer dial turns (when the rod expands) by pressing the micrometer pin

with your finger. When you begin heating, the dial may move more than one turn, and may move

in a counterclockwise direction to smaller numbers on the scale, so check this before you start

heating.

c) The steam is generated by a small device similar to a “hot pot” which should be filled

about ¾ full with distilled water (from the jugs). This is done to prevent buildup of mineral

deposits in the hot pot. Remember that steam can burn you! So be careful when handling the

hose and metal rods once they get hot. You might want to start the pot heating right at the

beginning of the lab, while the instructor goes over the experiment.

d) When you are ready to heat the rod, note the position of the micrometer dial or, better yet,

set the dial to zero by rotating the outside rim by hand. Using a glove, attach the hose (once it has

steam coming out of it) to the rod and watch the dial rotate. You should be measuring the

temperature, and will notice a rapid rise at first, and then it will stabilize at around 90ºC. Once

the temperature stabilizes, record the (maximum) values of final temperature and change in

length. Calculate the change in temperature ∆T and the coefficient of thermal expansion.

9-2

Physics 124 Data and results for Lab 9 Name: _____________________________

Type of rod Aluminum Copper Steel

Initial length L0

Initial micrometer

setting

Final micrometer

setting

∆L

Initial temperature

T0 (ºC)

Final temperature

T (ºC)

∆T = T −T0

α (Measured)

α (Accepted

handbook value) 23.1 × 10−6 (1/oC) 16.5 × 10−6 (1/oC) 11 − 13 × 10−6 (1/oC)

10-1

Name: ____________________________________

Physics 124 Lab 10: Spring Force and Simple Harmonic Oscillator

Goal:

In this lab exercise, your goal is to use the motion detector to measure and study various

aspects of a spring force, and investigate the simple harmonic motion of a “mass on spring”

system.

Procedure:

I. Determining the spring constant

a) Set up a vertical rod, right-angle clamp, and horizontal rod from which to hang the spring.

b) Suspend an empty weight hanger from the other end of the spring. Now, describe in the

space below how you intend to determine the spring constant k of your spring by adding various

masses to the weight hanger. (Hint: there should be a meter stick nearby). Indicate exactly what

measurements you will make, what quantities you intend to plot on a graph, and how the graph

will allow you to find k. A detailed sketch is necessary here.

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

c) Once your procedure for part b has been approved by the lab instructor, follow your

procedure and calculate k. Include your data table below. Print out and attach your (properly

labeled, as always) graph.

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

10-2

II. Measuring the period of a simple harmonic oscillator

a) Fix a mass on the weight hanger, say 100 g, and set the spring system in motion by

pulling down (not too far) and releasing the mass. Make sure the oscillations are up and down in

a vertical line. Minimize any side-to-side motion. Place the motion detector directly below the

oscillating mass so that the distance vs. time and velocity vs. time graphs can be observed. This

will require some “playing” with the position of the motion detector and the scales of the plots in

the Logger Pro program.

b) When you are sure that you are detecting the motion of the harmonic oscillator, set it in

motion and track it for 10 seconds. Measure the period T between the maxima on the distance vs.

time graph in three different places, and then do the same in three different places on the velocity

vs. time graph. Record your measurements below.

Distance vs. time Velocity vs. time

# T (sec) # T (sec)

1 1

2 2

3 3

Are the three measured periods from the distance vs. time graph equal? Should they be?

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

Are the three measured periods from the velocity vs. time graph equal? Should they be?

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

Are the periods the same for the distance vs. time and velocity vs. time graphs? Is this

expected? Why?

______________________________________________________________________________

______________________________________________________________________________

10-3

______________________________________________________________________________

______________________________________________________________________________

c) From the distance vs. time graph, what is the amplitude in meters? ________________

Now set the harmonic oscillator in motion again, but this time, give it a significantly different

amplitude. Track its motion again for 10 seconds and make the same measurements you made in

part b above:

Distance vs. time Velocity vs. time

# T (sec) # T (sec)

1 1

2 2

3 3

What is the new amplitude in meters? _____________________

Is the period different from before? What can you conclude about how the period depends on

the amplitude?

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

Finally, from your measured period calculate the frequency f = 1/T and the angular frequency

ω = 2π f of your harmonic oscillator.

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

III. Dependence of period T on mass m

a) Using equations from Chapter 13 of your textbook, derive this equation for the period T of

a simple harmonic oscillator in terms of the mass m and the spring constant k.

T 2 = (4π 2/k) . m

10-4

Notice that this is a linear equation of the form y = ax if we think of T 2 as the dependent variable

y and m as the independent variable x. That is, if we vary the value of m by hanging different

weights on the spring, then we see that T2 is a linear function of m. The slope of the linear

function (which is the a in y = ax) is now the quantity in parentheses:

slope of the graph of T2 vs. m = 4π2/k

Therefore, if we plot T 2 vs. m on a graph, the points should fall along a line. We can fit a line to

this set of data points using the Graphical Analysis program (or Excel), and find the slope. Then

we can find the spring constant by the calculation:

k = 4π2/slope

Make sure you understand this idea before moving forward.

b) Now use the motion detector to measure the period T for various masses and fill in the

table below. Calculate the value of T 2 from the measured value of T.

m (kg) T (sec) T2 (sec2)

0.15

0.25

0.35

0.45

0.55

Describe how you can use this data to verify the equation derived in part a (think about

making a graph to get a linear relation, and decide which of the quantities to plot).

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

Make the proposed plot. How is the slope related to k?

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

Calculate your experimental value of k from the slope, and compare it to the value of k that

you measured in part Ic.

10-5

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

Are the values for k equal? Should they be? How do you account for any discrepancy? Does

the mass of the spring affect the static measurement, or the dynamical measurement, or both?

Should we have used some of the spring mass in the calculations of the dynamical situation?

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

Label the graph, print it out and attach to the lab report.