Download Physics Laboratory Manual PHYC 10190 2011-2012

Physics Laboratory Manual
PHYC 10190
Aspects of Physics for Ag. Science
2011-2012
Name.................................................................................
Partner’s Name ................................................................
Demonstrator ...................................................................
Group ...............................................................................
Laboratory Time ...............................................................
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2
Contents
4
Introduction
Laboratory Schedule
5
Experiments Current
7
Resistance
21
Voltage
31
Voltage, Current and Resistance
39
Conservation of Momentum
47
Newton’s Second Law
55
3
Introduction
Physics is an experimental science. The theory that is presented in lectures has its
origins in, and is validated by, experimental measurement.
The practical aspect of Physics is an integral part of the subject. The laboratory
practicals take place throughout the semester in parallel to the lectures. They serve a
number of purposes:
•
•
•
an opportunity, as a scientist, to test theories;
a means to enrich and deepen understanding of physical concepts
presented in lectures;
an opportunity to develop experimental techniques, in particular skills
of data analysis, the understanding of experimental uncertainty, and the
development of graphical visualisation of data.
Some of the experiments in the manual may appear similar to those at school, but the
emphasis and expectations are likely to be different. Do not treat this manual as a
‘cooking recipe’ where you follow a prescription. Instead, understand what it is you are
doing, why you are asked to plot certain quantities, and how experimental uncertainties
affect your results. It is more important to understand and show your understanding
in the write-ups than it is to rush through each experiment ticking the boxes.
This manual includes blanks for entering most of your observations. Additional space is
included at the end of each experiment for other relevant information. All data,
observations and conclusions should be entered in this manual. Graphs may be
produced by hand or electronically (details of a simple computer package are provided)
and should be secured to this manual.
There will be six 2-hour practical laboratories in this module evaluated by continual
assessment. Note that each laboratory is worth 5% so each laboratory session makes
a significant contribution to your final mark for the module. Consequently, attendance
and application during the laboratories are of the utmost importance. At the end of each
laboratory session, your demonstrator will collect your work and mark it. Remember,
If you do not turn up, you will get zero for that laboratory.
You are encouraged to prepare for your lab in advance and bring
completed pre-lab assignments to the lab
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Laboratory Schedule
Depending on your timetable, you will, attend as detailed below, on either a Friday
(15:00-17:00) or Wednesday (14:00-16:00) afternoon. The class is divided into groups,
numbered 1-5 in the table below.
Please consult the notice boards in the School of Physics, Blackboard, or contact the
lab manager, Thomas O’Reilly (Room 1.30) to see which of the experiments you will be
performing each week. This information is also summarized below.
Dates
19-23 Sept
Semester
Week
2
26-30 Sept-
3
3-7 Oct
4
10-15 Oct
5
31 Oct-4 Nov
8
7-11 Nov
9
14-18 Nov
10
21-25 Nov
11
Lab 127
Current:
1,4
Current:
3
Resistance:
2,5
Room
Lab 131
Momentum:
2,5
Momentum
1,4
Momentum:
3
Voltage:
1,4
Voltage:
3
Voltage, Current:
2,5
Newton 2:
2,5
Newton 2:
1,4
Newton 2:
3
5
Lab 132
Current:
2,5
Resistance:
1,4
Resistance:
3
Voltage:
2,5
Voltage, Current:
1,4
Voltage, Current:
3
6
Name:___________________________
Date:___________
Student No: ________________
Demonstrator:_________________________
Current
What should I expect in this experiment?
In this experiment you will carry out a number of investigations on simple
electric circuits in order to determine some of their characteristics. Through these
investigations you will develop rules of your electric circuit model which allow you to
make predictions on other circuits.
Pre-lab assignment
Shown below are three arrangements of a bulb, battery one copper wire.
Choose the arrangements in which the bulb will light. You may choose more than one
arrangement. Explain your answer.
Introduction Circuit Diagrams
In this experiment you will encounter circuit diagrams which represent different
electric circuits. Circuit diagrams consist of lines and symbols, the ones which you will
encounter in this lab are shown below,
Please note the following carefully:
1. Direct contact and connection by a wire are represented by a line or a group of
lines. It is not possible to tell whether two circuit elements are connected directly
together or if they are connected by a wire.
Circuit diagrams only show electrical connections, they do not represent a physical
layout.
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The diagram above illustrates two different physical layouts; both are represented
by the same circuit diagram, shown to the right.
Experiment 1: Current
In this and the orther electronics experiments, you will develop a model for electric
circuits. The development of your model will always be guided by the observations you
make. All reasoning you do to make predictions should be based on your model only,
not on prior knowledge of electric circuits.
In today’s experiment you begin your investigation of electric circuits and some
of their properties. Starting from the basics of electric circuits, you will develop a
consistent model of simple resistive circuits.
Make sure you check your answers with a tutor when asked to do so.
Equipment/Apparatus check
Check that you have at your disposal: a battery, a bulb and a single wire.
Section 1: Complete Circuits
i. Consider the three arrangements of a battery, a bulb and a single wire in the pre-lab
assignment. Use your pre-lab answers to complete the “Idea” column of the table below.
Arrangement
1
2
3
Idea (on/off)
Observation (on/off)
ii. Connect the circuits and verify your ideas, enter your observations in the final column
of the table.
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9
10
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15
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Name:___________________________
Date:___________
Student No: ________________
Demonstrator:_________________________
Resistance
What should I expect in this experiment?
In this experiment you will carry more investigations on simple electric circuits in
order to determine some more of their characteristics. Through these investigations you
will develop more rules of your electric circuit model which allow you to make
predictions for other circuits.
Pre-lab assignment
In your own words describe what is meant by electrical current and electrical resistance.
In the circuit below all the bulbs are identical.
How does the brightness of bulb A
compare to the brightness of bulb B?
Choose one answer.
o Bulb A is brighter than bulb B
o Bulb A is as bright as bulb B
o Bulb A is dimmer than bulb B
o I do n’t know
Explain your answer to the previous question.
How does the brightness of bulb A compare to the brightness of bulb C?
Introduction
In the Current laboratory we discovered some properties of basic electric circuits.
These laid the foundations for our model of electric circuits. We will treat the two
assumptions we made: that there is a flow called current in a complete circuit, and that
the brightness of a bulb indicates the magnitude of the current through it, as the first two
rules of our model. In today’s experiment we expand our model and broaden our
understanding of electric circuits by investigating other types of circuits.
Equipment/Apparatus Check
Check to make sure you have a power supply, an ammeter, six wires, three bulb
holders, three bulbs and two crocodile clips.
Section 1: Power Supply
In the Current laboratory you worked solely with batteries, bulbs and wires. In this
experiment you will use a new component called a power supply.
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i. Attach two crocodile clips to the leads
of the power supply and set up a single
bulb circuit as shown in the diagram at
right. The switch on the power supply
should be set to 9 V.
Figure 1.1 A single bulb connected to a power
supply
ii. Do you think the brightness of the bulb would change if another bulb were
added in series to the circuit as shown in Figure 1.2? Explain.
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Set up the circuit shown at right and verify
your ideas. What did you observe?.
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Figure 1.2 Two bulbs in series connected to a
power supply
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iii. How do your observations compare to your observations from the Current
laboratory?
Do the circuits containing a battery behave differently to circuits
containing a power supply or do they behave the same?
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Section 2: Resistance in Series Circuits
In what follows, you may assume that a power supply and a battery behave identically.
In the last electronics experiment we observed that when a bulb was added in
series, the bulbs in the circuit dimmed. We took this as evidence that the current
through the bulbs and the battery decreased. We now try to incorporate this finding into
our model for electric circuits.
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i. Consider the two bulb series circuit which you have set up in Section 1. We label the
bulbs A and B. Predict what would happen to the brightness of bulb A if a third
bulb were added in series to the circuit as shown in Figure 2.1 above.
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ii. Set up the circuit and verify your prediction.
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To explain why the brightness of bulbs and the magnitude of current through the battery
is different in different circuits, it is helpful to think of bulbs as providing an obstacle or a
resistance to the current. In this picture, an increase in the circuit’s resistance causes
a decrease in current through the battery and vice versa.
iii. What can you infer about the total resistance of a circuit as more bulbs are added in
series?
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iv. Formulate a rule which allows you to predict how the current through the battery
would be affected as the number of bulbs added in series were increased or decreased.
Include the concept of resistance in your rule. This is the third rule of our model, to
go with the two rules you made in the first electronics laboratory.
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Discuss your answers with a tutor.
Section 3: Parallel Circuits
We have seen how adding bulbs in series affects the current through the battery
and how it affects the brightness of the bulbs in the circuit. We now look at a different
circuit and compare its properties to that of the circuits we have seen previously.
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The circuit shown in Figure 3.1 is called a parallel circuit.
Figure 3.2: Single bulb circuit.
Figure 3.1: Two bulbs in parallel.
i. Compare the circuit diagram of the parallel circuit above to that of a single
bulb circuit shown in Figure 3.2 to the right. What are the similarities and
differences between the two circuits represented by the diagrams? How many
complete conducting routes/pathways exist in each circuit?
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ii. How do you think the brightness of each bulb in a parallel circuit will compare to that
of a bulb in a single bulb circuit?
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Set up the parallel circuit as shown below in Figure 3.3. Compare the brightness of the
bulbs in the parallel circuit to that of a bulb in a single bulb circuit. Write down your
observations below.
_________________________________
_________________________________
_________________________________
_________________________________
_________________________________
Figure 3.3 Parallel circuit set-up
Compare the brightness of each of the bulbs in parallel.
through the bulbs compare to each other?
How do the currents
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In a parallel circuit we often think
the current splitting and recombining
junctions or nodes in the circuit.
junction or node can be defined as
electrical connection between three
more components.
of
at
A
an
or
Draw nodes on figure 3.5, where appropriate.
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Figure 3.4 A node
iv. Consider the following student statements about the circuits above.
Student 1:
“When the current reaches the first node in the parallel circuit,
it splits evenly between bulbs D and E. I know that the bulbs are equal in
brightness to a single bulb and they are also equal in brightness to each other.
Therefore the current through battery 2 must be double the amount of current through
battery 1.”
Student 2:
“I disagree. I know that all batteries have the same current and
all bulbs are the same brightness, so the same current flows through each bulb.”
Which of the students, if any do you agree with? Explain.
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Discuss your answer to part iv with a tutor
Section 4: Measurement of current
In this section, we make a series of measurements that will add some quantitative
evidence to the student statements shown in the previous section.
i. Use an ammeter to measure the current in a single bulb circuit as shown in Figure
4.1. Write down your measurement below.
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How does the current through the
battery compare to the current
through the bulb. Explain briefly
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_________________________________
_________________________________
_________________________________
_________________________________
Figure 4.1
ii. In the circuit of Figure 4.2, the ammeter is measuring the current through one of the
bulbs in a parallel circuit. On the basis of your observations and measurements, predict
the reading on the ammeter.
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Set up the circuit and verify your prediction.
iii. Predict the reading on the ammeter when it is connected to read the current
through the battery in a parallel circuit as shown below.
Explain briefly
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_________________________________
_________________________________
_________________________________
_________________________________
Figure 4.3 Parallel circuit with ammeter
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Set up the circuit shown of Figure
4.4, which measures the current
through the battery in a parallel
circuit.
How does your observation compare
to your prediction?
_________________________________
_________________________________
_________________________________
_________________________________
_________________________________
_________________________________
iv. Compare the current through the battery in the parallel circuit to the current through
the battery in the single bulb circuit. Do your measurements support the idea that the
current through a battery can be different in different circuits?
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v. Which of the student statements in part iv of Section 3 is consistent with your
measurements?
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What can you infer about the resistance of a parallel circuit as compared to that
of a single bulb circuit?
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Discuss your answers with a tutor
Section 5: Resistance in parallel circuits
In the previous section we have seen that when we add a bulb in parallel to a
single bulb circuit the current through the battery increases. We now carry out more
experiments to investigate the properties of parallel circuits.
Figure 5.2 A two bulb series circuit
i. Consider the circuit shown at in figure 5.1.
The black box represents an
arrangement of circuit elements. A change is made within the black box and as a result
the brightness of the indicator bulb A increases. What can you infer about the change
in resistance of the circuit after the connections in the box have been changed?
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ii. Set up a two bulb series circuit. We call bulb A an indicator bulb as,
throughout this experiment, it indicates the current through the battery.
Suppose that you added a third bulb, C, in parallel with bulb B as shown in figure 5.3.
Do you expect the brightness of bulb A to change when bulb C is added? Explain briefly
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Predict how the brightness of the bulbs in the diagram of Figure 5.3 would rank
from greatest to least. Carefully explain how you used your model to make your
prediction.
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iii. Now add bulb C in parallel to bulb B as shown in Figure 5.3.
brightness of the indicator bulb A change?
How does the
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iv. Considering your answer to question i, what can you infer about the change in the
resistance of the circuit as bulb C is added in parallel to bulb B?
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Is your answer consistent with what you found in Section 3 when you added a bulb in
parallel with a single bulb? Explain briefly.
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v.
Revise the third rule so that it describes how the current through the battery
changes when a bulb is added in parallel or in series to a circuit. Include the concept of
resistance in your rule. Make sure you rule incorporates the results from Sections 4 and
5.
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Check your rule with a tutor
vi. Through the investigations carried out in the previous sections and in the
Current laboratory, you have developed a large portion of your model on electric
circuits. To help you summarise some of the major concepts, complete the table below.
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Name:___________________________
Date:___________
Student No: ________________
Demonstrator:_________________________
Voltage
What should I expect in this experiment?
In the Current and Resistance laboratories we started to build a model for electric
circuits. In the next experiment we will investigate more complicated circuits and
introduce the third and final concept to our model.
Pre-lab assignment
1. A bulb is added in series to a given circuit. What happens to the resistance of the
circuit? What happens to the current through the battery?
2. A bulb is added in parallel to a given circuit. What happens to the resistance of the
circuit? What happens to the current through the battery?
Equipment/Apparatus Check
Check to make sure you have a power supply, two crocodile clips, five pieces of wire,
four bulb holders, four bulbs and a voltmeter.
Section 1: Voltage
i. Set up a single bulb circuit with the power supply switch at 3 V, 6 V and 9 V, and
describe any changes in bulb brightness.
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__________________________________
_________________________________
In the Current and Resistance laboratories, you changed the brightness of bulbs by
adding other bulbs to the circuit. Is there a difference in the way you changed the
brightness in this experiment? Explain briefly.
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Section 2: Power Supply
In the previous section we saw that a change in the power supply affected bulb
brightness. In the following experiments you will investigate this further.
We introduce another circuit element, called a
voltmeter. A voltmeter measures a
quantity known as voltage which is related to the ability of
a battery or power supply to push/drive current around the
circuit. The voltmeter must be connected in parallel to the
element which you are measuring, as shown in Figure 2.1.
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Name:___________________________
Date:___________
Student No: ________________
Demonstrator:_________________________
Voltage, Current and Resistance
What should I expect in this experiment?
In this experiment we will complete the model of electric circuits.
Pre-lab assignment
Consider the circuit to the right in which all the bulbs are the
same:
(a) Based on current, rank the bulbs by their brightness
(b) Based on voltage, rank the bulbs by their brightness.
Introduction
In the voltage experiment, we investigated a number of complex circuits and added the
concept of voltage to our model. The model thus far consists of the following parts:
1. There is a flow in a complete circuit, which we call current.
2. The brightness of a bulb is an indicator for the current through the bulb.
An increase in brightness indicates an increase in current through a bulb. Conversely,
if the current through a bulb increases, the brightness of the bulb increases.
3. When the resistance of a circuit increases, the current through the battery or
power supply decreases, and vice versa.
4. At a node, current splits according to the resistance in each branch. The branch
with greater resistance gets less current.
5. The brightness of a bulb is an indicator for the voltage across the bulb.
6. In a series circuit consisting of a power supply, a bulb and a box, the voltage across
the power supply is constant. The greater the resistance of the box, the greater the
voltage across it, and the smaller the voltage across the bulb.
7. Kirchhoff’s Loop Rule: along any loop that contains a power supply, the sum of the
voltages across all elements other than the power supply is equal to the voltage
across the power supply.
Section 1: Voltage in parallel circuits
39
Connect the voltmeter across bulb A as shown in the diagram above. Note the
reading on the voltmeter.
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40
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Section 3: Ohm’s Law
In this section, you will further investigate the relationship between voltage, current, and
resistance.
i. Set up the circuit shown at right with the power supply switch at 3 V.
In the space below, draw the corresponding circuit diagram.
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Connect the voltmeter at the 15 V terminal.
Note the reading on both the
voltmeter and ammeter while the switch on the power supply is at 3 V and enter the
values in the table below. Move the switch through 6 V, 9 V and 12 V, each time writing
down the corresponding reading on the voltmeter and ammeter. Enter your values in
the table below. If your power supply allows you to make more measurements, do so.
Voltmeter Reading (V)
Ammeter Reading (mA)
ii. Replace the bulb with a resistor as
shown to the right.
Measure current and voltage for each of
the four settings of the power supply.
Enter values in the table below.
Caution:
Do not delay in making
measurements and turn off power
supply when finished.
Voltmeter Reading (V)
Ammeter Reading (mA)
iii. Using the values in the tables, plot the data points for bulb and resistor in
the graph below. Plot current on the horizontal axis and voltage on the vertical axis.
Clearly label each data set. Do not draw any lines on the graph yet.
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iv. The data points for the resistor should lie on straight line that passes the axes close
to the origin.
Draw this line, and find a numerical value for its slope. What units does the slope have?
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The slope of your graph is equal to the resistance (R) of the resistor. Show that Ohm’s
Law holds for a resistor: V = IR.
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Determine the value for R. Show you work.
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Name:___________________________
Date:___________
Student No: ________________
Demonstrator:_________________________
Conservation of Momentum
What should I expect in this experiment?
You will investigate whether or not momentum is conserved in collisions.
Pre-lab assignment
In your own words, give definitions of conservation and momentum. Two cars have the
same mass but one is travelling twice as fast as the other, which has the larger
momentum?
Introduction
Momentum is a vector and is defined as mass multiplied by velocity: p = mv
The principle of the conservation of momentum states that in any interaction the total
momentum before is equal to the total momentum after. Momentum is conserved in
both collisions (think of two snooker balls colliding) and explosions (the vector sum of
the momenta of all the debris will sum to zero).
In this experiment you will take data before and after collisions, and see whether or not
the experimental data confirms or rejects the theory of conservation of momentum.
First though, let’s try an example of the principle in action. Suppose your 50 kg friend
faces you, at rest, wearing roller-blades and you throw a 5 kg bowling ball at 1 ms-1 to
them which they catch. How fast will they move backwards?
What is the momentum of the bowling ball before the
collision?
What is the momentum of the skater before the
collision?
What is the total momentum before the collision?
What is the total momentum after the collision?
What is the total mass after the collision?
What is the velocity of the combined ball + skater after
the collision?
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Apparatus
The apparatus you will use is shown here
and consists of two carts that can travel
along a low friction track. Each cart has a
mass of 0.5kg which can be adjusted by
the addition of steel blocks each of mass
0.5kg.
To make sure gravity isn’t assisting the
carts moving in one direction,
ensure the track is completely level!
(Use the height adjustment and a spirit
level and don’t move the track once
everything is correctly aligned.)
Investigation 1: Test the conservation of momentum in a head-on collision between
carts of equal mass where one cart is at rest.
You are going to fire cart ‘A’ at a stationary cart ‘B’ and observe the collision. Small
springs on the edge of cart ‘A’ allow it to be launched from the end of the track. After an
initial acceleration due to the spring it travels at constant velocity. First of all you must
estimate the velocity of cart ‘A’.
Explain how you can measure the velocity of cart ‘A’ using ruler and stopwatch.
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Make three independent estimates of the velocity of cart ‘A’ and fill in the table below.
Make an estimate of the uncertainty (error) on your estimate of the velocity. Think about
whether distance or time has the most significant uncertainty.
Cart ‘A’
Distance (m)
Time (s)
Trial 1
Trial 2
Trial 3
48
Velocity (m/s)
What is your best estimate of the velocity of cart A before the collision? Why is this the
best estimate? How large do you think the error (uncertainty) is?
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Place cart ‘B’ at rest on the track and fire cart ‘A’ toward it. After the collision, how will
you work out the velocity of each cart? (There are at least two ways of doing it.)
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Fill in the table below for the velocities of each cart after the collision. Repeat the
measurements three times.
Distance (m)
Time (s)
Cart A
Trial 1
Cart B
Cart A
Trial 2
Cart B
Cart A
Trial 3
Cart B
49
Velocity (m/s)
What is your best estimate of the velocity of cart A after the collision? Comment if
necessary.
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What is your best estimate of the velocity of cart B after the collision? Comment if
necessary.
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Analysis
What is the total momentum of the carts before the collision?
What is the total momentum of the carts after the collision?
(Don’t forget the units)
Do your results confirm or reject the hypothesis that in collisions momentum is
conserved.
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50
Investigation 2: Test the conservation of momentum in a head-on collision between
carts of unequal mass where one cart is at rest.
Change the mass of the stationary cart by adding a series of steel bars each of 0.5 kg.
Measure the velocities of each cart after the collision and fill in the table below.
Mass
Cart
B
Velocity
Momentum
Total momentum
Cart A
0.5kg
Cart B
Cart A
1.0kg
Cart B
Cart A
1.5kg
Cart B
Cart A
2.0kg
Cart B
Comment on the numbers in the final column. What should they be if the conservation
of momentum holds?
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51
Draw a graph of the velocity of cart B after the collision against the mass of cart B. Use
either the graph paper below or JagFit (see back of manual) and attach your printed
graph below.
52
Draw another graph of the velocity of cart A after the collision versus the mass of cart B.
Use either the graph paper below or JagFit (see back of manual) and attach your
printed graph below.
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Suppose you were sitting in a car at rest when another car hit you. With reference to
the graphs you have just plotted, explain whether you would prefer being in a more or
less massive car?
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Suppose you are driving a car and around a bend see a stationary car which you can
not avoid. With reference to the graphs you have just plotted, would you hope to hit a
more or less massive stationary car.
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54
Name:___________________________
Date:___________
Student No: ________________
Demonstrator:_________________________
Newton’s Second Law.
What should I expect in this experiment?
This experiment has two parts. In the first part you will apply a fixed force, vary the
mass and note how the acceleration changes. In the second part you will measure the
acceleration due to the force of gravity.
Pre-lab assignment
In your own words, give a definition of acceleration. Explain what gravity is.
Introduction
Newton’s second law states F = m a , a force causes an acceleration and the size of
the acceleration is directly proportional to the size of the force. Furthermore, the
constant of proportionality is mass.
Apparatus
The apparatus used is shown here and
consists of a cart that can travel along a
low friction track. The cart has a mass of
0.5kg which can be adjusted by the
addition of steel blocks each of mass
0.5kg. String, a pulley and additional
masses allow forces to be applied to the
carts.
Take care to ensure that the track is
completely level before starting the
experiments
55
Investigation 1: Check that force is proportional to acceleration and show the constant
of proportionality to be mass. Calculate the acceleration due to gravity.
The apparatus should be set up as in the
picture. Attach one end of the string to
the cart, pass it over the pulley, and add
a 0.012kg mass to the hook.
The weight of the hanging mass is a force, F, that acts on the cart. The whole system
(both the hanging mass mh and the cart mcart) are accelerated. So long as you don’t
change the hanging mass, F will remain constant. You can then change the mass of
the system, M, by adding mass to the cart, noting the change in acceleration, and
testing the relationship F=ma.
If F=ma and you apply a constant force F, what do you expect will happen to the
acceleration as you increase the mass?
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There remains the problem of working out the acceleration of the system.
According to kinematics, distance travelled is related to the acceleration by the formula
s = ut +
1 2
at , where s is distance, u the initial velocity, t is time, and a acceleration.
2
If the cart starts from rest write down
an expression for ‘a’ .
Place different masses on the cart. Using ruler and stopwatch measure s and t and
hence the acceleration a. Fill in the table below.
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mh
(kg)
mcart
(kg)
M=
mh+mcart
(kg)
a (m/s2)
M.a (N)
1/a (m-1s2)
s (m)
0.012
0.5
t (s)
0.012
1.0
s (m)
t (s)
s (m)
0.012
1.5
t (s)
From the numbers in the table what do you conclude about Newton’s second law?
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Analysis and determination of the acceleration due to gravity.
If Newton is correct, F = (mh + mcart ) ⋅ a
You have varied mcart and noted how the acceleration changed so let’s rearrange the
formula so that it is in the familiar linear form y=mx+c. Then you can graph your data
points and work out a slope and intercept which you can interpret in a physical fashion.
F = (mh + mcart ) ⋅ a ⇒
m
1 1
= mcart + h
a F
F
So if Newton is correct and you plot mcart on the x-axis and 1/a on the y-axis you should
get a straight line.
In terms of the algebraic quantities above,
what should the slope of the graph be equal to?
In terms of the algebraic quantities above,
what should the intercept of the graph equal?
Plot the graph and see if Newton is right. Do you get a straight line?
What value do you get for the slope?
What value do you get for the intercept?
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Use JagFit to create your graph (see back of manual) and attach your printed graph
below.
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Now here comes the power of having plotted your results like this. Although we haven’t
bothered working out the force we applied using the hanging weight, a comparison of
the measured slope and intercept with the predicted values will let you work out F.
From the measurement of the slope, the constant force applied can be calculated to be
From the intercept of the graph you can calculate F in a different fashion. What value
do you get?
You’ve shown that F is proportional to a and the constant of proportionality is mass. If
the force is the gravitational force, it will produce an acceleration due to gravity
(usually written g instead of a) so once again a (gravitational) force F is proportional to
acceleration, g. But what is the constant of proportionality? Are you surprised that it is
the same mass m? (By the way, a good answer to this question gets you a Nobel prize.)
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So since that force was just caused by the mass mh falling under gravity, F= mhg, you
can calculate the acceleration due to gravity to be
Comment on how this compares to the accepted value for gravity of about 9.785 m/s2
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Investigation 2: Acceleration down an inclined plane.
The apparatus should be set
up as in the picture. Raise one
end of the track using the
elevator. The carts can be
released from rest at the top of
the track.
A cart on a slope will
experience the force of gravity
which causes the cart to
accelerate and roll down the
incline. The acceleration due
to gravity is as shown in the
schematic. The component of
this acceleration parallel to the
inclined surface is, g.sinθ and
this is the net acceleration of
the cart (when friction is
neglected).
Note
the
acceleration depends on the
angle of the incline.
Vary the angle of the incline (repeat for at least four different angles) and measure the
1
acceleration of the cart using s = ut + at 2
2
How will you measure the angle of the incline?
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Summarise your results in this table.
Angle
(radians)
Sine Angle
Distance (m)
Time (t)
Acceleration (ms-2)
Since the acceleration a = g sin θ , there is a linear dependence on the sine of the
angle. Make a graph with sin θ on the x-axis and a on the y-axis.
What value do you expect (theoretically) for the slope?
What value do you expect (theoretically) for the intercept?
What value do you obtain (experimentally) for the slope?
What value do you measure for the intercept?
Comment on your results. How could you improve your measurements of g?
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61
Use JagFit to create your graph (see back of manual) and attach your printed graph
below.
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Using JagFit
In the examples above we have somewhat causally referred to the ‘best fit’ through the
data. What we mean by this, is the theoretical curve which comes closest to the data
points having due regard for the experimental uncertainties.
This is more or less what you tried to do by eye, but how could you tell that you indeed
did have the best fit and what method did you use to work out statistical uncertainties on
the slope and intercept?
The theoretical curve which comes closest to the data points having due regard for the
experimental uncertainties can be defined more rigorously1 and the mathematical
definition in the footnote allows you to calculate explicitly what the best fit would be for a
given data set and theoretical model. However, the mathematics is tricky and tedious,
as is drawing plots by hand and for that reason....
We can use a computer to speed up the plotting of experimental data and to improve
the precision of parameter estimation.
In the laboratories a plotting programme called Jagfit is
installed on the computers. Jagfit is freely available for
download from this address:
http://www.southalabama.edu/physics/software/software.htm
Double-click on the JagFit icon to start the program. The working of JagFit is fairly
intuitive. Enter your data in the columns on the left.
•
•
•
Under Graph, select the columns to graph, and the name for the axes.
Under Error Method, you can include uncertainties on the points.
Under Tools, you can fit the data using a function as defined under
Fitting_Function. Normally you will just perform a linear fit.
The electronics experiments in this manual was developed by the Physics Education
Group, CASTeL, Dublin City University
1
If you want to know more about this equation, why it works, or how to solve it, ask your
demonstrator or read about ‘least square fitting’ in a text book on data analysis or statistics.
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