2. Physics 12 Course Syllabus. Teacher: M. Turton (
) http://
hrsbstaff.ednet.ns.ca/max/. Location: Rm 321 (classroom), Rm 216 (Lab).
Table of Contents Course Syllabus …………………………………………………………………………... pg. 2 Class Schedule ………………………………………………………………………..…… pg. 3 Mark Tracking Template ……………………………………………………..……. pg. 6 Physics Lab Safety Policy and Procedures ……………………..…….. pg. 7 Lab Report Format………………………………………………………………………. pg. 8 Sample Lab ……………………………………………………………………………..……. pg. 10 Significant Digits and Rounding…………………………………….………….. pg. 14 Scientific notation and Error Calculation………………………………… pg. 15 Using Data Studio and the Sensors ………………………………………….pg. 16
Experiments #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 #12 #13 #14 #15 #16 #17
Projectile Motion ………………………………………………………………… pg. 18 Air Resistance ……………………………………………………………….……. pg. 19 Dilution Of Gravity ………………..…………………………………………… pg. 21 Projectile on Air Table ……………………………………………………… pg. 22 Torque & Centre of Gravity……………………………………………… pg. 24 Collisions on Air Table……………………………………………………….. pg. 25 Whirlygig ……………………………..………………………………………………. pg. 26 Vertical Circles and the Turning Point …………………………… pg. 29 Circular Motion: The Conical Pendulum…………………………… pg. 30 SHM and Weighing Oneself in Microgravity.………………… pg. 33 Electrostatic Equilibrium……………………………………………………. pg. 35 Ohm’s Law With One Component…………………………………… pg. 36 Ohm’s Law in a Series Circuit……………………..………………….. pg. 37 Ohm’s Law in a Parallel Circuit……………………..………………….. pg. 38 Watt’s Law and Energy Stored in a Battery ………………… pg. 39 Electromagnetism ………………………………………………………………. pg. 40 Measuring Planck’s Constant ……………………………………………. pg. 42
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Physics 12 Course Syllabus Teacher: M. Turton (
[email protected]) http://hrsbstaff.ednet.ns.ca/max/ Location: Rm 321 (classroom), Rm 216 (Lab) Phone: (902) 479-4612 extension 5701321 (classroom) Texts: Physics, McGraw-Hill Ryerson (replacement cost: $135) Supplies Required:
1 large binder or covered clipboard (notes, handouts, homework) 1 Duotang (labs) pencils, pens, erasers lined paper (200 sheets), graph paper(50 sheets) scientific calculator protractor, ruler 3 ½” computer disk or USB memory stick
Grading Scheme:
Assignments Labs Project Tests Quizzes Exam
15% 20% 10% 25% 5% 25%
Text Book Policy: You will be issued textbooks which must be returned at the end of the semester in good condition. If the texts are not returned you will be required to reimburse the school for the value of the texts before you receive any of your grades. The replacement costs of the textbooks are $135 each. Attendance/ Missed work: You are responsible for any missed work. Any work not passed in will receive a mark of zero. Late work will be scaled according to degree of lateness unless prior arrangements have been made. Work handed in after answers are given out will receive a maximum grade of 30%. Cheating/Plagiarism Policy: Cheating on a test or quiz will result in a zero for that assessment. Plagiarism (submission of another’s work as your own) on an assignment, lab or project will result in a zero for that assessment. Extra Help: Any Lunchtime. Please book in advance Course Design: This course is designed around the Atlantic Canada Curriculum outcomes framework. Many different forms of assessment and evaluation are used to best allow you to demonstrate the outcomes. If you feel your specific needs as a learner are not being met, please arrange to meet with me so I might better understand your concerns. I look forward to a great year M. Turton
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Class Schedule Class Number
Unit
1
Intro
Units, Proportionality, Approximation
2
Intro
Grade 11 review
3
Vectors
RAD Notation, Graphical method of vector addition
4
Vectors
Component method , resolving, combining
5
Vectors
combined
6
Vectors
combined
7
Projectile motion
Separateness of x and y components
8
Projectile motion
resolving vi
9
Projectile motion
different cases general
10
Projectile motion
numerical solutions
11
Projectile motion
practice problems
12
Projectile motion
Lab Intro
13
Projectile motion
Projectile Motion Lab 1
14
Projectile motion
Test1
15
Dynamics
2D tug of war
16
Dynamics
Air resistance Lab 2
17
Dynamics
Inclined Planes
18
Dynamics
Inclined Planes
19
Dynamics
Dilution of Gravity Lab 3
20
Dynamics
Multiple mass systems
21
Dynamics
Buoyancy
22
SE & Torque
Defined, locating forces, equilibrant
23
SE & Torque
tension, hanging masses
24
SE & Torque
Torque, law of levers, Centre of mass/gravity
25
SE & Torque
Torque with F on angle
26
SE & Torque
SE problems with torque (demos)
27
SE & Torque
Balance and stability Sample problems and practice
28
SE & Torque
Torque Lab 4
29
SE & Torque
Test 2
30
Momentum
Conservation of momentum in 2D
31
Momentum
practice problems
32
Momentum
elastic vs inelastic collisions
Class Description
3
33
Momentum
air table lab 5
34
Momentum
explosions
35
Momentum
recoil and rockets
36
Momentum
Review
37
Momentum
Test 3
38
Circular motion
Centripetal acceleration and Force
39
Circular motion
horizontal circles
40
Circular motion
Whirlygig Lab 6
41
Circular motion
Vertical Circles
42
Circular motion
Banked Turns & Circular pendula
43
Circular motion
Vertical Circles Lab 7
44
Circular motion
Test 4
45
Gravitation
History, Keplers Laws, Newton's Law of Gravity
46
Gravitation
Video
47
Gravitation
Fg = FG
48
Gravitation
FG = Fc
49
Gravitation
Calculating aspects of orbit (alt vs orbital radius)
50
Gravitation
Review
51
Gravitation
Geosynchronous orbit
52
Gravitation
practice problems
53
Gravitation
Test 5
54
SHM
Defined w/ sinusoidal nature
55
SHM
energy considerations of spring mass system
56
SHM
period of pendula and spring mass system
57
SHM
Big spring Lab 8
58
SHM
Review
59
Fluids
Static Characterisics: Density, Pressure, Depth
60
Fluids
Dynamic Characteristics: Fluid Speed, continuity, & Bernoulli's equation
61
Thermo
Heat at atomic level, Brownian Motion, elongation of solids
62
Thermo
Rate of heat transfer, specific heat capacity, latent heat
63
Thermo
Ideal gas law
64
Thermo
Laws of Thermodynamics, PV diagrams
65
Thermo
Engines and heat pumps
66
Thermo
Review
67
SHM-Thermo
Test 6
68
E&M
Fields and non contact forces gravity and magnetic
4
69
E&M
Coulombic force with demos
70
E&M
Forces in a drop of water
71
E&M
E field and vector nature of electric field and force
72
E&M
Voltage charges and E fields
73
E&M
Current resistance and Ohms law
74
E&M
Watts law and Battery power Lab 9
75
E&M
B field assosciated w/ current in a wire and coil RHR 1&2
76
E&M
F=BIL and F = qvB
77
E&M
Torque on a coil and motor effect
78
E&M
Generator effect and Lenz's law
79
E&M
Transformers
80
E&M
Magnetic Lab 10
81
E&M
Test 7
82
Nuclear
radiation types, stable nuclei, nuclear conventions
83
Nuclear
Decay equations, conservation of charge and mass number
84
Nuclear
Strong nuclear force and binding energies
85
Nuclear
mass defect and E=mc^2
86
Nuclear
energy from nuclear reactions (fission vs fusion)
87
Nuclear
video
88
Nuclear
Review
89
Nuclear
Test 8
90
Modern
EM waves and Spectroscopy
91
Modern
Early quantum evidence Blackbody radiation
92
Modern
Bohr atom and Hydrogen energy levels
93
Modern
Photoelectric effect
94
Modern
Wave particle duality
95
Modern
Plancks Lab 11
96
Modern
Test 9
97-106
Review
2 weeks review
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Mark Tracking Template Assignments 1 2 3 4 5 6 7 8 9 10 11 ICA 1 ICA 2 ICA 3 ICA 4 ICA 5 Total Average (avg) %total =avg x 0.15 = Projects 1 2 Total Average %total =avg x 0.1 =
Labs 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Total Average %total =avg x 0.2 =
Exam %total = Exam mark x .25
Quizzes 1 2 3 4 5 6 7 8 9 10 11 Total Average %total =avg x 0.05 = Tests 1 2 3 4 5 6 7 Total Average %total =avg x 0.25 =
Final Grade : Add all 6 % totals together
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Physics Lab Safety Policy & Procedures 1. No “horseplay” in the lab will be tolerated. The safety of you and your classmates depends on your responsible behavior. 10 % of each lab mark is awarded for your conduct in the lab and how clean you leave your station. 2. Never perform any activity or use any lab equipment without the permission of the teacher. 3. Report any injuries or health issues to the teacher immediately. 4. Listen to and follow all instructions given by the teacher. 5. Know the location of safety equipment – fire extinguisher, first aid kit, etc. 6. Wear appropriate clothing to the lab. Avoid long, loose clothing and jewelry. 7. Proper footwear is essential as well. Avoid sandals and high heels. 8. No food or drink is permitted in the Lab. 9. Read any written lab instructions before you come to the lab. 10. Be prepared to work as soon as you come into the lab. 11. Make sure the tables and aisles are kept free of bookbags to prevent tripping. 12. Keep the lab benches free of books, clothing and anything not needed in the lab. 13. Always use the proper tools. Use electrically insulated tools when working with electricity. 14. Use caution when working with electrical circuits, devices, and capacitors. 15. Make sure all electrical devices are turned off and/or unplugged both before and after an experiment. 16. Make sure your lab area is clean and the chairs placed on the tables at the end of the period.
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Lab Report Format Labs will be done in groups of 2 – 4 persons. The report is due one week after completion of the work in the lab. Each person must submit their own report. Labs are the basis for our understanding the key concepts in physics. Here are the guidelines for success in writing a quality lab report. 1. All laboratory reports are to be typed on plain paper (type on one side only). 2. Your name (in bold type), and the names of all members of your lab team and the date the investigation was performed is to be written in the upper right hand corner of the first page of each report. 3. An appropriate and descriptive title for the report should be placed at the top center of the first page of the report. 5. Each of the following sections of the laboratory report should be prefaced with the section names. Background (5 points) This is a brief list of the relevant formulae used and or investigated in the lab and or a general description of the phenomenon to be investigated. Purpose (5 points) This is a statement of the problem to be investigated. It provides the overall direction for laboratory investigation and must be addressed in the conclusion. Equipment (5 points) - A list of all laboratory equipment used in the investigation. - A detailed and labeled diagram to illustrate the configuration of the apparatus. Procedure (20 points) - Identify and name all experimental variables. - Briefly describe how the independent variables are controlled. Someone who was not present during the lab should be able to understand how the experiment was performed and be able to reproduce the results by reading your procedure.
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Data (20 points) - Data measured directly from the experiment. - Derived values obtained by way of mathematical manipulations (for example: average values, or unit conversions) or interpretations of any kind should be included in this section of the report as well. - A sample calculation must appear describing the method of obtaining all derived values. - The units for physical measurements in a data table should be specified in column headings only. Data Analysis (30 points) - Include all graphs, analysis of graphs, post laboratory calculations and percent errors. - All graphs should have a title, labeled coordinate axis and units. - Unusual results or trends should be noted and explained if possible. - State the meaning of the slope and discuss the significance of the y-intercept when appropriate. - Explain the possible source of any error or questionable results. - Suggest changes in experimental design which might test your explanations. Conclusion (10 points) - Discuss whether the goals in the purpose were achieved. - State any significant numerical results with associated error. - Comparison of results with known or expected values Lab Behaviour (10 points) - Full marks are awarded if you work well and your lab table is tidy with the chairs on the table, equipment turned off, and borrowed supplies returned. - Marks are deducted for disruptive behaviour, careless work habits and/or an untidy lab table. Sample Lab Found on Next Page
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Sample Lab:
Background:
Pendula Length & Period relationships
According to theory, the period of a pendulum (T) is related to gravity (g = 9.8 m/s2) and the length of the pendulum ( l ) by the equation
l g
T = 2π Purpose:
Your Name Partner’s Name(s) Sept 10, 2007
To verify that the period of a pendulum is related to its length by the equation shown above.
Procedure: The pendulum was set up as shown in Figure 1-1 Figure 1-1
length Rest position mass displacement
1 cycle or period The mass was 1.0 kg and the displacement was 0.15 metres. These two variables remained constant throughout the entire experiment. The time to complete 20 cycles was measured using a digital stopwatch with a precision of 0.01 seconds. Three trials at each length were measured and the data was recorded in Table 1-1. The period of a single cycle was calculated by dividing the measured time by 20 as seen in Sample Calculation 1-1, and was recorded in Table 1-1. The average period was then calculated by summing the periods for each trial at that length and dividing by three as seen in Sample Calculation 1-2, and was recorded in Table 1-1. A graph of period vs. length was plotted (see Graph 1-1). A second graph was plotted of the period vs. the square root of the length and named Graph 1-2 .
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The slope of this line was compared to the theoretical value obtained in Sample Calculation 1-3. The percent error was calculated in Sample Calculation 1-4. Data: Table 1-1 Length (l) (metres)
Length
( m)
0.50
0.7071
1.00
1.0000
1.50
1.2247
2.00
1.4142
2.50
1.5811
Trial
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
Time (t) for 20 cycles (s) 27.06 29.13 28.90 43.02 39.96 39.01 49.16 49.97 48.28 55.73 55.70 55.86 62.57 63.83 62.42
Period (T) (s) 1.35 1.46 1.41 2.15 2.00 1.95 2.46 2.50 2.41 2.79 2.79 2.79 3.13 3.19 3.12
Sample Calculation 1-1
Sample Calculation 1-2
T = t / 20 T = 27.06 s / 20 T = 1.35 s
Tave = Tave Tave
T1 + T2 + T3 3 1.35s + 1.46s + 1.41s = 3 = 4.22s / 3
Tave = 1.41s
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Average Period (Tave) (s) 1.41
2.03
2.46
2.79
3.15
Analysis:
Graph 1-1
Period (s)
Period vs. Length 3.5 3 2.5 2 1.5 1 0.5 0 0
1
2
3
Length (m) Graph 1-2
Period vs Square root of Length
Period (s)
y = 1.99x 5.00 4.00 3.00 2.00 1.00 0.00 0.00
0.50
1.00
1.50
2.00
Square root of Length (m)^0.5
12
2.50
Analysis (cont’d) As expected, Graph 1-1 has the approximate shape of y = x and Graph 1-2 is linear. 2π The slope of Graph 1-2 is less than 1% off from the expected value of . This error g is likely due to error in measuring the length of the pendulum as well as the error in measuring the period times.
Sample Calculation 1-3 l T = 2π g T = 2(3.14) T=
6.28
Sample Calculation 1-4 o
l 9.8 m s 2 l
m
error =
observed − theoretica l
theoretica l 2.01 − 1.99 % error = × 100 % 2.01 % error = 0.00995 × 100 % % error = 0.995 %
9.8 m s 2
T = 2.01 s
o
× 100 %
l
Conclusion Our observations agreed to within 1% that the period of a pendulum is directly related 2π . to the square root of the length with a proportionality constant of g
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Significant Figures Significant figures (SF) are all the digits of a measurement that are certain plus one estimated digit. 56.4 mm has three significant digits. Rules 1. 2. 3. 4.
for Significant Digits All non zero digits are significant. All final zeros after the decimal point are significant Zeros between non zero digits are significant Zeros used as place holders only are not significant
Example 1:
180000
has two significant digits 1 and 8 the zeros are not significant since they are place holders
Example 2:
180000.0
has 7 significant digits. The final zero is significant because of rule 2. The other zeros are significant because of rule 3.
Example 3:
0.0243
has 3 SF because the zeros are placeholders
Calculations with Significant Figures The final answer should have the same number of significant digits as the least precise number in the calculation. Examples:
12.1kg + 0.130 kg = 12.2 kg 12.5m x 16m x 15.88m = 3176m3 the least precise number (16m) has 2 sf so the answer must be rounded to 3200 m3.
Rounding When performing calculations, a calculator will often display many digits only a few of which are significant. These must be rounded to maintain the correct precision. Numbers within a calculation are not rounded. Rounding is only done to the final answer. Rules 1. 2. 3.
for rounding Round down if the digits to be dropped are < 5, 50, 500 etc. Round up if the digits to be dropped are > 5, 50, 500 etc. Round to the even digit if the digits to be dropped are = 5, 50, 500 etc. 14
Rounding examples – each is rounded to 3 SF 125.6 = 126 125.4 = 125 125.5 = 126 124.501 = 125 124.5 = 124
Scientific Notation Scientific notation is a format used to conveniently express extremely large or small quantities. Any number can be expressed as the product of two numbers. The first factor is greater or equal to 1 and less than 10. The second factor is a power of ten. Examples: The mass of the Earth is 59 900 000 000 000 000 000 000 000 kg in standard notation. This is 5.99 x1024 kg in scientific notation. 90 kg would be 9.0x 101 kg in scientific notation. For numbers like this the only convenience is expressing the number 90 to a precision of 2 significant digits. The mass of an electron is 0.000000000000000000000000000000911 kg in standard notation. This is 9.11 x 10-31 kg in scientific notation. Only the digits in the first factor are significant. All of the digits in the first factor are significant.
Error Calculations In some of your experiments you will be required to check your results with a known value; This will be done by finding the percentage error in the experiment using the following equation: o
o error =
observed − theoretica l theoretica l
× 100 %
If your percentage error is less than 10% your lab can be considered a success.
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Getting Started With Any Sensor 1. Turn on the computer. 2. Turn on the “Science Workshop 500 Interface”. (The little black box has the on/off switch on the back and a green indicator light on the front.) 3. Open Data Studio by double clicking on the desktop icon. 4. A pop up window appears asking “How would you like to use data studio?” Select the “Create Experiment” option. 5. The next pop up window is “Experiment Set Up”. Click the “Choose interface” button. 6. Select “Science Workshop 500” and click “OK”. 7. Click the “Add Sensor or Instrument” button 8. Double click the sensor to be used from the scroll through menu. Most sensors are analog except the motion sensor which is digital. 9. Connect the sensor to the “Science Workshop 500 Interface” as shown in the pop up window. 10. Locate and follow the instructions specific to the sensor from the choices below.
Sound Sensor 1. Follow the steps in the getting started section to connect the sensor and turn on the equipment. 2. Once the sensor is connected, double click on the word “scope” in the lower left menu. 3. Click on the “start” button beside the red time counter near the top of the screen. There is a slight time delay between the detection of the sound and the creation of the graph. 4. The “Start” Button turns to a “Stop” button during data collection. 5. Click on the “Stop” button when the desired sound waveform is observed. 6. Click on the left or right arrow at the bottom of the scope window on either side of “ms/div” to horizontally stretch the sound waveform . 7. Click on the up or down arrow at the top right of the scope window to vertically stretch or translate (slide) the sound waveform .
Motion Sensor Making a position or velocity time graph(s) in real time Note: The sensor only measures what is directly in front of the gold screen. 1. 2. 3. 4. 5.
Follow the steps in the getting started with any sensor section. Click once on the word position in the upper left menu. Double click on the word graph in the lower left menu. A pop up window should appear. Select position time graph and click OK. A position should appear in the main body of the window with the units used for each axes and the word “Time” on the horizontal axes.
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6. A velocity time graph may be viewed simultaneously with the position time graph by dragging the word velocity from the upper left menu into the position time graph. 7. Start the collection of data by clicking on the start button next to the red time counter on the screen. Dots should appear on the graph and the motion sensor should be clicking away as the data is collected. 8. The Start button turns into a stop button while data is collected. Press the stop button once your data collection is complete.
Manipulating graphs. 1. The mouse pointer changes shape to indicate different options for manipulating graphs. The toolbar within the graph window gives other options. 2. Moving the mouse pointer over an axis changes the pointer to a grabbing hand which allows the movement of a graph in any direction with a click and drag. 3. Moving the mouse pointer over the numbers on an axis changes the pointer to a curly double ended arrow which allows the stretching of a graph in any direction with a click and drag.
Multiple Overlaid graphs After the first graph is created, simply press the start button again and a second graph will be created over the first. The first graph is called “Run 1” and the second graph is called “Run 2”. Deleting a graph Select “Run 1” (or the run you would like to delete) from the upper left menu then press delete then press return or select yes from the pop up. Creating a line of best fit 1. Select the region of the graph to be described by a line of best fit with a click and drag. (In the same manner text is selected in a word document.) 2. Click on the “Fit” button at the top middle of the graph window and select “linear fit” (or other desired graph type) from the pull down menu. 3. Delete a line of best fit in the same manner as deleting a graph.
Using The “Calculate” Feature To Create a kinetic energy vs time graph from a particular velocity time graph. 1. Click on the “Calculate” button next to the red timer. 2. Enter the formula with an equals sign. Use * for times and ^ for exponents. 3. Click the “accept” button once the formula is entered. 4. To define a variable click on the down arrow next to “Please define variable”. 5. Select “data measurement” and then the run # of the data to be used. 6. Drag the Equation from the upper left data menu into the graph window. The new Graph should appear below the original . 17
Lab 1:
Projectile Motion
Background: An object that flies through the air with no means of propulsion near the surface of the earth (within 100 km) will undergo projectile motion. Neglecting air resistance, the horizontal velocity is constant with zero acceleration and the vertical velocity has a constant acceleration downwards due to gravity. The kinematic equations derived in grade 11 suffice to describe this motion mathematically. These equations specifically are: r r ∆d vave = ∆t
r r r v f − vi a= ∆t
r r 1r 2 ∆d = vi ∆t + a (∆t ) 2
r r r v f + vi ∆d = ∆t 2
r r v 2f = vi2 + 2a∆d
Purpose: To observe and quantify various aspects of a tennis ball’s motion through measurement and calculation. Apparatus: tennis ball 25 metre measuring tape Stopwatch Procedure: 1. In a group of 2 or 3 collect the necessary materials. 2. Each person will throw the tennis ball a minimum of three times with the following trajectories. a. Low and fast b. Straight up c. As far as possible 3. While 1 person throws the other group members are responsible for measuring the time of flight and horizontal range for that throw. 4. Record your own individual data in a titled table in the data section 5. Measure the ∆y between the initial and final points of the tennis ball’s parabolic trajectory. 6. Record any other observations you feel are relevant in the data section. 7. In the analysis section, use your obtained measured quantities, the relevant kinematic equations and algebra to solve for each of the quantities listed here for each throw. Show the derivation and a sample calculation for each. Launch Speed
Launch Speed
Launch Angle*
Vxi
Vyi
Peak Height
Vxf
Vyf
Impact speed
Impact speed
Angle* of impact
km/h
m/s
Degrees
m/s
m/s
m
m/s
m/s
m/s
km/h
Degrees
8. In the analysis section, compare initial and final speeds and angles discus how reasonable your results are and estimate the precision of your results. 9. In the conclusion, state how fast, how far and how high you can throw a tennis ball with estimated precision/ uncertainty included. 18
Lab 2:
Air Resistance and Terminal Velocity
Background: Freefalling objects such as snowflakes, raindrops, or basket type coffee filters, accelerate under the influence of gravity, but quickly reach and then travel at a constant velocity. This constant velocity is called the terminal velocity of the object and it depends on the surface area, shape and mass of the object as well as the speed of the object with respect to the surrounding medium and the medium itself. (air, water, oil, to name a few). Your textbooks have tables with the terminal velocities of some everyday objects. A freebody diagram summarizes the forces acting on a falling body. By definition, the acceleration during terminal velocity is 0 m/s/s. Therefore, the magnitudes of the drag and gravitational forces are equal and opposite in direction. Generally speaking, the drag force is proportional to the square of the speed. Fdrag = bv2 where b is a proportionality constant specific to the object in freefall. The magnitude of the force of gravity is Fgravity = mg And so we have the following: bv2 = mg
Fdrag
Fgravity
b = mg/v2
and
Purpose: To learn about air resistance and terminal velocity. To determine the proportionality constant for the drag force acting on the lab’s basket type coffee filters. Apparatus:
5 basket type coffee filters Pasco Motion detector, Science workshop 500 interface Computer with Data Studio
Procedure: 1. Determine the masses of your coffee filters. 2. Set up the motion detector and Data studio to display position and velocity time graphs. 3. Place the motion detector on the floor pointing straight to the ceiling. 4. Start the motion sensor. 5. Hold 1 coffee filter approximately 2 m above the motion sensor and then drop the coffee filter. 6. Determine the terminal velocity from the position and velocity time graphs.
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7. Repeat Steps 5 and 6 three times for 1 coffee filter. This gives us a means of determining the error in our method (and in our terminal velocity values) 8. Nestle a 2nd coffee filter inside the first and repeat the terminal velocity measurements. 9. Do four trials for 3, 4, and 5 nested coffee filters. 10. Collect all data in a Table. Include masses, weights, velocities, the squares and the cubes of the terminal velocities. 11. Print off 1 sample position and velocity time graph for 1 of the trials. Analysis: 1. plot a graph of the following. Include (0,0) as a data point for each. a. the weights vs the terminal velocities b. the weights vs the squares of the terminal velocities c. the weights vs the cubes of the terminal velocities Place the weights on the vertical axis in each case. 2. Which graph is most linear? Is this what was expected? Why? 3. Determine the proportionality constant based on the slope of the linear graph. 4. If you placed a 10 gram mass inside 2 coffee filters, what would you expect the terminal velocity to be? Conclusion: Summarize your findings.
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Lab 3:
Dilution of Gravity Lab
Purpose: In this lab we will explore two aspects of acceleration down an inclined plane. 1. Does the acceleration depend on mass? 2. Does the acceleration depend on the angle? Procedure: 1. Determine the expected acceleration for any inclined plane by resolving gravity into its parallel (x) and perpendicular (y) components. Ignore friction. 2. Determine the relationship for the same general case but include friction now. Solve for a in terms of µ, g , and θ. Use a freebody diagram as an aid. 3. Determine the coefficient of friction for your lab cart. This can be done by determining the force of friction that is associated with a negative acceleration caused by friction when the plane is horizontal, and the normal force required to support the lab cart on a horizontal surface. Since the force of friction is equal to µ times the normal force, µ = Ff / FN 4. Test whether or not the acceleration down the inclined plane depends on mass for some angle θ chosen by you. (use 5 different masses) Collect this data in a table and display as a graph. 5. Measure the acceleration of your lab cart down an inclined plane for angles between 0 and 50°. (go up by increments of around 5°) Collect this data in a table. Display the data in a graph. Include the expected accelerations for each angle in both the table and graph based on your determination of µ and the formulas from steps one and two. Data: 1. Show your results for the relationship between mass and acceleration. 2. Show your results for the relationship between angle and acceleration. Analysis: 1. Does the acceleration show a dependence on mass? Do your observed results agree with what was predicted? Can the amount they are off be attributed to experimental error? Explain any discrepancies. 2. Does the acceleration show a dependence on the angle? Do your observed results agree with what was predicted? Can the amount they are off be attributed to experimental error? Explain any discrepancies. Conclusion: Summarize your findings. Comment on each statement or question in the purpose. Include error with any reported quantities.
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Lab 4:
Motion Along an inclined plane
Background: • For motion in the absence of forces we expect constant velocity described by the
r r ∆d vave = ∆t
equation: •
For motion subject to a constant force we expect constant acceleration in the direction of the force. The equations which describe motion with constant acceleration are:
r r r v f − vi a= ∆t
•
r r 1r 2 ∆d = vi ∆t + a (∆t ) 2
r r r v f + vi ∆d = ∆t 2
r r v 2f = vi2 + 2a∆d
Motion up or down a plane is accelerated at gx=g sinθ where θ is the angle of the plane to the horizontal.
Purpose: To examine the motion of an object on an inclined plane. To determine how well the equations of motion describe the observed motion. To determine the angle of the inclined plane. Apparatus: Spark table Metre stick
spark timer set to 50 Hz
carbon paper
Procedure: 1. Place a sheet of paper on the air table with a side aligned with the lower edge of the air table. 2. With Mr. Turton’s assistance, practice giving an air table puck an initial velocity with components both up and along the inclined air table so that the puck follows a parabolic trajectory. 3. With the spark timer activated allow a puck to slide down the plane to determine the fall line. (vertical) 4. Repeat step 2 with the spark timer activated. 5. Using the metre stick measure the horizontal and vertical positions of the marks left by the spark timer. Enter these values in tables as shown. 6. Calculate the horizontal and vertical displacements and velocities between two adjacent marks and enter these values in the tables as well. 7. Show one sample calculation for each displacement and velocity. Sample tables:
Dot Number 1 2
Horizontal Kinematic Data Time Horizontal Horizontal (s) Position Displacement 0 0 NA 0.02
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Horizontal Velocity NA
Dot Number 1 2
Vertical Kinematic Data Time Vertical Vertical (s) Position Displacement 0 0 NA 0.02
Vertical Velocity NA
8. Plot position and velocity time graphs for the horizontal and vertical motion separately. (total 4 graphs) Each graph should be minimum ½ page in size. Analysis Section: 9. Determine the acceleration experienced by the air puck and the angle of the air table from this acceleration. 10. Measure the angle of the air table using a metre stick and trigonometry. 11. Determine the % error between the angles found in steps 8 and 9. 12. Enter the horizontal and vertical positions into excel and plot the trajectory on a scatterplot. 13. Right click on one of the data points and select trendline. 14. Click on the Polynomial graph and set the order to 2. 15. Click the options tab and select “Display equation on graph” and “Display R value on Graph” 16. Does it make sense to set the y intercept to equal zero? Why or why not? 17. Discuss your results in light of the purpose of this lab. 18. Were the graphs what you expected in each case? Explain. 19. Was friction acting on the air puck? Does the data show this? 20. Summarize your results and state % error in a conclusion.
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Lab 5: 1.
Torque and Centre of Gravity Try closing or opening a door by pushing on the doorknob, in the middle of the door and close to the hinges. Why is there a noticeable difference? Why aren’t doorknobs placed in the middle of doors?
2. Grasp a metre stick firmly at one end and place a mass on a mass hanger on the metre stick. How is the torque affected by moving the mass towards the end of the metre stick opposite your hand? Towards your hand? 3. Take 2 known different masses, a metre stick and three mass hangers from the front. Calculate, using the law of the levers, where the masses should be hung from the metre stick so that they will balance (teeter totter style) around a point of rotation on the metre stick chosen by you. Record your choices and calculations. Verify your calculations by hanging the masses at your calculated positions. How well did your predictions test out? Account for any discrepancies between the expected and observed situations. (Hint: are the masses of the mass hangers negligible?) 4. Use a known mass, A metre stick and three mass hangers to weigh an object (textbook, bookbag, calculator, shoe, gold chain). Reweigh the same object on the triple beam balance or force sensor and calculate the ? % error of the metre stick method. 5. Determine where your centre of gravity is located. Recommended method: a. Hold yourself in a pushup position with both hands on a bathroom scale. b. Record the weight shown on the scale. c. Stand on the same bathroom scale and record your full weight. d. Draw a force diagram similar to the following: FN More detail is included here than necessary. This is for explanatory purposes only. Fg e. Solve for the location of your centre of gravity as a Static Equilibrium problem. f. Consider the location of your centre of gravity along your other dimensions.
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Lab 6 :
Collisions in 2D
2 people per group
Purpose: To determine if momentum and energy are conserved in a glancing 2D collision between unequal masses. Additional AP component: To track the center of mass (cm) of the system (the two pucks) as the system suffers an internal collision. Apparatus: Spark table with spark timer and air supply Blank newspaper Ruler Triple beam balance
Carbon paper Air table pucks Protractor
Procedure: 1. Use the spark table to obtain a dot pattern for a collision between two air pucks. 2. On the Newsprint label the initial and final paths for pucks 1 and 2 with labels and arrows to indicate direction. Also sketch and label coordinate axes on your newsprint. 3. Determine the masses of the two air pucks. Include this in your data section. 4. Make a photocopy of the collision for each person on 11x17 paper. Include this in your data section. 5. Determine the x and y components of the velocities for both pucks in both the initial and final states. Collect your results in table(s) for the data section. The spark table produces sparks at a rate of 50 Hz. 6. For the analysis section: Determine the x and y components of the momenta for both pucks in both the initial and final states. 7. Determine the kinetic energy of both pucks before and after the collision. 8. Discuss your results in the analysis section. a. Was momentum conserved? If not could the difference be attributed to error in measurement? b. Was energy conserved? If not could the difference be attributed to error in measurement? c. AP – Did the collision affect the velocity of the cm? Are these results what you would expect? Explain. 9. Summarize your results in a conclusion.
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Lab 7:
Circular Motion: Whirlygig Lab
Background: C = 2π ( radius )
Fc =
Purpose:
mv 2 r
v=
d t
To observe and measure components of circular motion. To quantify and record error in measurement. To apply graphing techniques in analysis of data. To determine how well the equations in the theory section apply to circular motion.
Apparatus: Glass Tube with rubber coating 7 metal washers stop watch metre stick
String rubber stopper triple beam balance
Procedure: 1. Obtain the circular motion apparatus (glass tube with rubber coating), 7 metal washers, string and rubber stopper. 2. Weigh the rubber stopper, record the mass on the next page. 3. Fix 3 washers to the string that comes out of the bottom of the glass tubing. 4. Weigh the washers on the string. Record their mass in table T- 1. 5. Practice spinning the rubber stopper in a horizontal circle keeping the radius constant. 6. Put pen marks on the string in 10cm intervals from 40cm to 80cm measured from the centre of the stopper. 7. Spin the stopper in a horizontal circle keeping the radius constant on one of the marks. 8. Time 20 revolutions and record data in T- 1. 9. Repeat steps 7 and 8 for the other four marks on the string. 10. Place an additional washer with the three original washers. 11. Repeat steps 4 and steps 7 to 9 with the four washers. Record all data in table T1. 12. Repeat procedure with 5 washers, then six and finally seven. 13. Graph the Data in table T-1 in Graph G-1. Plot Fg on the horizontal axis and mv2/r on the vertical axis. 14. Draw the line of best fit on the graph. Calculate the slope of the line of best fit. 15. Answer the questions in the analysis section 16. Write a conclusion.
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Observations: Identifying marks on apparatus: _______________ Mass of rubber stopper: __________ Data table T-1: Distance Time of Stopper Number Mass of Fg Number of travelled speed Radius “n” Washers washers of revolutions in “n” (m) revolutions V washers (kg) (N) (n) revolutions (s) (m/s) (m) 3 0.4 20 3 0.5 20 3 0.6 20 3 0.7 20 3 0.8 20 4 0.4 20 4 0.5 20 4 0.6 20 4 0.7 20 4 0.8 20 5 0.4 20 5 0.5 20 5 0.6 20 5 0.7 20 5 0.8 20 6 0.4 20 6 0.5 20 6 0.6 20 6 0.7 20 6 0.8 20 7 0.4 20 7 0.5 20 7 0.6 20 7 0.7 20 7 0.8 20
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mv 2 r (N)
Observations (continued): Graph G-1: Do a quick plot here before you leave to ensure your slope is ≈ 1
Analysis: 1. What does the graph tell you? What does the slope of the line tell you? 2. Which component ( mass, radius, time) has the greatest error associated with its measurement? 3. Use your judgement to determine the amount of error associated with each measurement. (Example: The error in mass would be ± 0.01g ) 4. How does the error appear on the graph? 5. Discuss any surprises and/or any expectations that were met by this lab activity. Conclusion:
(Comment on each of the statements in the purpose section.)
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Lab 8:
Circular Motion: The Conical Pendulum
Background: Uniform circular motion is common in nature and in mechanical devices. The net force directed towards the center of the circle is called centripetal force. A special case of circular motion is the conical pendulum where the pendulum=s Abob@ is swung in a horizontal circle of radius R while attached to a string of length L. The time required for the bob to make one complete revolution is called the period T. Newton used a conical pendulum to measure the acceleration of gravity g from an expression he developed for g in terms of T, L, and the angle θ between the string and the vertical. His results were accurate to within 4 percent. Purpose: Determine the acceleration of gravity g from the circular motion of a conical pendulum, and determine the centripetal force, acceleration, and tension in the supporting string. Apparatus: rubber stopper on a string, pendulum clamp, stopwatch, meter stick Procedure: 1. Derive an equation for g in terms of the angle θ, R, and v, and anequation for g in terms of the period T, the angle θ, and L. Measure the mass of the billiard ball. 2. Examine the free body diagram of the conical pendulum from the class notes. Note that angle θ can be defined as the sine of R/L or the tangent of R/LCos θ. 3. Arrange to take accurate measurements of R, T (period, not tension), and L while the billiard ball is in its path as a conical pendulum at a constant angle of ≈ 15o. Collect data for 6 different trials of different string lengths at the same angle θ. Analysis: 1. Determine the centripetal acceleration ac, the tension in the string and the centripetal force Fc for your conical pendulum for each trial. Calculate the acceleration of gravity for Brockport using the formula in the room. 2. Plot a graph of L as a function of T2 and perform a regression (find the slope!). What does the slope of the line represent? Determine g using the slope of the line and compare with your calculated value. 4. Compare your results to Isaac Newton. 5. Suggest a relationship between the angle θ and centripetal acceleration. 6. What are some sources of error in this lab? 7. How would the lab results be different if performed on the moon?
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Lab : 9
Vertical Circles and The Turning Point L
M
O
S
D
Path of the pendulum
P R
Figure 1—The Turning Point Schematic Diagram
Background: The Turning Point is based on a problem commonly encountered in homework sets in the Physics B and Physics C courses. The situation is pictured in Figure 1 above. A pendulum is held out so that the pendulum’s string is parallel to the ground. The pendulum bob is released, and it describes a circular arc of length L as it descends. When the bob passes through its lowest point, the pendulum string encounters a peg P located a distance D below the pivot point 0 of the pendulum. The bob continues its motion, but in an arc of reduced radius R. The bob performs a circular arc, passing above the peg P at a point S. The problem, as usually formulated, is to find the minimum distance D for which the string will remain taut as the bob passes through S. The condition on the string as the bob passes through S may be represented, by applying Newton’s Second Law, as Equation 1. Ma = T+Mg (1) Here M is the mass of the bob, T the tension in the string, a the acceleration of the bob, and g the acceleration due to gravity. Since the bob is undergoing circular motion as it passes through 5, we have Equation 2. (2) A = V2/R Here V is the velocity at point S, and R is the radius through which the bob is moving. At the minimum distance D, the tension T goes to zero, so we may substitute Equation 2 into Equation 1 to obtain MV2/R = Mg This simplifies to the Equation 3. V2=Rg (3) Thus we could find R, and thus D, if we know V. Upon examining the diagram we see that we may apply the conservation of energy to determine V. If we take the zero of gravitational potential energy as the lowest point of the bob’s path, we may write Equation 4. MgL = Mg(2R) + MV2/2 (4) Substituting Equation 3 into Equation 5 yields 30
MgL = 2RMg + MRg/2 This simplifies to R=2L/5 Examination of the diagram shows that the distance D is the difference between L and R, so we have Equation 6. D=3L/5 (6). Apparatus: The equipment for the lab consists of a ring stand or long rod, about a meter in length, two right-angle clamps, two short rods, string, and a mass, such as a rubber stopper or lead weight. If you use a long rod as the vertical support for the apparatus, you should fasten it to the table with a table clamp. Procedure: The lab set-up is straightforward. Fix the vertical rod to the table with a clamp, or set the ring stand up on the table. Attach one short rod to the vertical rod at the top of the vertical rod by a right-angle clamp. Attach the other short rod to the vertical rod about halfway up the vertical rod. This second rod is the pivot rod that the string attached to the bob strikes as the bob moves through its arc. The apparatus is shown in Figure 2 below. Care must be taken in attaching the string to the support rod. The string should not stretch much, and should be easily tied. Monofilament fishing line works well. It is best to drill a hole close to the end of the rod, through which the string may be passed, rather than attempting to tie the string around the support rod. This prevents the movement of the point of attachment of the string to the upper rod while the bob is in motion. It also makes it easier to change the length of the string, so that data may be taken at different L values, where L is the length of the circular arc through which the bob swings before the string strikes the lower rod. Drilled support rod at O to hold pendulum
Pivot rod at P
Table clamp
Figure 2—The Turning Point Physical Diagram
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There are several ways to do the experiment. One way is as follows. The students calculate the position at which the lower rod must be placed so that the bob rotates about the lower rod, while keeping the supporting string taut. They place the lower rod at the distance, release the bob from a horizontal position as indicated in Figure 1, and see if the bob describes the desired path. If the bob does not, the students adjust the position of the lower rod to obtain the desired path. Even if the bob does follow the desired path, the students should convince themselves, by moving the lower rod, that they have found the minimum distance D for which that path occurs. A more systematic approach is to start with the lower rod a distance of 0.75 L below the upper rod, then decrease D in small increments until the bob revolves around the lower rod with the string taut. The amount by which D is decreased should be a few millimeters for each trial. One question that the students should answer before they start their measurements and trials is how to measure the distance D. Should they measure to the middle of the lower rod, to its bottom, or to its top? Which measured distance more accurately represents the distance used in the derivation? If there is enough time, students should repeat the experiment for a range of values of L, preferably from 0.4 meters to 0.9 meters. Once this is done, the students have a table of L and D values. If D is plotted versus L, the data should fall on a straight line with a slope of 0.6. This procedure eliminates some systematic errors that may be present in students’ procedure. For instance, if L or D is measured in such a way that the measurements are always too short or too long, compared to their actual values, the graph will eliminate those systematic errors as it depends on the rate of change of D with L. Students should compare the value of the slope of the D vs. L plot with the values they obtain for the ratio of L and D for each trial. If the slope is close to the expected 0.6 value, while the ratios are not, this indicates that the students have a systematic error in their data. The students should address this discrepancy in their write-up of the experiment.
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Lab 10: Weighing Oneself in a microgravity Environment. Background: Mass measurements aboard Skylab were part of the medical experiments conducted there. Prior to the Skylab mission it was observed that both US and Russian astronauts returning from space had lost weight, and NASA worried whether this implied some physical deterioration which could grow worse on longer flights. To better observe the process, Skylab carried three massmeasuring devices--two small ones (experiment M074) for measuring the intake and outgo of each astronaut, and a large one (experiment M172) with an oscillating chair, designed for daily monitoring of the weight of the astronauts. The motion of the oscillating mass was tracked electronically, typically over three backand-forth oscillations, and from this the instrument derived the oscillation period T. Theory predicted that T would be proportional to the square root of the oscillating mass; this was confirmed by calibrations in space, using previously weighed objects, and those calibrations suggested that when carefully performed, such mass measurements were accurate within 0.1%. Measuring body mass in the M172 chair (see illustration) was not a simple matter. The human body is not rigid, and any internal motion--even breathing--could affect the oscillation of the chair. After emptying their pockets, astronauts would climb into the chair, always wearing a suit which had been weighed before the flight. They would then be strapped in rigidly, brace their feet against a bar at the front of the chair, grab hold of another such bar with their hands, hold their breath and then release the seat by pushing a trigger on the hand bar. Astronauts of Skylab-2 lost 3-6 pounds during their one-month stay, and measurements of intake suggested they were not eating enough. On Skylab-3 food rations were therefore increased, and additional excercises were also ordered, to make sure that "body muscle was not exchanged for fat." Weight loss was comparable, even though the stay in space was twice as long, and it was noted that most of the loss occurred in the first five days. The Skylab-4 crew was given still more food and more excercises. All three astronauts of that group lost mass during the first 10 days, but for the remaining 74 days they held their own or even gained mass back. Source: http://www-spof.gsfc.nasa.gov/stargaze/Sskylab.htm
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Background cont’d:
T = 2π
m k
Purpose: To weigh a person by timing their oscillation on a spring of known constant. Apparatus: Stopwatch Garage door spring with seat Bathroom scale Procedure: 1. Weigh yourselves on a bathroom scale. Record your individual masses and calculate your individual weights. 2. Practice bouncing vertically without feet touching the floor and with no horizontal displacement. 3. Turn on the computer and set up the motion detector for measuring position vs time and velocity vs time graphs. 4. Place the motion detector directly below the seat and record the SHM of one group member for ten seconds. 5. Select a region of data and apply a sine curve fit to the region from the toolbar. 6. From the stated frequency determine the period. 7. Use the formula from class to determine the spring constant of the spring. 8. Repeat steps 4 through 6 for each of the other group members 9. Using the spring constant found in step 7, and each person’s measured period, determine the masses of the other group members. 10. Determine the percent error of this method by comparing the masses from step 9 to the masses from step 1. 11. Where in the motion does maximum velocity occur? 12. Where in the motion does maximum acceleration occur? 13. Write a conclusion summarizing your results.
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Lab 11:
Electrostatic Equilibrium Lab
Background: Objects with like charges repel each other with an Electrostatic Force “FQ”. This can be found by comparison to other forces, or through the formula FQ =
kqq r2
Purpose: to determine the number and percent of electrons lost on an object based on Coulombs law. Apparatus: 2 Balloons
Metre stick
String
wooden support
Procedure: 1. Blow up the balloons to the largest spherical shape possible. 2. Tie a balloon to either end of a 1-1.5 metre long string. 3. Drape the string over the wooden support so the balloons are level with each other and not touching anything except each other. See drawing below. 4. Rub both balloons against another object to transfer some electrons. 5. Release the balloons and allow them to come to electrostatic equilibrium. 6. Measure the dimensions indicated in the drawing below. 7. Determine the electrostatic repulsive force through FBD and the skills gained in our study of static equilibrium. (opposite forces are equal) 8. Assume the charges on the balloons are the same. Determine the charge on each balloon using Coulombs Law. Is this assumption necessarily true? 9. Determine the number of electrons required to make a charge of this magnitude. 10. Given that the mass of the balloon is 1.0 gram, determine how many electrons are in the neutral balloon. Assume that the number of protons is equal to the number of neutrons and also equal to the number of electrons. As a formula: mass balloon = n(proton mass) + n(neutron mass) + n(electron mass) 11. Use the results from steps 9 and 10 to determine the mass, and percent of electrons lost or gained on a balloon. 12. Format your work in a standard Lab report format with this as the first page, further data / observations are then on the second page followed by calculations in an analysis section and summarized in a conclusion on the 2nd and third pages if necessary. Data / Observations:
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Lab 12:
Ohm’s Law
Background: Ohm’s Law relates the voltage, current and resistance of all DC circuits and applies to individual components, groups of components and to the entire circuit. Expressed as a formula, Ohm’s Law is V= IR where V is voltage, I is current, and R is resistance. Measuring Voltage drop across a component Assemble the circuit this way (Note: the DMM is parallel to the circuit)
Measuring the current in a circuit Assemble the circuit this way (Note: the DMM is in series with the circuit)
Procedure: 1. Fill in the calculated current column in the table using Ohm’s Law and the measured voltages and resistances. 2. Place the 100 Ω resistor in the circuit board and measure the voltage and current in the circuit. Fill in the measured values in the table. 3. Repeat step two for 5 more resistors. Resistance ( Ω ) Bands read
Measured
Voltage ( V ) Determined
100
9
220
9
1000
9
2200
9
3300
9
6800
9
Measured
Current ( A ) Calculated
Measured
Analysis: Discus your results in terms of how well the measured and calculated quantities agree. Conclusion: State the % difference of your calculated and measured currents 36
Lab 13:
Ohm’s Law, voltage, current and resistance relations in Series circuits
Assemble the circuit this way. You may need a different Voltage setting on your DMM. (Here the DMM is measuring the voltage drop across the 100Ω resistor.)
Wire connector
Wire connector
“A”
“B”
Only connect your 9V battery when you are taking measurements to preserve your battery. Measure the voltage drops across each resistor and record the information here: Add the voltage drops together they total: __ V Resistance Voltage drop Compare the total voltage drop to the voltage (Volts) produced by the battery. Are they the same or Stated Measured different ? If different by how much? 100Ω 470Ω 2200Ω Determine the amount of current flowing in the circuit using Ohm’s law. Use the total resistance of the circuit and the battery’s voltage. Show your calculation here: Remove wire connector “A” and measure the current* flowing in the circuit. I= ____mA Remove wire connector “B” and measure the current* flowing in the circuit. I= ____mA Calculate the voltage drops across each resistor using Ohm’s law. How do the calculated voltage drops from this table compare to the measured voltage drops from the previous Stated Measured table?_______________ 100Ω ________________________ 470Ω ________________________ 2200Ω ________________________ Analysis: Discus your results in terms of how well the measured and calculated quantities agree. Conclusion: State the % difference of your calculated and measured quantities Resistance
Current (A)
Calculated Voltage drop (Volts)
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Lab 14:
Ohm’s Law in Parallel Circuits
Set up your circuit like this with two 1000 Ω resistors:
Wire connector “A”
Wire connector “B”
Determine the total resistance from combining the two resistors in parallel.
Total R = ______Ω Considering the power supply is a 9V battery, use ohms law to calculate the current you would expect to flow in the circuit.
Wire connector “C”
Expected current = ________ amps or _______ milli amps Remove wire connector “A” and measure the current flowing in the circuit. Measured current =________ amps or _______ milli amps How does this compare with what you expected? Replace wire connector A. Remove wire connector B and measure the current flowing through that side of the circuit/ Measured current =________ amps or _______ milli amps Replace wire connector B Remove wire connector C and measure the current flowing through that side of the circuit/ Measured current =________ amps or _______ milli amps How does the total current flowing compare to the sum of the currents in each side? Measure the voltage drop across each resistor . A C _____ V, BD _____V Measure the voltage between points A and B ______ V also between C and D _____V What does this tell you? Analysis: Discus your results in terms of how well the measured and calculated quantities agree. Conclusion: State the % difference of your calculated and measured quantities 38
Lab 15:
Watt’s Law and the Energy stored in a Battery
Background: Batteries are useful devices that store energy in a chemical potential form and release it as electrical energy. Watts Law states that the power at any instant is equal to the product of the current and the voltage in a circuit, or P=IV. Recall that power is the rate of change of energy and can also be expressed through the formula ∆E P= in other words, the change in energy over the change in time. The total energy ∆t in a battery can then be expressed as the power provided by the battery multiplied by the time the power was provided for. ∆E = P∆t Materials:
1 AA Battery Voltmeter Ammeter Resistor (1-5 Ω , 5 watt)
Procedure: 1. At the Start of 1st period, set the resistance of the variable resistor to as low as possible then connect the following circuit. Ammeter
Voltmeter
2. Start recording the Voltage and current using the probeware and Data Studio. 3. Record any initial observations of voltage and current. 4. Set the circuit and probeware aside and do not disturb it until the battery has fully discharged (1-5 hours) 5. During the last period of the day stop recording the V and I of the circuit. Analysis: 6. Using the calculate feature in data studio create a power vs time graph. 7. Use the integrate feature in data studio to determine the Energy stored in your battery. 8. Compare your results to those from other groups. 9. Why are the voltage and current graphs similar? 10. Is the voltage constant over time? Why? 11. Is the current constant over time? Why? Conclusion: State the amount of energy stored by your battery with estimated uncertainty. 39
Lab 16:
Electromagnetism
Background: Some materials are permanently or temporarily magnetic such as rare earth magnets or a nail that has been magnetized while other materials such as copper display little or no magnetic properties. Electric currents exhibit magnetic properties and do not exist without them. In a straight conductor the magnetic effects are small. These can be intensified by shaping the straight conductor into a coil (also called a solenoid). When a permanent magnet moves next to a conductor, a current is induced in the conductor. In straight conductors the currents are small. Again, these can be intensified by shaping the straight conductor into a solenoid. (1) V = IR
(2) B =
µ0 I 2πr
(3) Φ m = BA cos θ
(4) ε avg =
∆Φ m ∆t
Purpose : To measure and observe magnetic fields and the current produced by moving a magnet next to conductors. Apparatus: Permanent magnet Coil of magnet wire. Computer with data studio Magnetic, current and voltage sensors Procedure: 1. With the magnetic field sensor determine the shape of the magnetic field around the magnet and how the strength of the magnetic field varies with distance away from the magnet. 2. Produce two graphs to describe the magnetic field intensity along a longitudinal and cross sectional axis. Longitudinal
Cross sectional 3. Place the magnetic field sensor in the zero gauss chamber to tare the sensor. 4. Measure and record earth’s magnetic field in the lab. Which direction does the sensor have to be oriented to achieve a maximum reading? What does this imply about the direction of earth’s magnetic field at this location? 5. Measure and record the magnetic field around a solenoid with no current. 6. Connect your solenoid to a 1-3 volt power supply and remeasure the magnetic field around the solenoid producing two graphs as in step 2. Compare your results to those expected from equation (2). 40
7. Disconnect the solenoid from the power supply and connect it to an ammeter and voltmeter. 8. Record the current and voltage in the solenoid in the absence of a permanent magnet. 9. Place a permanent magnet close or into the solenoid and record the corresponding current. Is the current induced by the presence of the magnet or the movement of the magnet near the solenoid? 10. How well do the equations from the background agree with your observations? Consider Ohm’s Law as it applies to the solenoid, and the voltage ( or emf) produced by the rate of change of magnetic flux. Justify your answer with two graphs of voltage vs time. The first graph should record a slow movement of a magnet across the front of a solenoid, the second, a fast movement of the same type. 11. Discuss your results in the analysis. 12. Address the purpose in a conclusion.
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Lab 17:
Measuring Planck’s Constant
Background: Some numbers appear so often in calculations that we give them names. Planck’s constant named after Max Planck appears in many (nearly all) quantum mechanical calculations and has the value of 6.63 x 10-34 J ⋅ s . c = fλ
U E = qV
E = hf
In a light emitting diode (LED) visible photons are produced when an electron (with charge q) looses energy (UE) as it passes through a voltage drop (V). The energy possessed by an individual photon is equal to the product of the photon’s frequency and Planck’s constant. LED’s give off very little heat so virtually all of the energy lost by the electron is given to the photon. In other words E = UE or more helpfully hf = qV. If the voltage readings are plotted against the frequencies the slope of the line will equal h/q (planck’s constant divided by the electron’s charge.) Purpose: To determine Planck’s constant to the correct order of magnitude (exponent). Apparatus: Various colours of LED’s 10 MΩ variable resistor cardboard tube Breadboard 9V battery or power supply 470 Ω current limiting resistor Voltmeter Procedure: 1. Set up the circuit shown above. 2. Check that the red LED goes completely out when the variable resistor is adjusted. View the LED directly from the top with the cardboard tube blocking out any stray light from the room. Adjust the LED to be as faint as possible. 3. Record the voltage drop across the LED with the sensor or digital multimeter. 4. Repeat steps 3 and 4 with each of the other LED colours available. 5. Determine the wavelength of each LED colour and record all data in a table. 6. Determine the frequency of each LED. 7. Plot Voltages from step 4 against their respective frequencies. (Voltage on vertical axis). 8. Draw the line of best fit and determine the slope of the line. 9. From the slope determine Planck’s constant. 10. Discuss your results including any possible sources of error in the analysis. 11. State your measured value of Planck’s constant and address the purpose in a conclusion. 42
