physics for society lab manual - western illinois...

Physics 100

Physics for Society

Lab Manual

Fall 2017

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 and Mass

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


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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


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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.

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


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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

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.


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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”

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


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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.

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.

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.


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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 2.0 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.

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


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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

""0.2 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 qustionable.

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.

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?


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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?

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.


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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.

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.


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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 and Mass

Objectives: Explore the nature of the cause of acceleration, understand the nature of

inertial mass, and understand the nature of gravitational force.

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


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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 spread sheet to record

your data and draw the graph.

Mass (kg) Force (N)

0.25

0.55

0.75

1.05

1.25

What is the relationship between your measured 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. 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?


3-3

Mass (kg) 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

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


3-4

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 N

#2 0.055 0.539 N

#3 (Optional)

0.055 0.539 N

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


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 diagram form as illustrated below; i.e., draw a figure

showing the points of application of all the forces, and 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.


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



−=×−= 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.


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


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


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.


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.


5-4

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?


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)


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.


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. 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: ________________________________________________________________.


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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

.cm

QT

∆=∆ (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


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.


7-3

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.


7-4


7-5

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.


7-6

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.

physics for society lab manual - western illinois...

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