physics for society lab manual - western illinois university
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Physics 100
Physics for Society
Lab Manual
Fall 2018
Department of Physics
Western Illinois University
Revised by Pengqian Wang
Contents
Lab Report Guidelines
Lab 1. Motion and Measurement
Lab 2. Gravity and Acceleration
Lab 3. Force, Mass and Acceleration
Lab 4. Torques and Center of Gravity
Lab 5. Buoyancy
Lab 6. Heat and Temperature
Lab 7. Electromagnetic Fields
Lab 8. Electronics
Lab Report Guidelines Physics 100
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Lab Report Guidelines
Welcome to Physics 100 laboratory! It is my great pleasure to explore the wonders of physics
with you, my students, in the lab.
Please let me first explain to you how to write the lab reports. 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 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. We do not have a huge lot of students in the class, so
your vigorous participation in the lab will soon catch the eyes of the instructors.
Each lab consists of a number of experiments that give you a chance to experience the process of
exploring science and to investigate some aspects of physics. In the lab you will make
observations and measurements, and you will try to understand and analyze what you have
observed. You will use your 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.
Each lab report should be about 3-5 pages long, and be organized in the following way:
• (4 pts) Before you come to the lab, you should have read the lab manual and reviewed the
sections in the text that deal with the topic. You are asked to write an introductory
paragraph of your lab report, describing the objectives of the lab and the important
concepts to be studied. You can also include your preliminary questions to the lab here.
• (4 pts) During the lab, please make sketches of the apparatus and various activities that
you do. The sketches do not need to be artistic, but they should be careful enough that
they illustrate the important features of the experiment, such as indicating measured
distances, identifying the important objects, and detailing observations of the outcome of
the experiment. The sketches should be supplemented with legible notes, equations and
experimental results.
• (4 pts) You should make data tables and graphs when asked in the lab manual. Data
tables should be orderly, with a clear title and headings for each column, including the
units of the measured quantities. Graphs should also have a title, clearly marked axes and
a scale with units. If you make the tables and graphs in a computer program, please print
them out and paste or staple them into your lab report.
Lab Report Guidelines Physics 100
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• (4 pts) In your lab report please answer the questions that appear in the lab write-up as
you work through the exercises. You can also include the answers to the questions that
you have asked yourself. If you have unanswered questions of your own that have not
been answered during the lab time, please highlight the questions so that the lab
instructors can attempt to address them.
• (4 pts) Finally, you should provide a summary of what you have seen and what you have
learned through the lab exercises.
Each lab is therefore worth 20 points. The lab is not just an isolated activity, but should be the
basis for a lot of classroom discussions. It is a good opportunity for you to employ scientific
methods in order to develop a habit of scientific thinking.
Finally, please ask me if you have any questions about the lab. I hope you all like the lab and I
wish you have a successful semester.
Lab 1 Motion and Measurement Physics 100
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Lab 1. Motion and Measurement
Objectives: In this lab you will be introduced to some of the different ways motion can be
measured. You will learn things that are necessary to take a “good” measurement. You
will also learn what can be done with “good” measurements.
I. Discussion: Measurement principles
Introduction: From the earliest times, human beings have recognized the importance of
making measurements when counting money, making clothes, designing buildings or
ships and buying and selling properties. But it took a while for the people who spent their
time thinking about nature and how it works to understand how important measurements
were in doing “natural philosophy”. When they finally did so, they began to unlock the
secrets of the universe! Galileo himself wrote in The Assayer (1623), “One cannot
understand it [nature] unless one first learns to understand the language and recognize the
characters in which it is written. It is written in mathematical language.…” In brief,
measurement turns observations about nature into numbers, and relationships between
measured quantities into mathematical equations. You too can unlock the secrets of the
universe when you master the principles of making good and meaningful measurements.
The first thing to be studied and analyzed based on measurements was motion. On the
one hand, astronomers had been studying the motion of the planets, the moon and the sun
for many centuries. On the other hand, Galileo was really the first to begin making
systematic measurements of the motion of objects on earth. One can say that the birth of
modern science occurred when it was finally understood that motion in the heavens obeys
the same rules as motion on the earth.
In particular, Galileo understood the importance of controlling as many variables as
possible, in order to focus on the variable of interest. One famous example is dropping
two balls of different mass from the same point on the tower of Pisa, and observing their
fall. Another is his study of horizontal motion by considering motion along smoother and
smoother surfaces, which led him to conclude that in the absence of friction or other
forces, objects will move in a straight line forever – the law of inertia.
In today’s lab, you’ll learn some of the basics of making meaningful measurements by
carrying out your own investigation of motion. You’re lucky! You have the benefit of
technology to help you to take good measurements with only a little effort. Still, you
should get a taste of what the early pioneers went through to turn the “experience” of
motion into a quantifiable measurement in doing this exercise.
Measuring space
Lab 1 Motion and Measurement Physics 100
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Look around you. Consider all the places you could access in the room. Can you reach
every spot? What if you had a ten foot pole? Could you reach every spot? The collection
of all the spots you could reach defines the physical space of the room. In some cases,
those “spots” are being occupied by something already, like a chair, table, light bulb, etc.
If something is already there, can you be there too? In most cases, the answer is no.
Therefore it makes sense to consider each spot as identifiable and separate from all the
other spots. But there are so many of them! How can we keep them all distinct in our
mind?
You should already know, of course, that the way to do that is to create a “coordinate
system” for organizing and labeling all the points in space. A coordinate system does
many things all at once.
• A coordinate system defines an origin. The origin is the special point in your
space you chose to make as the starting point for all measurements.
• A coordinate system defines the measurement axes. Space is three
dimensional. It means that there are three directions you can move along in space
to reach a given point, starting from your origin – ahead, over and up. Once you
chose which directions are which, you can think about labeling each point with 3
labels – how far ahead, over and up you need to move from the origin to reach a
given point. Those directions are often given the more abstract names of “x”, “y”
and “z”. If instead of going “ahead” (or +x) you have to go “back”, you say the
object is in the negative “ahead” (or –x) direction
• A coordinate system defines the measurement scale. Distance is measured
relative to a scale. It can be the size of a human foot, the size of a pinky finger, the
size of our nose, whatever you chose. For the sake of agreement between
engineers and scientists, we will use the metric system, with the meter as the
standard unit of length. It is a little more than a yard, that is, 3.281 feet, or 39.37
inches. By choosing the measurement scale, we are simply choosing the system
for labeling each point. For example, having picked the origin, we label a point 1
meter ahead, over and up from the origin as (1m, 1m, 1m). But if we had used
inches for our scale instead, we would just write (39.37 in, 39.37 in, 39.37 in). It
would be the same point in space. It is only the label that changes as we change
the measurement origin, axes or scale. (Don’t forget that space is a part of reality.
Our labels for space are only a matter of convenience. If you don’t like one
system for labeling, choose a different one!)
Exercise 1: In this exercise we are going to learn how to build a coordinate system and
how to measure the coordinates of objects. We will also practice on how to calculate the
distance between two objects once their coordinates are known.
Make a two dimensional coordinate system for labeling the space on your lab table.
Define your origin, axes and measurement scale. Sketch this in your lab notebook. Now
Lab 1 Motion and Measurement Physics 100
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use the rulers provided to measure the location of two pennies taped to your tables. Please
indicate the positions of the two pennies on your sketch. Please record the coordinates of
the two pennies below.
The first penny: x1=________________, y1=___________________.
The second penny: x2=________________, y2=___________________.
Let us calculate the distance between the two pennies:
Distance calculated = 2 2
2 1 2 1( ) ( )x x y y− + − = _________________.
Now we can test our expectation by directly measuring the distance between the pennies:
Distance measured =_________________.
In your lab report please briefly discuss how well your calculated distance matches the
actual value.
Measuring time and motion
Think back to when you surveyed the “space” of our lab room. You imagined a collection
of tiny, distinct spots which filled the room, so that any “spot” you pointed to have its
own place and its own label. But that is not a complete picture of space. In moving from
one point to another, you must pass through a connected series of points in space, not
missing even one. Physical motion of objects is always observed to behave like this.
Motion is a continuous process of passing through “spots” in space.
However, motion can appear to be discontinuous – jumping from point to point – in the
following scenario. Imagine that you open your eyes for just a moment, enough to record
where your friend is standing according to your coordinate system. Then you close your
eyes and wait 20 heartbeats. You open them again, and find that your friend is now in a
quite different spot in the room, some three meters over from where he or she was! It’s
reasonable to ask, what was your friend doing during the 20 heartbeats you kept your
eyes shut?
If you happened to have your webcam (30 frames a second) focused on your friend at the
same time, you could go back and look at what it recorded. Each frame would show your
friend at one of the spots “on the way” from where he or she started to where your friend
ended up. The sequence would not be random – your friend would appear to move closer
and closer to the final position. Now, if you look close enough, you’ll notice that each
frame of the webcam video shows your friend in a distinct position, located some finite
distance from the previous and next positions. But you might have gotten the idea of what
you need to do.
Lab 1 Motion and Measurement Physics 100
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If you have a video camera used for recording sporting events (250 frames a second), or
better yet, for recording assembly line processes (10,000 frames a second), you would
find that as you take more records of intermediate positions during motion, the closer
each successive position in the motion becomes. You might guess that if you could make
an infinite number of records, you would find the successive positions becoming
infinitely close, though still all in a strictly ordered fashion creating a thread or path from
the initial position to the final one. (This “truth” about motion has only recently been
challenged as we began to make measurements of motion of objects smaller than
individual atoms. It is essentially true for any motion visible to our eyes.)
Of course, in imagining this scenario, we have introduced the concept of “time”. Time is
“how long you wait between measurements.” Just as we needed to standardize distances
to something better than “my foot”, we need to use a better standard than “one heartbeat”
to measure time. It is interesting that “time” is generally measured with respect to a
repeated motion, like a pendulum in a clock, our heartbeat, the rotation of the earth about
its own axis or about the sun, etc. The point is that “time” is inseparable from “motion”.
The universally accepted fundamental unit of time is the second, which is roughly one
heartbeat for a fairly fit person. If we need to consider shorter intervals than that, of
course we just take fractions of a second. “Motion” is understood as an ordered sequence
in time of the positions an object occupies on its way from its initial position to its final
position. Generally, we identify the initial position as occurring at time t = 0 seconds.
Nowadays, the second is defined in relation to the characteristic time of repetition (called
the period) of radiation coming from atomic Cesium.
Regarding time and motion, there were two extremes in the scenario described above.
The first was that of waiting the whole time of the experiment, and only looking at the
beginning and end of the motion. The second extreme was that of making an infinite
number of measurements, so that each successive position was infinitely close to the
preceding one. The first extreme considers the outcome of the motion only. It is a way of
“averaging” all the motions that make up the final result. The second extreme considers
the entirety of the process in detail. It contains information about the infinite sequence of
“instantaneous” motions that resulted in the final change. In reality, it is not possible to
measure the instantaneous motion. In practice, however, we can easily convince
ourselves that we have gotten close enough to “instantaneous” for our purposes.
Instantaneous is the limit of averages taken over shorter and shorter time intervals.
Therefore, we will consider two types of measurements of motion – average and
instantaneous. Let’s focus on the measurement of averages, first.
II. Measuring average velocity
Lab 1 Motion and Measurement Physics 100
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Introduction: In this section, you will make measurements of the motion of a cart as it
moves “ahead” in one dimension along a track. Your measurements will represent an
average of the motion, since you are only going to measure initial and final positions.
You will also learn the relationship between motion and time.
Exercise 2: Measuring average velocity. The average velocity measurement requires two
measurements of position, one at the beginning and one at the end of the motion. Please
make the two positions separated about 1.5 m on the track. You will need to use a stop
watch to record the times when the cart is at those two positions. Use the ruler that is on
the track, and pick a special agreed point or mark on the cart for measuring its
instantaneous position. Measure the average velocity for the following two scenarios.
i) A cart moving along a level track without the friction pad touching the track.
ii) A cart moving along a level track with the friction pad touching the track.
Sketch your procedure in your lab book. Indicate the beginning and ending positions and
the times for each scenario. Then show how you calculate the “average velocity”.
Describe what you observed about the motion and what the average velocity is telling
you about the motion.
III. Measuring instantaneous velocity and acceleration
Introduction: Rulers and stop watches have a limitation due to our finite reaction times.
Today we will use a device that has the ability both to make faster measurements and to
make them over shorter and shorter intervals – the motion detector. It has the ability,
when hooked up to a modern computer, to make hundreds of measurements in one
second, and since it uses sound waves which travel at ~340 m/s to reflect off from the
moving object, it can measure positions of objects traveling up to about a hundred meters
per second precisely. On the motion detector there is a switch for choosing person/ball or
cart to optimize the function of the detector.
You will need to use the Logger Pro program on your computer, with your motion
detector plugged into Dig/Sonic 1 on your LabPro interface. Once the detector is plugged
in and the program is opened, the graphs for position vs. time and velocity vs. time should
appear automatically. You can add the acceleration vs. time graph simply by going to
Insert in the menu, and then clicking on Graph. Go to Page and then click on
AutoArrange to make the graphs fit nicely on the page. All of these values are
“instantaneous” in the sense described above. Notice that everything results from having
an essentially continuous record of the position of the object over time. (The actual
position vs. time measurements can be seen by right-clicking on the position vs. time
graph, choosing Graph Options, and deselecting the option Connect the Points.) The
continuous record of the motion produced by Logger Pro describes a “functional”
Lab 1 Motion and Measurement Physics 100
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relationship between position and time – for each possible measurement time, there is a
unique position, and the curve connecting the measured points implies that we know the
position at every time.
The time duration of your experiment is suggested to be 5 seconds. You may need to
change it. Just go to the Experiment item on the menu, click on Data Collection, and
then set the duration of the experiment to the time you want.
You may need to make the curves appear to be finer by reducing the time interval
between two points that the motion detector takes. This is done by going to Experiment
on the menu, clicking on Data Collection, and setting the data collecting frequency at
about 30 samples/second.
Your measurement is no longer a single number but an entire graph consisting of
hundreds if not thousands of measurements. The detector cannot measure positions closer
than 0.4 meter. Keep your cart farther away than that distance at all times.
Exercise 3: Measure the instantaneous position, velocity and acceleration of a cart
moving down an inclined frictionless track.
Please print the graphs obtained in the above exercise. To save paper, please always do a
print preview before making the actual print. What can you learn from the graphs of
instantaneous motion that you cannot determine from the average values obtained earlier?
What is the relationship between the different graphs (for example, between position vs.
time and velocity vs. time)? What are some potential drawbacks to measuring
instantaneous values of the motion compared to average values?
IV. Reading graphs of motion
Introduction: Each graph of position vs. time tells a story. The individual points of
course tell where the object was, is or should be, moment by moment. But there is more.
The slope (rise over run) of the position vs. time graph tells how quickly the position is
changing with time (velocity). If that slope is increasing, so is velocity, which means
there is an acceleration. Learning to read these “experimental functions” is a good way to
gain a feeling for the meaning of all these measurements, and what they can do for us.
Clearly, if the graphs (functions) can tell you what to do, they can tell machines what to
do as well, and they do.
Exercise 4: In this exercise you will let the graphs tell you how to move, and test your
understanding by doing what the graph says, and comparing your measured motion with
the prescribed motion.
Lab 1 Motion and Measurement Physics 100
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Please open the File menu, then click on Open, then choose the folder _Physics with
Vernier, then select the file “01b Graph Matching.cmbl” for the distance vs. time
matching. Then, 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. Please
try to match the fixed graph with the graph of your motion. You may need to discuss with
your group partners on how you should move before you actually start. Let us see who
does the best in your group in matching the prescribed motion.
Questions: What did you have to change when you were moving back toward the
detector, compared to moving away from the detector, for the distance matching
exercise?
Make sure to answer in your lab notebook all the questions asked in this write-up. Then
make a summary of what you have learned from this exercise.
Lab 2 Gravity and Acceleration Physics 100
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Lab 2. Gravity and Acceleration
Objectives: Measure the gravitational acceleration of masses at the surface of the earth.
Explore other methods of measuring acceleration.
I. Measuring acceleration due to gravity
Introduction: The most obvious motion on the earth is the fact that “what goes up must
come down”. It is obvious that when things fall, they go faster and faster, but it isn’t so
easy to measure that motion, because things rapidly begin to fall so fast that measurement
becomes very difficult. Galileo himself stumbled at this point. Nevertheless, Galileo did
notice that objects which fall twice as long in time fall four times as far in distance. That
is, motion under gravity is proportional to time squared. He also was able to show that the
motion was not proportional to the amount of mass an object had, although the
combination of size and mass did have some consequence.
The crucial step in understanding the motion of things on earth was the discovery that all
things are accelerated the same amount near the surface of the earth. That is, the rate of
increase in velocity is constant for falling objects. In this lab, you will explore the nature
of this acceleration, and also investigate ways of measuring acceleration directly,
independent of any velocity measurements, for various types of motion.
Exercise 1: Motion detector and falling objects. You will use a motion detector
connected to the computer through your LabPro interface to measure the acceleration of
various falling objects.
Your motion detector has been set up at a distance of about 1.6 m above the floor,
pointing downwards. Therefore, left to itself, it will measure positions of objects closer to
the floor as being greater and more positive. It will also record motions downward as
movement in the “positive” direction. If we want the detector as set up to measure what
we normally think of as “height” (distance above the floor) and “down” as being toward
the floor, we have to tell Logger Pro how to interpret properly the data it receives from
the detector.
Setting up the motion detector. Open up Logger Pro, and make sure the computer “sees”
the LabPro interface and the motion detector. If it does, then it should automatically
display position and velocity vs. time graphs. Please go ahead and select Insert and then
select Graph. It should be a graph of acceleration vs. time. Go to Page and select Auto
Arrange to arrange the three graphs.
Lab 2 Gravity and Acceleration Physics 100
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You may need to make the curves appear to be finer by setting the data collecting
frequency at about 30 samples/second.
In order to display “height” of the object relative to the ground and motion “downward”
as negative, we need to redefine the position, velocity and acceleration. Go to Data in the
menu at the top, and then select New Calculated Column. Give your new column the
name “Height”, with “H” as the short name, and “m” as the units. Then enter in the
Equation box the formula for the height, which is
1.6 " "Position− .
Make sure you understand why this is right. Then select Done. Create new columns for
your velocity and acceleration as well. Call them V and A, with units of m/s and m/s/s. In
the Equation box, simply write –“Velocity” and –“Acceleration”, respectively. Then go
to the space alongside the vertical axis of each graph, left-click on it, and select Height,
V, and A, respectively, as the y-component of the three graphs. Remember that your
detector cannot see things that are closer than 0.4 meter, and therefore when the object
gets too close, your graph will become questionable.
Use two different objects as below and drop them underneath the motion detector. Record
the falling motion of each, and then examine the motions, comparing each to the motion
of the other objects. Print all three graphs (H, V, and A) for both cases.
• A large ball
• A small ball
Questions: What is the value of the acceleration of both objects at the beginning of their
motion? According to your experimental results, what is the acceleration of all objects
due to the earth’s gravity? Do your results confirm Galileo’s observation that objects
which fall twice as long fall four times the distance? Justify your answer.
Exercise 2: Motion detector and “free fall”. You have seen for yourself in several
cases that the acceleration due to gravity is pointing down and has the same value of 9.8
m/s2. But it can be hard to believe that everything in free fall is accelerating at that rate.
Probably we’re most likely to question that belief when we observe rising objects. At first
sight, it doesn’t make sense to us that rising objects are in fact accelerating downward.
For one thing, they are moving up. For another, they are not moving faster, but going
slower. Our difficulty is in our misconception about acceleration, due to our experience
with things like car “accelerators,” etc. Things would be a lot easier in physics if
automobile makers had called the brake the “negative accelerator” and the gas pedal just
that.
Lab 2 Gravity and Acceleration Physics 100
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Do an experiment with the larger ball. Throw it straight up from below toward the motion
detector, and record its motion on the way up as well as on the way back down.
Look carefully at the H vs. time graph. What is the shape of that curve? At what time
does the ball reach its peak?
Look carefully at the V vs. time graph. What is happening to the velocity throughout the
ball’s motion? At what time is the velocity zero? Where in its motion does that occur?
Now, look carefully at the A vs. time graph. What is the value of the acceleration
throughout the ball’s motion? What effect does this acceleration have on the motion on
the ball’s way up? At its peak? On its way down? Explain why an object that is thrown
upward is said to be in “free fall” even while it is still moving up.
II. Inertial acceleration
Introduction: Measuring acceleration required the use of pretty high tech equipment and
lots of measurements. But now that we understand how important acceleration is for
understanding motion, and we have a kind of natural unit of acceleration, that is, 1 g for
the acceleration due to the earth’s gravity, we can begin to explore ways of measuring
acceleration directly, without the need for high tech or a large number of velocity
measurements.
The key to measuring acceleration directly is the observation of inertia, first recorded
systematically by Galileo. Inertia is the tendency of moving things to keep moving, and
for things that are at rest to stay at rest. The “amount” of inertia an object has is directly
proportional to its mass. All other things being equal, a push on a less massive object
(having less inertia) will result in a greater acceleration than a more massive object.
(Think of trying to push a dead VW beetle and a dead Ford Expedition off the road and
up the repair station ramp. Which one would you prefer?) So, if you could somehow
create a device that would compare the response of two substances of different inertia,
you might have something.
Two-fluid Accelerometer
One simple way to do that is to have two immiscible fluids of different density. The
denser (often colored) fluid would have more inertia, and the less dense fluid would have
less inertia. If these two fluids are confined and not accelerating, the lighter fluid floats
on top of the denser fluid. Why?
Lab 2 Gravity and Acceleration Physics 100
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However, as soon as you began to accelerate, the denser fluid tends to be left behind
relative to the less dense fluid (since the denser fluid is harder to accelerate), so that their
interface would become inclined away from horizontal, and the incline of the denser
(colored) fluid would point down in the direction of the acceleration. The more you
accelerate, the greater the incline.
What would be the greatest possible incline in the interface between the two fluids? What
would the horizontal acceleration have to be for that to occur? Think about it. What
would the value of the horizontal acceleration be if the incline angle were 45 degrees?
Explain your reasoning. How would the operation of this device change if you were on
the moon? In outer space?
Your instructor will demonstrate how the two-fluid accelerometer reacts when
accelerating and decelerating along a line, and when moving in a circle. Record (sketch)
what you see. What is the second fluid?
Hanging mass accelerometer
The two fluid accelerometer is good for visualizing acceleration, but isn’t always so easy
to use for measurement. A variation of this accelerometer is the hanging mass
accelerometer. A mass is tied to a string, and that string is tied in a knot, passing through
the hole at the base of a protractor. Hold the protractor upside down, so that when the
mass is hanging straight down, the string is lined up along the 90º angle. It is easy to use,
and it is possible to make direct measurements of the acceleration if the motion is
horizontal and the acceleration is constant. Again, the idea is that the mass has inertia,
and therefore it will be “left behind” when accelerated, relative to the protractor.
More importantly, the angle that the mass makes is directly related to its acceleration.
The key observation is to realize that if the acceleration down equals the acceleration
over, the mass will be equally pointing over and down, that is, it will be at a 45º angle.
That is, a one to one ratio in accelerations would produce a 45º angle. No acceleration (a
0 to 1 ratio) would read as 90º. Infinite acceleration would read as 0º (straight across). In
general, a ratio of the acceleration over (a) to the acceleration down (g) will be equal to
one over the tangent of the angle made by the mass and the string. That is
,tan
1
θ=
g
a
where the angle is in degrees from 90° (no acceleration) to 0° (infinite acceleration). You
need a scientific calculator in order to find the tangent value of an angle. Make sure that
the unit of angle is set into degree (DEG) on your calculator.
Lab 2 Gravity and Acceleration Physics 100
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Exercise 3: As you may have noticed, it is much easier to produce larger accelerations by
moving in circles than by going in a straight line. Try to compare the maximum
accelerations you can measure by holding your accelerometer at two different distances
away from you while spinning about.
What is the angle recorded in each case? What acceleration does that angle correspond
to? According to your results, which part of a rotating object is accelerating more?
Don’t forget to make sketches of your observations in your lab book. Record your
calculations as well as your final answers. Summarize what you have learned in doing
these exercises.
Lab 3 Force and Mass Physics 100
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Lab 3. Force, Mass and Acceleration
Objectives: Understand the nature of gravitational force. Test Newton’s second law of
motion.
I. Gravitational force and mass
Introduction: It is curious that the fact that all objects are accelerated at the same rate by
gravity was not articulated sooner than Galileo did. Many intelligent people had spent a
lot of time thinking about gravity. One obstacle in understanding this, as we noticed when
attempting to measure motion and acceleration, is that it is difficult without very good
equipment to obtain reliable data on the motion of objects, particularly in the case of
falling objects. The greater obstacle to accepting the constancy of gravitational
acceleration was the very clear perception that more massive, “heavier” objects
experience a greater pull downwards than do less massive, “lighter” ones. If more
massive objects are being pulled down harder, of course they will move faster downward,
right?
Think about it. First, let’s verify with observation what we’ve experienced with gravity.
Let’s agree that a push or pull is to be called a force. We need some way to quantify,
however, how great the force that gravity exerts on various objects is. Obviously, we
need something that can pull (or push) back in a way that cancels the gravitational force,
and registers how much it is pulling.
One such device is a spring scale. Springs have a natural unstretched length. To stretch
them a little bit requires a little pull, while a large pull is needed to stretch them a lot.
Therefore, the amount of force that a spring scale exerts depends on how far it has been
stretched. Measuring the amount the spring has been stretched in opposing the pull of
gravity is a way of measuring the amount of the force of gravity. Each spring has its own
stiffness, therefore we need a consistent unit of force as our force scale.
You are probably most familiar with the unit of “pounds” or lbs. This scale was
established for the sake of comparing weights, that is, the amount of force exerted by
gravity on objects. But here we’ll use the standard metric scale of force, Newtons (N),
named after Isaac Newton. The two scales are related, of course. 1 Newton equals about
0.225 lb. Therefore, to have a rough idea of how much you weigh in Newtons, take your
weight in lbs and multiply by 4.
We also need a way of comparing objects, so that we can say two objects are equivalent
as far as gravity is concerned, or one is going to be pulled harder by gravity than another.
You might be familiar with this quantity as the object’s mass. Mass can be measured on a
Lab 3 Force and Mass Physics 100
3-2
balance scale against a standard amount of material. The English unit of mass is “slug”,
but we’ll stick to the metric unit of mass, kilogram (kg).
By working with mass instead of weight, we make the important distinction that the
amount of material in an object is different from the amount of force gravity exerts on it.
This distinction would be irrelevant if gravity were everywhere the same. But it isn’t.
Gravity is different even if you go to the top of a mountain compared to being at sea
level. For example, the world record for the long jump set in 1968 at Mexico City, with
an elevation of more than a mile above sea level (7200 feet), lasted more than 20 years,
because the jumper (Bob Beamon) didn’t have to push so hard to oppose the earth’s pull
on him. His mass didn’t change, but his weight (the force of gravity) did! It is interesting
that he beat the existing record by more than 20 inches! He himself never got closer than
20 inches to the record he set at any other event. He was also aided in this feat by the
maximum allowable wind speed blowing behind him.
Exercise 1: Take a spring scale, and hang different amounts of mass under it, as
indicated below in the table. Please note that the hanger itself has a mass of 50 g, or 0.05
kg. Please fill in the data for the five masses in the table, and sketch a graph of
gravitational force (as measured in Newtons by your scale) vs. mass (measured in
kilograms) in your lab book. You can directly use Microsoft Excel spreadsheet to record
your data and draw the graph.
Mass (kg) Gravitational force (N)
0.25
0.55
0.75
1.05
1.25
What is the relationship between your measured gravitational force and your measured
mass? Determine the slope of your graphed curve using the “Trend line” function of
Excel. Does the number sound familiar? The graph you’ve drawn represents an
experimental function. What kind of function is it?
Exercise 2: Repeat Exercise 1, except instead of using a spring scale, use a force probe
that can be hooked up to the computer through the LabPro interface. Your probe is based
on a substance that not only changes length when stretched (not as much as a spring,
though), but produces an electrical signal whose strength increases in proportion to the
amount it is stretched. You may need to zero the force probe. This is done by following
the sequence of Experiment → Set up sensors → Show all interfaces → Click on the
Lab 3 Force and Mass Physics 100
3-3
sensor and “zero”. Please fill in the data in the following table. Recreate the graph that
you sketched in your lab book. Does the slope of this curve match your first slope? What
is the difference?
Mass (kg) Gravitational force (N)
0.25
0.55
0.75
1.05
1.25
Your results should convince you that indeed, the greater the mass, the greater the
gravitational force on the object, and that the ratio of force to mass equals g, the
acceleration due to gravity. So, what is wrong with our expectation that more massive
objects will fall faster than less massive ones?
II. Inertial mass and Newton’s Second Law
Introduction: Maybe something bothered you in last week’s experiment on gravity and
acceleration. When we switched to measuring horizontal accelerations, we found that the
easiest way to do so was to compare the effect of a push (force) on different density
fluids. Always, the denser fluid got left behind, because it has more inertia than does the
less dense fluid. The hanging mass always got left behind as you accelerated forward.
In short, the same push does not always result in the same acceleration. Instead, objects
with less inertia are more easily accelerated than objects with more inertia. Objects with
more inertia have more stuff, and in fact, it is pretty easy to verify that an object’s inertia
is exactly related to its gravitational mass (the quantity you measured using the balance
scale).
Exercise 3: Verify the statement made in the paragraph above. We’ll let gravity provide
the push by using a pulley system to connect a hanging mass with a cart that can move
horizontally along a track. You know from above how much force gravity is exerting on
the hanging mass (mhang). That is,
gmF hang=
You can measure the acceleration of the “mtotal =cart + hanging mass”, using the motion
detector. To verify that the resistance to acceleration (inertia) is the same as gravitational
Lab 3 Force and Mass Physics 100
3-4
mass, you need to show that 1) the same force on different gravitational masses produces
different accelerations, and that 2) the ratio of force to gravitational mass (in metric units)
always results in the measured value of the acceleration.
You can vary the mass of the cart by adding iron bars or other masses to it. Don’t forget
to include the hanging mass as part of the total mass being accelerated. Also before
you let the cart go please test if there is any noticeable friction which may prevent the
cart from moving smoothly. Please fill in the data table below. Please show to what
extent your data verifies the result claimed by taking a percentage difference, which is
[(Ameasured – F/Mtotal) / (F/Mtotal)] × 100%. Why might you see a slight disagreement in
your values?
Trial Mhang
(kg)
F =
Mhang×g
(N)
Mcart (kg) Mtotal =
Mcart +
Mhang
(kg)
F/Mtotal
(N/kg, or
m/s2)
A(measured)
(m/s2)
Percentage
difference
#1 0.055 0.539
#2 0.055 0.539
#3 (Optional)
0.055 0.539
This relationship, that force divided by mass equals acceleration, or amF =/ , can also be
written as
,maF =
which is known as Newton’s second law of motion. Newton’s second law is the
cornerstone of classical physics. In this simple equation we have the statement that 1)
Forces produce (cause) acceleration, not velocity, and 2) when under force, objects
accelerate in inverse proportion to their mass.
Now, let’s see if we can tie all this together. We have found that gravity pulls down on
masses in proportion to their mass. More mass, the greater the gravitational force. On the
other hand, masses respond to any force by accelerating at a rate inversely proportional
to their mass.
I’ll leave it to you to make the summarizing statement in the answer to the question, why
is it true that all masses will accelerate at the same rate when falling under the influence
of gravity?
Lab 4 Torques and Center of Gravity Physics 100
4-1
Lab 4. Torques and Center of Gravity
Objectives: Understand how to calculate a torque. Use balanced torques to find the
mass of an object, or determine unknown forces exerted on an object. Understand the
role of center of gravity in evaluating torques.
1. Torques and Newton’s First Law of Rotational Motion
Torque is a twist or spin exerted on an object. How an object rotates is closely related to
the torques it receives. To calculate a torque with respect to a rotational axis, we use
⊥×=
×=
Frτ
or arm,lever thelar toperpendicu force armlever torque (1)
Here lever arm is the distance from the rotational axis to where the force is exerted. Only
the force component that is perpendicular to the level arm contributes to the torque. In
today’s lab we are going to explore torques exerted on a stationary meter stick. In our
case all forces are perpendicular to the lever arm. However, toque has a sign with respect
to the rotational axis. We take the convention that if the torque tends to rotate the stick
counterclockwise around the rotational axis, it is said to be positive. Otherwise if the
torque tends to rotate the stick clockwise, it is negative.
Newton’s First Law of Rotational Motion states that a rigid object that receives no net
external torque either does not rotate or rotates at a constant angular velocity. In our case
of a stationary meter stick, suppose there are n forces Fi exerted at a distance of ri to the
rotational axis, then
.02211 =×±±×±×± nn FrFrFr ⋯ (2)
Here for each torque a proper sign should be chosen, depending on whether the torque is
tending to rotate the object counterclockwise or clockwise. This equation can then be
used to find the magnitude of an unknown force exerted on an object.
2. Center of Gravity
The rotational effect of a rigid body is often associated with its center of gravity, which is
defined as the point at which a single upward force can balance the gravitational
attraction on all parts of the body. In calculating the torque caused by the weight of a
rigid body, the gravitational forces on all parts of the body can be thought of as if they are
“concentrated” at the center of gravity of the body. This principle can help us to find the
overall torque caused by the weight of a rigid body. On the other hand, if the torque
Lab 4 Torques and Center of Gravity Physics 100
4-2
caused by the weight of a rigid body is known by some other methods, e.g., through
solving Eq. 2, then the mass of the body can be calculated.
3. Experiment
This experiment is designed to study the conditions of equilibrium of a rigid bar acted
upon by several parallel forces. When a rigid body is in equilibrium with respect to
rotation, the algebraic sum of the torques about any axis is equal to zero, as Eq. 2 shows.
Please record all your data in the diagrams illustrated below; i.e., write down the
positions of the points of application of the forces, and write down the magnitudes of the
forces. Please remember to specify the axis of rotation when calculating torques.
Whenever possible, please use weights over 300 grams.
Exercise 1: Find the center of gravity (CG) of the meter stick by balancing it on the knife
edge.
CG=_____________ cm.
Exercise 2: With the knife edge at the CG of the meter stick, balance it with a load on
each side using two different weights.
Take the axis of rotation at the CG, and calculate
=×= 111 Wrτ ___________cm ×____________gram = ______________ gram·cm,
−=×−= 222 Wrτ ___________cm ×____________gram = −______________ gram·cm.
Now find the sum of the two torques and check if it is zero.
Lab 4 Torques and Center of Gravity Physics 100
4-3
=+ 21 ττ ______________ gram·cm.
In general you may not get exactly zero, but if you can find that the absolute value of
21 ττ + is much smaller than the absolute values of 1τ and 2τ , then we can make a safe
conclusion that the two torques are balanced when the meter stick is not rotating.
Exercise 3: Repeat exercise 2 with two weights on one side and one weight on the other
side of the knife edge.
Take the axis of rotation at the CG, and calculate
=×= 111 Wrτ ___________cm ×____________gram = ______________ gram·cm,
=×= 222 Wrτ ___________cm ×____________gram = ______________ gram·cm,
−=×−= 333 Wrτ ___________cm ×____________gram = −______________ gram·cm.
Now find the sum of the three torques and check if it is close to zero.
=++ 321 τττ ______________ gram·cm.
Exercise 4: Move the knife edge about 20 cm away to the left of the CG. Balance the
meter stick with one weight on the short end.
Take the axis of rotation at the knife edge. The distance r1 is then measured from the
weight to the knife edge, while the distance r0 is measured from the CG to the knife edge.
Lab 4 Torques and Center of Gravity Physics 100
4-4
Use the fact that the net sum of torques is zero, 001101 WrWr ×−×=+ττ =0, we can find
the weight of the meter stick as
gram. cm
gram cm
0
110 =
×=
×=
r
WrW
Now let us actually weigh the meter stick on a balance:
balance). (by the gram ,0 =balanceW
Please compare the weighed value to the calculated value above.
Exercise 5: Support the meter stick by means of two spring balances as shown in the
figure.
Assuming F2 is unknown, let us use the 10cm mark as the axis of rotation. Remember
that all the distance r’s are measured from the force or the weight to the axis of rotation
that we choose. The equation for the sum of the torques is
.02220011021 22=×+×−×−×−=+++ FrWrWrWr FFττττ
Solving for F2 we have
gram.
cm 10)(90
gram cm 10)(75gram cm 10) (gram cm 10)(20
2
2200112
=
−
×−+×−+×−=
×+×+×=
Fr
WrWrWrF
Lab 4 Torques and Center of Gravity Physics 100
4-5
We now read the spring balance for F2:
spring). (by the gram ,2 =springF
Please compare the spring reading to the calculated value of F2 above. Please also discuss
on why we choose the 10 cm mark as the axis of rotation.
Lab 5 Buoyancy Physics 100
5-1
Lab 5. Buoyancy
Objectives: Investigate the concepts of pressure, density and buoyancy.
Introduction: The atmosphere is an ocean of air, just as the Pacific and Atlantic Oceans are
oceans of water. The weight of the air above us creates an atmospheric pressure, or force per area
which presses on us and everything else with a force great enough to crush cans. That pressure
also serves to compress the air so that its density, or mass per volume, is far greater at sea level
than it is even 1 mile high, where the air is said to be “thinner.” In this sense, the atmospheric
“ocean” is different from our water oceans, because water is far less compressible than air. All
the same, in both cases, it is pressure and density that determine the buoyant force upward which
all objects in those oceans experience. It is the buoyant force that causes the heated exhaust from
heat engines and furnaces to rise and carry with it the pollutants which then become part of our
living environment.
In today’s lab, we will investigate some characteristics of the buoyant force in water. The
buoyant force in water is actually part of an equilibrium between two opposing forces. In a body
of water, the force of gravity is acting to pull down on all the molecules that make up the fluid.
Instead of considering the force of gravity on individual molecules, we look at a certain volume,
say a cube with sides 1 meter in length, and ask what the overall force on the molecules is within
that cube. The answer is of course
gmassFgravity ×= ,
where g = 9.8 m/s2. The mass is the mass of the fluid inside that box, and the force of gravity is
thought to be acting on the center of the box. As we know, if any object experiences a force
acting on it, it should begin to move in the direction of the force. However, since the fluid is part
of a body of water, then of course that volume of fluid does not move. For example, there is
always some water at the top on the surface of an ocean, and some at the bottom – it is not all at
the bottom! According to Newton’s first law, it means that there must be another force acting in
the opposite direction and of equal strength to counteract the force of gravity. What can it be?
Well, remember what happens to the air that is at the bottom of the atmosphere. It gets
compressed, so that the air down here is much “thicker” than the air that is higher up. Think of
what happens when something, like a sponge or a spring is compressed and then let go. It
bounces back up! The compressed object applies a force to resist being compressed. The same is
true in the atmosphere as well as in the oceans, although water is compressed far less than air
because it is a much “stiffer” spring. Because the water is compressed more below than above,
the force resisting compression is greater from below than above. Of course, the water in the
oceans does not spring up and away from the earth. The force resisting compression and the
force of gravity are in perfect balance, so that any given volume of fluid is floating very nicely
Lab 5 Buoyancy Physics 100
5-2
wherever it happens to be in its ocean. The force that balances the force of gravity is the buoyant
force, first described by Archimedes. Again, since we are talking about forces acting on the
surface of a volume, we really need to talk about pressures. A picture of a body of fluid in
equilibrium with its surroundings is shown below.
Now that we have described the situation of our oceans in equilibrium, and let’s now examine
the situation when we disturb that equilibrium by displacing our cubic volume of fluid with
something else, say a boat or a balloon. The buoyant force will be unchanged, since it is the
result of the resistance to compression by the surrounding body of fluid. That is, the buoyant
force always equals to the force of gravity on the displaced fluid, which is the famous
Archimedes principle. On the other hand, if the object displacing the fluid has a different density
than that of the fluid, such as an iron bar in water, or a helium balloon in air, the force of gravity
on that object will be different.
• If the object has a density greater than that of the surrounding fluid, the force of gravity will
be greater than the buoyant force, and the object will go down.
• If the object has a density less than that of the surrounding fluid, the force of gravity on that
object will be less than the buoyant force, and the object will rise up.
In general, the net downward force on the object can be described in the following way.
buoyantgravitynet FFF −=
The net force is zero if the density of the object and the fluid are the same. This is the
equilibrium. The net force is positive (downward) if the density of the object is greater, and
negative (upward) if the density of the object is less.
Lab 5 Buoyancy Physics 100
5-3
Some useful equations:
The equation describing the buoyant force is
The equation describing the force of gravity on an object is again
The mass of a volume of fluid can be determined from its density.
Experiment 1: Buoyant force on a solid object
In this experiment, we will measure the buoyant force in water on a solid object of known
density and test the Archimedes principle.
Take the solid object provided in class, and find its mass by using a triple-beam balance.
Remember to convert the units, if necessary.
Mass = __________ kg.
Calculate the force of gravity on the solid object and write down your answer below.
Force of gravity = ________ Newton.
Now attach the object to the spring scale and let it hang from the scale. Was your calculation
correct? If not, check your calculation. If everything is ok there, please tell the lab instructor.
Prepare a graduated cylinder with enough water in it to be able to completely submerge the
object you are testing. Record the volume of water you are starting out with.
Initial volume of water = ____________ ml.
Fbuoyant = Mass of fluid displaced × g
Fgravity = Mass of object × g.
Mass of fluid = Density × Volume.
Lab 5 Buoyancy Physics 100
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Now, lower the object into the water until it is completely submerged. Record the new volume
reading in the graduated cylinder. Make sure that the object does not touch the bottom or the wall
of the cylinder container. Record the new force reading on the spring scale.
Final volume of water = _____________ml.
Final spring scale reading = _______________Newton.
Your final scale reading when the objected is submerged in water is actually the net force on the
object when considering only the gravity and the buoyant force: buoyantgravitynet FFF −= . From this
equation, the buoyant force can be solved in terms of the net force and gravitational force:
.netgravitybuoyant FFF −=
Please find the experimental buoyant force on the object in Newton using the above equation.
Fbuoyant (experimental) = _______________________ Newton.
Let’s now compare the buoyant force you have experimentally found with what would be
expected from the Archimedes principle.
Calculate the difference in the volume readings of the water in the graduated cylinder before and
after you immerse the object in it.
Difference in volume = ______________ ml.
The difference in volume must be equal to the volume of the object that was immersed in the
water. It is also equal to the amount of water displaced by the object. Using the equation for the
mass of volume of fluid given above, calculate the mass of water displaced. Remember that
water has a density such that 1 milliliter of water has a mass of 1 gram, or density of water = 1
g/ml. Remember to convert your units from grams to kilograms.
Mass of water displaced = _____________ g = ________________ kg.
Now, use the equation for the buoyant force given in the introduction (the Archimedes principle)
to calculate the expected buoyant force on the object.
Fbuoyant (expected) = ________________ Newton.
What is your percentage error between your experimental value of the buoyant force and your
expected value?
Lab 5 Buoyancy Physics 100
5-5
Percentage error = (expected) F
(expected) Ftal)(experimen F
buoyant
buoyantbuoyant −
= ___________%.
In your lab report please summarize what you have learned about buoyant force in this
experiment.
Lab 6 Heat and Temperature Physics 100
6-1
Lab 6. Heat and Temperature
Objectives: Investigate the relationship between heat and temperature. This relationship will be
shown to depend on the amount and type of materials being heated.
Introduction: Temperature is the most direct way in which we can sense and measure the presence
of heat energy. However, the relationship between temperature and heat is not as straightforward as
we might like. In particular, each substance has its own heat capacity, which is a way of
characterizing the amount of heat that a certain substance (say, water) requires in order to experience
a 1- degree rise in temperature. Substances which have a high heat capacity, such as water, require a
lot of heat energy (say, from a flame) to experience a significant change in temperature, while others,
such as most metals, have a low heat capacity, and require very little heat energy to experience a
large change in temperature. In spite of these complications, the general relationship between heat
and temperature can be expressed by a relatively simple equation:
where ∆Q is the amount of heat gained or lost, ∆T is the change in temperature, m is the mass of the
material, and c is the specific heat capacity, or heat capacity per mass of material. In fact, the heat
capacity of most materials changes with temperature, but this can be ignored if the change in
temperature is not too much.
The units of c depend on the units we are using to measure heat, temperature and mass. In fact,
several measures of heat are defined by the heat capacity of water. The calorie is the amount of heat
required to raise the temperature of one gram of water by one degree Celsius in temperature. The
BTU or British Thermal Unit is the amount of heat needed to raise the temperature of one pound of
water by one degree Fahrenheit. Each unit is a measure of heat energy, but obviously, it takes many
calories of heat to equal one BTU. In addition, each unit has a fixed relationship to the measure of
work energy, joules, as shown below.
Energy Unit
in joules
in calories
in BTU
1 joule
1
0.239
9.49 x 10−4
1 calorie
4.18
1
3.97 x 10−3
1 BTU
1055
252
1
Please load the Logger Pro program on the computer at your station. There then should be a graph
displayed, which relates temperature on the vertical axis, and time on the horizontal axis. If not, go
T m c = Q ∆∆ , (1)
Lab 6 Heat and Temperature Physics 100
6-2
to File in the menu, then click on Open, go to folder Additional Physics/Tools for Scientific
Thinking/Heat and Temp/ and then open the file “Hp1sec_SST.cmbl”. You can control the scale
on either axis by clicking on the last number of either axis and typing in the largest temperature or
time you want to be displayed on your graph in the highlighted area. The Collect button on the
upper right of the screen starts the program recording the temperature of the temperature probe(s) as
a function of time. The Pulse button on the upper right of the screen causes the heat source to emit a
fixed amount of heat over 1 second of time. You need to click on that button each time you want to
introduce heat into your sample.
I. Measuring the amount of heat produced by the heat source
Exercise 1: In this experiment, we will determine the amount of heat introduced during each pulse
with our heat source. The source is just a little heating coil used in heating up water in cups for
making tea or instant coffee. The computer controls how much current the coil receives and for how
long, which determines the amount of heat produced by the coil. To find out how much heat that is,
we will use the known heat capacity of room temperature water (at 15°C), which is
C/gcal1 °⋅ = cwater
Because of slight variations in conditions, it is always better to take a number of measurements, and
then average the results. When heating water in your cup, remember that the water should be stirred
continuously to make sure that all of the water is at the same temperature. One partner should be
stirring the water, while the others operate the computer and the heater. Don’t spill the water on the
computer.
The procedure of the experiment is as follows. Put 100 ml of water in a Styrofoam cup. 1 ml of
water has a mass of 1 gram. Set your temperature scale from 20 to 40 degrees Celsius. Set your time
scale from 0 to 120 seconds. Start the collection of data by clicking on the Collect button. You
should immediately see a red line which indicates the temperature recorded by the probe as a
function of time. Wait 10 seconds, and then click on the Pulse button, once every 10 seconds, for 8
times. Keep recording data until the temperature reaches its highest value. The temperature change
∆T is just the difference between the highest temperature and the temperature you started at.
Start temperature = ___________ °C.
Final temperature = ___________ °C.
∆T = ___________ °C.
Then, calculate the total amount of heat added to the water, using equation 1 on page 1.
Lab 6 Heat and Temperature Physics 100
6-3
∆Q = ________________ calories.
The amount of heat introduced by each pulse is just this number divided by the number of pulses,
which is 8.
∆Q per pulse = ____________ calories/pulse.
Repeat this experiment (starting with an identical amount of cool water) one more time, and
calculate the ∆Q per pulse for the experiment:
∆Q per pulse (trial 2) = __________cal/pulse.
Were your values the same? ______ . Why might your values be different? _________________
____________________________________________________________________________.
Now, average your two values.
∆Q per pulse (average) = _______________ cal/pulse. (2)
We will use this value for the following sections of the experiment.
Now, repeat the same experiment once more, but double the number of heat pulses, up to 16. Set the
total collection time to be more than 200 second. Make sure that the end of the trial is at least 20
seconds after your last pulse is made, to give the water some time to reach equilibrium at its final
temperature.
∆T = ___________ °C.
∆Q = ________________ calories.
∆Q per pulse = ____________ cal/pulse.
Approximately by how many times (2×, 4×, etc.) does the total temperature change in this trial
compare to that observed in the first trial?
_____________________________________________________________________________
Does this make sense, given equation 1? ____.
Explain: ________________________________________________________________.
Lab 6 Heat and Temperature Physics 100
6-4
II. How mass affects heat capacity
Exercise 2: In this experiment you will simply double the amount of water to 200 ml. Run the same
experiment as in exercise 1, using 8 pulses of heat. Here we will assume that the value for ∆Q per
pulse that you obtained in exercise 1 is correct. First please record the number from your results
above (equation 2) in the space given below.
∆Q per pulse (average) = ____________ cal/pulse.
Before doing the experiment, let’s see what change in temperature we expect, based on our equation
1 from page 1. Remember, we are going to use 8 heat pulses, with each pulse introducing a fixed
amount of heat. Calculate the total amount of heat that will be introduced into the water:
∆Q (total) = ______________ calories.
Now, let’s do the algebra. Starting from equation 1, to solve for the change in temperature, we have
.Q
Tc m
∆∆ =
⋅ (3)
Using equation 3, calculate the expected
temperature rise of 200 ml of water for 8 heat
pulses.
Now please perform the experiment and record the
observed change in temperature.
The difference between your predicted value for ∆T and the observed value is due to the variations in
experimental conditions and experimental error. The quality of your observed value can be described
using something called the percentage error:
Percentage error = observed value − expected value
expected valueµ 100% =___________________%.
In your lab report please summarize what you have learned in doing these exercises.
∆T expected = ___________ °C
∆T observed = ___________ °C.
Lab 7 Electromagnetic Fields Physics 100
7-1
Lab 7. Electromagnetic Fields
Objectives: Explore the ways of observing and describing electric and magnetic fields.
Understand the interrelationship between electric and magnetic fields.
I. Fields
Introduction: The discovery of electricity and magnetism and the mathematical tools
necessary to describe these phenomena in the 1800’s did more than anything else to break
the hold of the Newtonian world view that was prevalent from the mid 1600’s.
So what is the big issue with electricity and magnetism? They seem to be just another
kind of force, like that of gravity. However, unlike gravity, the electricity and magnetism
forces depend on a new property of matter, called “charge”. Remember that in gravity,
mass is both the cause of gravitational attraction and the property that is accelerated by
the force. In electricity and magnetism, the strength of the interaction is determined by
the amount of charge (it is a much stronger interaction than that of gravity) and has
nothing to do with the amount of mass present. The mass of the charged objects becomes
only a passive participant in the interaction, being accelerated due to the presence of this
other force.
Therefore, these two forces could be studied easily under many different circumstances.
It soon became apparent that the concept of force that works so well for gravitational and
inertial forces was a little lacking. Initially as a matter of convenience, and later as a
matter of necessity, the electric and magnetic forces were thought of as being
communicated by “fields”. You may have seen at some point or another a picture of a
magnetic or electric field. They are useful pictures to guide our eyes in understanding
how these forces are transmitted. They have turned out to be revolutionary in our
understanding of what is space and time. Today’s lab should give you a sense of how we
go about observing and measuring electric and magnetic fields.
II. Magnetic field maps
Introduction: Magnetic fields are the easier of the two types of fields to visualize,
primarily because magnetic poles always come in pairs of equal poles (charges) but
having opposite sign (north and south, right?) – known as dipoles. Magnetic fields, like
all fields, represent a sort of “force per charge”. Therefore, in a magnetic field, magnetic
dipoles receive two pushes of roughly equal strength but opposite in direction. As a
result, the dipoles (say, iron filings) line up in the presence of a magnetic field, but don’t
go anywhere. Actually, in the presence of a field that is rapidly increasing in strength, the
dipoles will tend to move toward the region of greater field strength because even over
the length of the small dipoles, there is enough difference in field strength to produce a
Lab 7 Electromagnetic Fields Physics 100
7-2
net force. Therefore, the dipoles tend to bunch up (get closer) near regions of high field,
and to otherwise line up in regions where the field is pretty uniform in strength. Magnetic
fields are also easier to observe because they always form closed loops. This is also
related to the fact that magnetic poles always come in pairs of opposites.
Exercise 1: Magnets and filings. Place a bar magnet underneath a sheet of thin, clear
plastic, and then put a nice, white sheet of paper over it. Shake the iron filings over the
position of the magnet, and tap the paper to help the filings spread out if necessary.
Sketch in your lab notebook what you observe. You may take a photo of the pattern of
the filings if you have a camera with you. Add comments or questions, and any answers
your lab group came up with.
To make you understand things easier, two figures are shown below. One is a picture of
the aligned filings from a textbook, the other is an illustration of the magnetic field near a
bar magnet.
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Exercise 2: Coils of wire and compasses. Remarkably, magnetic fields are not only
produced by magnets. They can also be produced by electric currents. (Even more
remarkably, changing magnetic fields can produce electric currents!) This process of
induction was one of the driving “forces” that led to the realization that the field picture is
not just convenient, but somehow a “real” reality.
One particular configuration of wires and current, the double loop (known as a Helmholtz
coil) produces a fairly large region of nearly uniform magnetic field near its center. Your
coil is hooked up to a power supply. It is also running through a digital multimeter
(DMM) as a current meter. Turn on the power supply with all the knobs turned off. Then
turn up the current knob. Your DMM should still read no current. Finally, turn up the
voltage knob slowly. You should see current being recorded by your DMM. Turn the
knob until you get 2.0 A of current through your loops.
Please use a small compass to observe the field direction in and about your Helmholtz
coil, on its middle horizontal plane. The compass acts as a single magnetic dipole that is
free to line up with whatever magnetic field is present. Usually, of course, it responds to
the earth’s field. But it will point elsewhere if a stronger field is present. Sketch the
“field lines” of the coil in your lab notebook.
For your convenience the field around a Helmholtz coil on its middle horizontal plane is
shown in the picture in next page. The direction of each small arrow indicates the
direction of the magnetic field at that place, and the length of the arrow shows the
strength of the field. On the graph please circle each arrow that you have tested the
direction using the compass in the above exercise. Please try to test as many points as
possible.
Lab 7 Electromagnetic Fields Physics 100
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Lab 7 Electromagnetic Fields Physics 100
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III. Electric field maps
Introduction: Electric fields are harder to visualize because electric charges can be
isolated (positive or negative) so that they are simply accelerated out of the region of
interest. For the same reason, electric field lines are not always closed. However, they do
originate at positive and terminate at negative charges. Another difficulty in observing
electric fields is that electric charge is a lot more mobile than magnetic poles. When you
gather a bunch of charges in a single place, they dissipate rather rapidly, especially when
you happen to live in very humid conditions (like Macomb), carried off by the very polar
water molecules in the air.
Although a static configuration of charge is hard to maintain, it is a bit easier to create a
kind of dynamic configuration of charge through the use of a battery and some
conductive paper. Instead of fixing the amount of charge on various objects, we fix the
“electric potential” or “voltage” on those objects. A surface at high voltage has more
positive charge than a surface at low voltage. The conductive paper will let the charge
flow from the high to the low, but the battery will replenish what is lost, so that the
voltage difference is maintained. This will act “like” a static electric charge
configuration, and the flowing charge will in fact flow, guided by the electric field lines
originating at the high voltage surface and terminating at the low voltage surface.
How do we detect the electric field? There are materials that act like the iron filings do
for magnetic fields, but that’s not needed here. Instead, we can first map the voltage at
various points in the space between the surfaces. Then, we can use the fact that the
electric field
1) is perpendicular to lines along which the voltage is a constant and
2) starts from positive charges and ends at negative charges.
Notice that there is no electric force acting along the constant voltage lines (equipotential
lines), since they are perpendicular to the field everywhere.
Exercise 3: Field between two “spheres”. Hook up your battery (about 1.5 V) so that
the positive terminal is connected to a needle touching one metallic circle, and the
negative terminal is hooked up to another needle connected to the other circle. Then, use
the DMM set to read voltage and make maps of the voltage in the space between the two
circles. Have the black “ground” terminal of your DMM hooked up to the negative
terminal of the battery. Have the red terminal hooked up to a third needle which you can
move about. Whenever you touch the paper with the needle, you should be able to read
the voltage at that point. Don’t touch the paper with any other part of your body while
mapping the voltage.
Lab 7 Electromagnetic Fields Physics 100
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Since we’re interested in seeing the field, we just need to map out a few of the
equipotential lines between the two surfaces. Please map the following equipotential
lines: 0.3 V, 0.6 V, 0.9 V, and 1.2 V. Identify each equipotential line with about 10
points. These points should be roughly evenly spaced and stretched out across the entire
paper. An accuracy of 0.01 V for each point is good enough for our purpose. These points
can be marked by poking holes on the conductive paper using the needle on the DMM
probe. Please put some plain papers for each of your group members just below the
conductive paper, and poke through all papers when marking the points. Please also mark
the two metallic circles, which are equipotential lines for the two terminals of the battery.
Once you have a set of equipotential lines mapped out, sketch what the electric field
looks like between the plates, remembering the rules outlined above.
For your convenience the equipotential lines and the field between two electric charges
are displayed in the following figure. Please compare what you have measured with the
picture shown here.
If you were to place a positive charge between the two spheres, and slightly above the
line connecting them, how would it tend to move? Sketch your answer on your map and
label it clearly.
Please summarize what you have learned through this lab about electric and magnetic
fields, and how you can observe them.
Lab 8 Electronics Physics 100
8-1
Lab 8. Electronics
Objectives: Learn about the basic elements involved in constructing electronic circuits
and building useful circuits with these elements.
I. Electronics
Introduction: You are to use the self-paced EKI Electronics Kits to explore the function
of some electronic elements, including wires, circuit boards, batteries, resistors,
potentiometers, LED’s, photodetectors, capacitors, diodes, transistors and speakers. All
the circuits you construct with these elements are DC circuits and the power supply is a
9V battery.
II. Building circuits
Excersises: The electronic kit and exercises are described in the paper packet you
received in class prior to the lab, through which you are expected to have some ideas on
the functions of various electronic elements before actually doing the lab experiments.
Your group should work through the first eight exercises (A1-A8) in your electronics kit.
Please inform the lab instructor if you have any missing items in the inventory.
Each time your group completes one exercise, please ask the lab instructor to come and
verify that your circuit really works before moving on to the next exercise.
You don’t have to sketch your circuits in your lab book. Instead, you should have a
record of the exercises you did, and a short description of the function of each element
used in the exercises.