pfs 9 summer 2006 table of contents
TRANSCRIPT
PFS 9 Summer 2006
Table of Contents
Schedule for summer 2006....................................................................................................................2
Proposed Guiding Structure for PFS 9 ..................................................................................................4
Day One Introduction to PFS 9 ............................................................................................................10
Day One Afternoon ..............................................................................................................................14
Dimensional Analysis Introduction ...................................................................................................14
Gravitational Potential Energy and its Conversion to Other Forms of Energy .................................16
Coefficient of Restitution Activity ......................................................................................................20
Radioactive Decay and Half Life Activity ..........................................................................................22
Day Two Morning.................................................................................................................................24
Gravitational Potential Energy, Friction and Temperature ...............................................................24
Thermodynamic Paradox .................................................................................................................26
Effervescence!..................................................................................................................................28
Day Two Afternoon ..............................................................................................................................30
Introduction to Forces.......................................................................................................................30
Newton’s 3rd Law and Friction Inquiry ..............................................................................................31
Observing Forces .........................................................................................................................32
Interacting/Opposing Forces.........................................................................................................34
Friction and Weight .......................................................................................................................36
Day Three Morning ..............................................................................................................................40
Nuclear Reactions in Stars and Heavy Element Production ............................................................40
Gravitational Forces and Kepler’s Laws...........................................................................................48
PFS 9: Physical/Earth Science
Schedule for summer 2006
Time Monday Tuesday Wednesday Thursday 8:00am Review of Monday/
Questions Review of Tuesday/Questions
Review of Wednesday/Questions
8:30am
Pre-test
9:00am Community building activity 9:30am Group expectations 10:00am
Nature of Forces (see specific indicators below)
10:30am Ohio Academic Content Standards for grade 9 science
11:00am 11:30am
Introduction to the learning cycle, 5E’s, and scientific inquiry
Nature of Energy (see specific indicators below)
Forces and energy that shape the earth (see specific indicators below)
Forces and energy that shape the earth (see specific indicators below)
12:00pm Lunch on your own Lunch on your own Lunch on your own Lunch on your own 1:00pm 1:30pm
Forces and energy that shape the earth (see specific indicators below)
2:00pm 2:30pm
Wrap up and reflection of the four days
3:00pm
Nature of Energy (see specific indicators below)
Nature of Forces (see specific indicators below)
Forces and energy that shape the earth (see specific indicators below)
3:30pm Reflection of the day Reflection of the day Reflection of the day Looking forward to the school year
4:00pm Dismiss Dismiss Dismiss Dismiss
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PFS 9: Physical/Earth Science Indicators to include in summer 2006
Forces and Energy – Summer 2006 Theme Original location Indicator
The Universe 3. Explain that gravitational forces govern the characteristics and movement patterns of the planets, comets and asteroids in the solar system.
Nature of Matter 6. Explain that the electric force between the nucleus and the electrons hold an atom together. Relate that on a larger scale, electric forces hold solid and liquid materials together (e.g., salt crystals and water).
Forces
Nature of Forces 24. Demonstrate that whenever one object exerts a force on another, an equal amount of force is exerted back on the first object.
25. Demonstrate the ways in which frictional forces constrain the motion of objects (e.g., a car traveling around a curve, a block on an inclined plane, a person running, an airplane in flight).
The Universe 1. Describe that stars produce energy from nuclear reactions and that processes in stars have led to the formation of all elements beyond hydrogen and helium.
Processes That Shape Earth
5. Explain how the slow movement of material within Earth results from: a. thermal energy transfer (conduction and convection) from the deep interior; b. the action of gravitational forces on regions of different density.
Earth Systems 4. Explain the relationships of the oceans to the lithosphere and atmosphere (e.g., transfer of energy, ocean currents and landforms).
Energy
Nature of Energy 11. Explain how thermal energy exists in the random motion and vibrations of atoms and molecules. Recognize that the higher the temperature, the greater the average atomic or molecular motion, and during changes of state the temperature remains constant.
12. Explain how an object's kinetic energy depends on its mass and its speed (KE=½mv 2). 13. Demonstrate that near Earth's surface an object's gravitational potential energy depends upon its
weight (mg where m is the object's mass and g is the acceleration due to gravity) and height (h) above a reference surface (PE=mgh).
14. Summarize how nuclear reactions convert a small amount of matter into a large amount of energy. (Fission involves the splitting of a large nucleus into smaller nuclei; fusion is the joining of two small nuclei into a larger nucleus at extremely high energies.)
15. Trace the transformations of energy within a system (e.g., chemical to electrical to mechanical) and recognize that energy is conserved. Show that these transformations involve the release of some thermal energy.
17. Demonstrate that thermal energy can be transferred by conduction, convection or radiation (e.g., through materials by the collision of particles, moving air masses or across empty space by forms of electromagnetic radiation).
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Proposed Guiding Structure for PFS 9 Summer 2006-May 2008
Forces and Energy – Summer 2006 Theme Original location Indicator
The Universe 3. Explain that gravitational forces govern the characteristics and movement patterns of the planets, comets and asteroids in the solar system.
Nature of Matter 6. Explain that the electric force between the nucleus and the electrons hold an atom together. Relate that on a larger scale, electric forces hold solid and liquid materials together (e.g., salt crystals and water).
Forces
Nature of Forces 24. Demonstrate that whenever one object exerts a force on another, an equal amount of force is exerted back on the first object.
25. Demonstrate the ways in which frictional forces constrain the motion of objects (e.g., a car traveling around a curve, a block on an inclined plane, a person running, an airplane in flight).
The Universe 1. Describe that stars produce energy from nuclear reactions and that processes in stars have led to the formation of all elements beyond hydrogen and helium.
Processes That Shape Earth
5. Explain how the slow movement of material within Earth results from: a. thermal energy transfer (conduction and convection) from the deep interior; b. the action of gravitational forces on regions of different density.
Earth Systems 4. Explain the relationships of the oceans to the lithosphere and atmosphere (e.g., transfer of energy, ocean currents and landforms).
Energy
Nature of Energy 11. Explain how thermal energy exists in the random motion and vibrations of atoms and molecules. Recognize that the higher the temperature, the greater the average atomic or molecular motion, and during changes of state the temperature remains constant.
12. Explain how an object's kinetic energy depends on its mass and its speed (KE=½mv 2). 13. Demonstrate that near Earth's surface an object's gravitational potential energy depends upon its
weight (mg where m is the object's mass and g is the acceleration due to gravity) and height (h) above a reference surface (PE=mgh).
14. Summarize how nuclear reactions convert a small amount of matter into a large amount of energy. (Fission involves the splitting of a large nucleus into smaller nuclei; fusion is the joining of two small nuclei into a larger nucleus at extremely high energies.)
15. Trace the transformations of energy within a system (e.g., chemical to electrical to mechanical) and recognize that energy is conserved. Show that these transformations involve the release of some thermal energy.
17. Demonstrate that thermal energy can be transferred by conduction, convection or radiation (e.g., through materials by the collision of particles, moving air masses or across empty space by forms of electromagnetic radiation).
Matter – 2006-2007 School Year Matter Nature of Matter 1. Recognize that all atoms of the same element contain the same number of protons, and
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elements with the same number of protons may or may not have the same mass. Those with different masses (different numbers of neutrons) are called isotopes.
2. Illustrate that atoms with the same number of positively charged protons and negatively charged electrons are electrically neutral.
4. Show that when elements are listed in order according to the number of protons (called the atomic number), the repeating patterns of physical and chemical properties identify families of elements. Recognize that the periodic table was formed as a result of the repeating pattern of electron configurations.
5. Describe how ions are formed when an atom or a group of atoms acquire an unbalanced charge by gaining or losing one or more electrons.
7. Show how atoms may be bonded together by losing, gaining or sharing electrons and that in a chemical reaction, the number, type of atoms and total mass must be the same before and after the reaction (e.g., writing correct chemical formulas and writing balanced chemical equations).
8. Demonstrate that the pH scale (0-14) is used to measure acidity and classify substances or solutions as acidic, basic, or neutral.
9. Investigate the properties of pure substances and mixtures (e.g., density, conductivity, hardness, properties of alloys, superconductors and semiconductors).
10. Compare the conductivity of different materials and explain the role of electrons in the ability to conduct electricity.
Nature of Energy 16. Illustrate that chemical reactions are either endothermic or exothermic (e.g., cold packs, hot packs and the burning of fossil fuels).
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Waves and Motion – Summer 2007 Theme Original location Indicator
Nature of Matter 3. Describe radioactive substances as unstable nuclei that undergo random spontaneous nuclear decay emitting particles and/or high energy wavelike radiation.
Waves
Nature of Energy 18. Demonstrate that electromagnetic radiation is a form of energy. Recognize that light acts as a wave. Show that visible light is a part of the electromagnetic spectrum (e.g., radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays).
19. Show how the properties of a wave depend on the properties of the medium through which it travels. Recognize that electromagnetic waves can be propagated without a medium.
20. Describe how waves can superimpose on one another when propagated in the same medium. Analyze conditions in which waves can bend around corners, reflect off surfaces, are absorbed by materials they enter, and change direction and speed when entering a different material.
Processes that Shape the Earth
6. Explain the results of plate tectonic activity (e.g., magma generation, igneous intrusion, metamorphism, volcanic action, earthquakes, faulting and folding).
Motion
Forces and Motion 21. Demonstrate that motion is a measurable quantity that depends on the observer's frame of reference and describe the object's motion in terms of position, velocity, acceleration and time.
22. Demonstrate that any object does not accelerate (remains at rest or maintains a constant speed and direction of motion) unless an unbalanced (net) force acts on it.
23. Explain the change in motion (acceleration) of an object. Demonstrate that the acceleration is proportional to the net force acting on the object and inversely proportional to the mass of the object. (F net =ma. Note that weight is the gravitational force on a mass.)
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Scientific Evidence – 2007-2008 School Year Theme Original location Indicator
The Universe 2. Describe the current scientific evidence that supports the theory of the explosive expansion of the universe, the Big Bang, over 10 billion years ago.
Processes that Shape the Earth
7. Explain sea-floor spreading and continental drift using scientific evidence (e.g., fossil distributions, magnetic reversals and radiometric dating).
Historical Perspectives and Scientific Revolutions/ Earth Science
8. Use historical examples to explain how new ideas are limited by the context in which they are conceived; are often initially rejected by the scientific establishment; sometimes spring from unexpected findings; and usually grow slowly through contributions from many different investigators (e.g., heliocentric theory and plate tectonics theory).
Historical Perspectives and Scientific Revolutions/Nature of Energy
26. Use historical examples to explain how new ideas are limited by the context in which they are conceived; are often initially rejected by the scientific establishment; sometimes spring from unexpected findings; and usually grow slowly through contributions from many different investigators (e.g., atomic theory, quantum theory and Newtonian mechanics).
27. Describe advances and issues in physical science that have important, long-lasting effects on science and society (e.g., atomic theory, quantum theory, Newtonian mechanics, nuclear energy, nanotechnology, plastics, ceramics and communication technology).
Scientific Evidence
Nature of Science 3. Demonstrate that reliable scientific evidence improves the ability of scientists to offer accurate predictions.
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Standards will be woven throughout Science and Technology Understanding Technology 1. Describe means of comparing the benefits with the risks of technology and how science can inform public policy. Abilities to Do Technological Design 2. Identify a problem or need, propose designs and choose among alternative solutions for the problem. 3. Explain why a design should be continually assessed and the ideas of the design should be tested, adapted and refined. Scientific Inquiry - Doing Scientific Inquiry 1. Distinguish between observations and inferences given a scientific situation. 2. Research and apply appropriate safety precautions when designing and conducting scientific investigations (e.g., OSHA, Material
Safety Data Sheets [MSDS], eyewash, goggles and ventilation). 3. Construct, interpret and apply physical and conceptual models that represent or explain systems, objects, events or concepts. 4. Decide what degree of precision based on the data is adequate and round off the results of calculator operations to the proper
number of significant figures to reasonably reflect those of the inputs. 5. Develop oral and written presentations using clear language, accurate data, appropriate graphs, tables, maps and available
technology. 6. Draw logical conclusions based on scientific knowledge and evidence from investigations. Scientific Ways of Knowing Nature of Science 1. Comprehend that many scientific investigations require the contributions of women and men from different disciplines in and out
of science. These people study different topics, use different techniques and have different standards of evidence but share a common purpose - to better understand a portion of our universe.
2. Illustrate that the methods and procedures used to obtain evidence must be clearly reported to enhance opportunities for further investigations.
Ethical Practices 4. Explain how support of ethical practices in science (e.g., individual observations and confirmations, accurate reporting, peer
review and publication) are required to reduce bias. Scientific Theories 5. Justify that scientific theories are explanations of large bodies of information and/or observations that withstand repeated testing. 6. Explain that inquiry fuels observation and experimentation that produce data that are the foundation of scientific disciplines.
Theories are explanations of these data. 7. Recognize that scientific knowledge and explanations have changed over time, almost always building on earlier knowledge. Science and Society 8. Illustrate that much can be learned about the internal workings of science and the nature of science from the study of scientists,
their daily work and their efforts to advance scientific knowledge in their area of study. 9. Investigate how the knowledge, skills and interests learned in science classes apply to the careers students plan to pursue.
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Day One Morning
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Day One Afternoon
Dimensional Analysis Introduction Dimensional analysis is a powerful technique for analyzing the behavior of physical systems. It is really very simple, just look at the units! You know that you cannot compare apples to oranges – that is the basic idea behind dimensional analysis. Consider the following scenarios. 1. You have a car that gets 15 miles per gallon, and you have to drive 300 miles. Gas costs $2.50 per gallon. How much does the trip cost you?
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2. You have a car that gets X miles per gallon, and you have to drive Y miles. Gas costs Z dollars per gallon. How many dollars, D, does the trip cost you? Explicitly write down how you figure out the answer, showing the units on X, Y, Z, and D.
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Gravitational Potential Energy and its Conversion to Other Forms of Energy
The unit of energy is the Joule, which in simplest terms has the dimensions of .
1. Suppose you have an object of mass M (in kg) and hold it at a height H (in m) above the ground. You know that if you let it go, the object will fall. You can view this from the concept that there is a force of gravity on the object, or that the gravitational potential energy is lower on the ground than at the height H. In other words, from an energy standpoint, the object falls in order to get to the lowest possible gravitational potential energy location. This type of situation will obviously involve the acceleration due to gravity, g, which has the units of (m/s2). Determine, using dimensional analysis, how the gravitational potential energy depends on M, H and g.
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2. Energy of motion, or kinetic energy, will obviously depend on the velocity, V, of the object (in m/s) and its mass (kg), but not on gravity or height. Determine, using dimensional analysis, how the kinetic energy depends on M and V.
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3. Consider the following graph:
Determine the mass of the object from this graph. Calculate the area under the curve in the appropriate units. What does the area under the curve represent physically?
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4. An object held stationary at height H above the ground is dropped. Use dimensional analysis to determine how the time it takes to hit the ground, t, in seconds, depends on H and g. It turns out that if the object bounces, it will rebound to a fraction of the original height. It will do this repeatedly, so that the total time from release until the ball stops bouncing is still described by what you determine by dimensional analysis! The kinetic energy that is “lost” in each successive bounce is not lost, but is converted to other forms of energy such as thermal energy (the ball and floor get warm) and sound (you hear it bounce).
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Coefficient of Restitution Activity Introduction The coefficient of restitution (COR, represented by the letter “e”) is a measure of how elastic a collision is, or in other words how much kinetic energy is retained by the objects involved during a collision. A value of e = 1 would represent a perfectly elastic collision, and a value of e = 0 indicates a totally inelastic interaction. The definition of the COR is the ratio of the final velocity after a collision (Vf) to that before the collision (Vi)
e = Vf/Vi. (1) The COR is very relevant to sports involving balls of various types. As long as a ball bounces from a massive and rigid surface, it is appropriate to discuss the COR of the ball, although there are actually two objects involved in a bounce (which is a collision). The COR is not really a constant but does depend slightly on velocity, and thus on the original release height in the case here of a ball held at rest and dropped without spin. However, these variations of the COR are minor, and we will assume that they are negligible in the experiment discussed below. Activity The activity is quite simple. Drop a ball vertically from rest at a known height (H0) as measured with a meter stick and use a stopwatch to measure the total time (ttotal) from release until the ball stops bouncing. The major uncertainties in the experiment come from the release of the ball (which may induce un-wanted spinning) and the quality of the horizontal surface on which the ball bounces. The surface needs to be horizontal, massive, hard and smooth. Otherwise the ball will not bounce vertically but will “wander off”, or too much energy will be transferred to the surface resulting in an artificially low value of the COR. Record sets of ttotal vs. H0 data with various balls and graph the data as discussed below. Analyzing the data Assuming no air resistance and only vertical motion, we can use conservation of mechanical energy (kinetic energy just before the ball hits the floor equals the original gravitational potential energy)
MV2/2 = MgH0 (2)
to see that the definition of the COR in terms of the ratio of the final velocity after a collision (Vf) to that before the collision (Vi) reduces to the square root of the ratio of the two relevant heights in our case,
e = Vf/Vi = (Hf/Hi)1/2 (3)
where the acceleration due to gravity (g) and the mass of the ball (M) divide out. The total time from the release until the ball stops bouncing is simply the sum
ttotal = t0 + t1 + t2 + t3 + … (4) with the time for the initial descent
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t0 = (2H0/g)1/2 (5)
and the subsequent bounces, including round trips, given by
t1 = 2(2H1/g)1/2 = 2(H1/H0)1/2(2H0/g)1/2 = 2e(2H0/g)1/2 (6)
t2 = 2(2H2/g)1/2 = 2(H2/H1)1/2(H1/H0)1/2(2H0/g)1/2 = 2e2(2H0/g)1/2 (7) and so forth, where the factor of two in front of each term is to account for the round trip time for each bounce. Note that we are neglecting the time of contact of the ball with the floor and also assuming that the COR is constant. Substituting expressions (5) – (7) and others that logically follow into (4), we find
ttotal = (2H0/g)1/2[1 + 2e + 2e2 + 2e3 + …] (8) which means that
ttotal = constant × (H0)1/2. (9) Therefore, graphing ttotal vs. H0 should yield a curve that follows a square-root dependence. Better yet, graphing ttotal vs. (H0)1/2 should yield a straight line! Try this for various balls and discuss the slope of the best-fit lines in terms of the properties of the balls. (For the original description, see "Measurement of Coefficient of Restitution Made Easy", N. Farkas and R.D. Ramsier, Phys. Educ. 41, 73 (2006).)
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Radioactive Decay and Half Life Activity Objective: To investigate the concept of half life in naturally occurring radioactive decay. Equipment Set of black/white chips (N(time t = 0) = 200 chips per person) Cup Baggie Methodology Let’s assume that the white sides of the chips represent unstable radioactive nuclei, and that the black sides represent stable end-product nuclei. Separate your chips from the sheet if they are still attached and put them in the cup. Shake it up and dump them out. Sort out all the ones that landed black side up and remove them (put them in the baggie). Count the number of white ones (N(time t = 1)) and record this as trial #1. Put them back in the cup and repeat until you have no unstable nuclei left. Let’s imagine that each trial represents 1,000 years on Earth. Plot your data, N(t) vs. time in 1,000’s of years on a scatter plot and fit it to an exponential curve fit. Hand in answers and graphs for the following: 1. Where is the half life as estimated from your graph? Print out the graph and show where the half life is. 2. What does the exponent of the fit mean? What would happen to the graph if the exponent got bigger or smaller? 3. What would happen to the graph if you combined your chips and started with 400 or 600? Do it, and discuss whether your prediction was correct or not.
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Day Two Morning
Gravitational Potential Energy, Friction and Temperature Basis for activity: You have two masses, M(big) and M(small), hooked together by a cord. You drape the cord over a cylinder with the big mass at a height H above the floor and the small mass on the floor. You know that when released, the big mass will fall to the floor and the small mass will be raised by a height H (assuming the cord does not stretch and there was no slack). You also know that the big mass lost an amount of gravitational potential energy equal to M(big)gH, and that the small mass gained an amount of gravitational potential energy equal to M(small)gH. If you do the experiment just right, immediately after release the masses will move at constant speed (i.e. at a terminal velocity, Vt), so you know that their kinetic energies (½M(big)Vt
2, and ½M(small)Vt2)
are constant through most of the process. So, if the kinetic energies stay fairly constant, but there is a net loss of gravitational potential energy equal to
[M(big)gH - M(small)gH] = [M(big) – M(small)]gH you also know that the energy had to go somewhere. That somewhere is the thermal energy generated by the cord rubbing on the cylinder. The model that we will be assuming is that the energy transferred into the cylinder will raise its temperature (T, in Kelvin (K)) directly, with a linear relationship. If you do this process N times with the same two masses, what you should expect to find based on the model is that
N[M(big) – M(small)] ~ [Tfinal – Tinitial] Activity: Use the apparatus provided to do this experiment for many combinations of M(big) and M(small), with multiple runs, and make a plot of N[M(big) – M(small)] (in kg) vs. [Tfinal – Tinitial] (in K). Fit a trend line and let’s discuss whether the model seems to work. Make sure not to touch the cylinder too much during the activity as it will begin to warm up from the thermal energy transferred from your hand.
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Thermodynamic Paradox The Science: Thermal energy is exchanged between two objects when they are at different temperatures until they reach the same temperature, when they are then said to be in thermal equilibrium. The net energy transfer is from the hotter of the two objects to the colder. The time it takes for the objects to reach thermal equilibrium with one another will depend on how well insulated the objects are, and on how fast the energy transfers. But eventually, if you wait long enough, they will come to thermal equilibrium. The Scenario: You are teaching a lesson about today’s scientific understanding of the planets, solar system, and universe. A very vocal and strong-willed student in your class speaks up that she/he thinks that the universe is infinitely old. This, of course, is contrary to what you are teaching in the lesson, but nothing that you say about how we estimate the age of the universe, the life cycle of stars, radioactive dating, big bang theories, etc. has an effect on the student’s opinion. Worse yet, other students are starting to buy in to her/his position, and your intended lesson is being diverted into a pseudo-science argument. The Task: Keep it simple. Use the science given above to explain what you would say to the class, but put it here in writing.
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Effervescence! Engagement Questions: How does the temperature of water effect the time it takes for an effervescent tablet to dissolve? How does the exposed surface area of the tablet effect the time it takes for it to dissolve? Does the dissolution process, or the fact that you are adding a tablet at one temperature to water of a different temperature, cause the water to warm up or to cool down, and does this depend on the initial temperature of the water? In other words, is the dissolution process exothermic or endothermic? Materials: Effervescent tablets Hot water Styrofoam cups Digital Thermometer Stopwatch Cold water Directions: 1. Write a plan that will allow your group to find out the answers to the above questions using only the
materials available. Your plan must include: • Hypotheses • What is to be measured during the experiment • How you will report your results and determine the uncertainties in your data
2. Remember to consider and control variables (e.g., what happens to cold water if it just sits in a warm room?).
3. Plot your data and write statements that clearly describe your results and conclusions. (adapted from OSCI-6, day 6, 2005)
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Day Two Afternoon
Physical Science Introduction to Forces
Name: __________________________ Group: ____________________________ ____________________________ ____________________________ ____________________________ Materials: Magnets, fur, rubber rod, very small pieces of paper, ball, two beakers, water, vegetable oil, and a medicine dropper. Time: 15 min.
A. Consult with your partners and give a definition for a force. Record your definition. B. Obtain a two magnets, a piece of fur and rubber rod, very small pieces of paper, a ball, a beaker half
filled with water and a beaker half filled with vegetable oil. Use this equipment, and any other items you can find, to demonstrate as many different forces as you possibly can. Record your observations here. C. Can you classify the forces into different categories? Record your results. D. What forces did other groups demonstrate that your group did not find?
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Physical Science Newton’s 3rd Law and Friction Inquiry
Ohio Benchmark and Indicators Supported by These Activities: Physical Science Benchmark D: Explain the movement of objects by applying Newton’s three laws of motion. 9-22 Demonstrate that any object does not accelerate (remains at rest or maintains a constant speed and direction of motion) unless an unbalanced (net) force acts on it. 9-24 Demonstrate that whenever one object exerts a force on another, an equal amount of force is exerted back on the first object. 9-25 Demonstrate the ways in which frictional forces constrain the motion of objects (e.g., a car traveling around a curve, a block on an inclined plane, a person running, an airplane in flight).
Scientific Ways of Knowing Benchmark A: Explain that scientific knowledge must be based on evidence, be predictive, logical, subject to modification and limited to the natural world. 9-3 Demonstrate that reliable scientific evidence improves the ability of scientists to offer accurate predictions. Benchmark C: Describe the ethical practices and guidelines in which science operates. 9-2 Illustrate that the methods and procedures used to obtain evidence must be clearly reported to enhance opportunities for further investigations. Scientific Inquiry Benchmark A: Participate in and apply the processes of scientific investigation to create models and to design, conduct, evaluate and communicate the results of these investigations. 9-3 Construct, interpret and apply physical and conceptual models that represent or explain systems, objects, events or concepts. 9-4 Decide what degree of precision based on the data is adequate and round off the results of calculator operations to the proper number of significant figures to reasonably reflect those of the inputs. 9-5 Develop oral and written presentations using clear language, accurate data, appropriate graphs, tables, maps and available technology. 9-6 Draw logical conclusions based on scientific knowledge and evidence from investigations.
Physical Science
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Newton’s 3rd Law and Friction Inquiry Name: __________________________ Group: ____________________________ ____________________________ ____________________________ ____________________________
Materials: Balloons, nylon string, string, scissors, ring stands, straws, tape, two Logger Pro force meters, twp spring scales, wooden blocks with hooks, string and four books (or assorted masses). Safety: Use gloves with the tug of war activity
Part I: Observing Forces … (30 min)
Since a good scientist is also a good observer, let us practice making careful observations and recording our findings.
A. Obtain a balloon, scissors, a straw, a piece of nylon string about 4 meters long, and two ring stands. Place the ring stands about 4 meters apart. Thread the nylon string through the straw and tie both ends of the string to the ring stands (or any other stable object). It may be necessary to place books on the ring stands to stabilize them. Repeat this process with another type of string going in the same direction. The two parallel strings should be at least five centimeters apart so they will not touch one another.
Blow up the balloon and pinch to the end to keep the air from escaping (do not tie the balloon). Devise a way to connect the inflated and untied balloon to the straw so that when the balloon is released the straw will travel from one end of the string to the other end. Release the balloon! What observations can you make about the balloon? Can you improve on your method of connecting the balloon to the straw so that the balloon moves faster? B. What forces are acting on the balloon? Sketch a diagram of the balloon and use arrows to show the
directions of the forces. C. Repeat the experiment using the second string. Record your observations.
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D. Which of the forces listed in part B causes the balloon to move? What is the source of this force? In what direction is this force pushing? E. Is the direction the balloon moves and the direction of the pushing force you identified in part C the
same? F. What is the balloon pushing on in order to move? G. Observe the balloon’s motion again. Where do you think the forward force is coming from? H. What is the source of the force(s) that is/are trying the slow the balloon down as it moves? How could
you increase the slowing force(s) on the balloon? Reduce it?
I. Newton’s 3rd law of motion states that for every action force there is an equal and opposite (pointing in the opposite direction) reaction force. For instance, consider a person kicking a ball. The action force is “the foot pushed the ball forward”. To find the reaction force, simply reverse the objects in the description of the action force and change the direction of the force. The reaction force is “the ball pushed the foot backward”. For the case of the balloon on the string, what was the action force? What is the reaction force?
Consider a student holding their book bag. What is the action force between the hand and the bag? What is the reaction force?
Let us continue to consider the student’s book bag. What is the action force between the Earth and the bag? What is the reaction force?
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Part II: Interacting/Opposing Forces … (30 min)
A. Get a partner and each should grab a spring scale of equal magnitude. Hook your scales together and one partner pull on his/her scale until it reads the force suggested by your instructor. What is your partner’s reading?
My Reading Partner Reading
B. Now use your scales to lift the wooden blocks. Each partner should hook onto one end of the block and
then lift the block straight up, so that it is supported in a horizontal position. What are the readings now?
My Reading Partner Reading
C. This time, have your partner hook his/her scale onto one end of the block. Then you hook onto the top of
his scale, so that the block is supported in a vertical position and the two scales are hooked end to end. Take the readings again.
My Reading Partner Reading
What do you notice about these situations? Any patterns developing?
D. Now to the Logger Pro software. Each partner should pick up a force probe and hook them together. Then each of you pull while running the program. Vary the pulls and watch what happens to the graphs on the screen. Can you explain what happened?
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Sketch the two force graphs below:
E. Now place the wooden block between the force probes, hooking onto each end with one of the probes. Repeat the experiment this time, pulling on the wooden block. Again, vary the pulls. Sketch your results below:
F. How do your computer results compare with your spring scale results?
Forces are interactions … they come in pairs, an agent acts on a body and the body acts on the agent. These forces are the same size, but are directed oppositely. No forces can be exerted without an agent. Newton’s Third Law is just a simple statement to that effect: that if body A exerts a force on body B, body B exerts a force on body A that is equal in magnitude (size) but opposite in direction. Another way to put it is for every action, there is an equal and opposite reaction. How many examples of Newton’s 3rd Law can you come up with that might be experience by a normal student on a normal day? Talk as a group and jot several ideas below. Examples of Newton’s 3rd Law in Everyday Life: When you are done with this activity, we will be going outside for a few minutes to explore opposing forces in a “tugging” kind of way. Hope you brought your muscles!!
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Part III: Friction and Weight … (45 min) Begin by numbering four books. Place a piece of masking tape on each book and number them 1 through 4. Open Book 1 and place a very large loop of string inside the covers and around all or most of the pages. Close the book and hold the book up by the loop of string.
A. Hang the loop of string on the hook of a spring scale. Read the spring scale and record the weight of Book 1 in the data Table 1 below.
Table 1: Books Weights
Book Weight of Book (Newtons)
1
2
3
4
B. Similarly, place the loop of string around each of the remaining books and hang each from the spring
scale. Record the weight of each book in data Table 1. C. Using the weights of each book, calculate the total weights of Books 1 and 2; Books 1, 2, and 3; and
Books 1, 2, 3, and 4. Record the total weights in data Table 2 below.
Friction and Weight Total Weight
(Newtons) Static friction Force
(Newtons) Kinetic Friction Force
(Newtons) Book 1
Books 1 and 2
Books 1, 2 and 3
Books 1, 2, 3 and 4
Table 2: Friction and Weight
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D. Place the loop of string back in Book 1 and place the book flat on the table. Place the hook of the spring scale on the loop of string and pull the spring scale parallel to the table. Pull gently and slowly. Watch the spring scale.
What is the maximum force you can exert on the book without moving it? This force is the static friction force holding the book to the table. Record this force in the Friction and Weight data table. E. Now pull the book across the table with the spring scale. Once the book is moving, keep the book
moving at a moderate, steady speed across the table. Be sure to keep the loop of string and the spring scale parallel to the table as you pull. Read the force on the spring scale while the system is moving. This force is the applied force from your hand and it is the kinetic friction force between the table and the moving book.
Is this force more or less than the static friction force? F. Pull the book across the table three more times to see if the force stays the same. Record this force in the Table 2. Before starting step G, make a prediction. If you increase the weight of books being pulled across the table, what will happen to the kinetic friction force? Will it increase, decrease or remain the same? G. Place Book 2 on top of Book 1. Repeat steps D-F. Record the static friction force and the kinetic friction force in Table 2. H. Place Book 3 on top of Books 2 and 1. Repeat steps D-F. Record the static friction force and the kinetic friction force in Table 2. I. Place Book 4 on top of Books 3, 2 and 1. Repeat steps D-F. Record the static friction force and the kinetic friction force in Table 2. J. As the weight of the books increases, what happens to the static friction force (the force needed to just
get the books started moving across the table)? K. As the weight of the books increases, what happens to the kinetic friction force (the force needed to keep
the books moving across the table at a steady speed)? L. On the diagram of the book below, draw the forces (draw arrows) acting on the book while it is moving
at a steady speed across the table.
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M. What was the factor or variable that you changed each time you measured the force of kinetic friction? N. Explain why it is harder to push a box full of books than it is to push an empty box. O. Give several examples of everyday motion that would not be possible if there were no friction. P. On graph paper or using a computer graphing program, plot a graph of the force of kinetic friction
versus the total weight of the books. Take a ruler and draw a best fit straight line through the points. Does the shape and trend of this line show the same relationship between the force of friction and the weight of the books as you described in steps J-N?
As you discovered with the balloon experiment, friction is a force that slows down the motion of moving objects. The source of this force is the microscopic interaction between surfaces that are sliding past one another. Although they may seem smooth to the unaided eye, on the microscopic level they are very rough. The hills and valleys on these surfaces catch or snag on one another like two pieces of Velcro. In addition, there may also be chemical attractions between the surfaces.
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Day Three Morning
Physical Science Nuclear Reactions in Stars and Heavy Element Production
Ohio Benchmark and Indicators Supported by These Activities: Earth and Space Sciences Benchmark A: Explain how evidence from stars and other celestial objects provide information about the processes that cause changes in the composition and scale of the physical universe. 9-1 Describe that stars produce energy from nuclear reactions and that processes in stars have led to the
formation of all elements beyond hydrogen and helium. Science and Technology Benchmark A: Explain the ways in which the processes of technological design respond to the needs of society. 9-2 Identify a problem or need, propose designs and choose among alternative solutions for the problem.
Scientific Inquiry Benchmark A: Participate in and apply the processes of scientific investigation to create models and to design, conduct, evaluate and communicate the results of these investigations. 9-3 Construct, interpret and apply physical and conceptual models that represent or explain systems, objects,
events or concepts. 9-4 Decide what degree of precision based on the data is adequate and round off the results of calculator
operations to the proper number of significant figures to reasonably reflect those of the inputs. 9-5 Develop oral and written presentations using clear language, accurate data, appropriate graphs, tables,
maps and available technology. 9-6 Draw logical conclusions based on scientific knowledge and evidence from investigations.
Scientific Ways of Knowing Benchmark A: Explain that scientific knowledge must be based on evidence, be predictive, logical, subject to modification and limited to the natural world. 9-1 Comprehend that many scientific investigations require the contributions of women and men from different disciplines in and out of science. These people study different topics, use different techniques and have different standards of evidence but share a common purpose – to better understand a portion of our universe. 9-3 Demonstrate that reliable scientific evidence improves the ability of scientists to offer accurate predictions. Benchmark B: Explain how scientific inquiry is guided by knowledge, observations, ideas and questions.
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9-7 Recognize that scientific knowledge and explanations have changed over time, almost always building on earlier knowledge.
Benchmark C: Describe the ethical practices and guidelines in which science operates. 9-4 Explain how support of ethical practices in science (e.g., individual observations and confirmations,
accurate reporting, peer review and publication) are required to reduce bias. Benchmark D: Recognize that scientific literacy is part of being a knowledgeable citizen. 9-8 Illustrate that much can be learned about the internal workings of science and the nature of science from
the study of scientists, their daily work and their efforts to advance scientific knowledge in their area of study.
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Physical Science Nuclear Reactions in Stars and Heavy Element Production
Name: __________________________ Group: ____________________________ ____________________________ ____________________________ ____________________________ Materials: Magnetic spheres, absorption spectra overhead, spectral tubes of various gases including hydrogen and helium, spectral tube power supply, emission spectra chart, spectrometers, fluorescent light, incandescent light bulbs with a variety of wattages, sun light, tape, yellow balloon, periodic table and a calculator. Safety: Use caution with the high voltage spectral tube power supply and hot spectral tubes. Do not allow hot spectral tubes or incandescent light bulbs to become wet while cooling. Time: 1 hour
A. Have you ever wondered what stars are made of? Now you can find out. Obtain a spectrometer. The numbers in the spectrometer range from 4 to 7 because our eyes can only see electromagnetic waves that have wavelengths between 4000 to 7000 angstroms (Å). An angstrom is 1 x 10-10 m. This is the width of a typical atom. Use the spectrometer to look at the fluorescent lights in the room, the incandescent light, and the sun light through the window.
Record your observations. Based on your observations, could you tell the difference between a fluorescent light source and an incandescent light source just by looking at the emission spectra? B. Observe the spectra of the gases that are heated by the power supply. Warning: Don’t get too close to the high voltage power supply (maintain a distance of at least one meter) or touch the hot spectral tubes once they have been removed from the power supply. Record your observations. Based on your observations, could you tell the difference between the various gases within the spectral tubes just by looking at the emission spectra?
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Observe the spectra of the fluorescent lights when all and half of them are turned on. Also observe the spectra of the incandescent lights with varying wattages. Record your results. Consider a 60 W and 100W light bulb. Which light bulb would you expect to be hotter? Consider the situations when the all of the fluorescent lights are on in the room and only half of them are on. Which situation do you expect to generate more heat energy? Based on your observations of the emission spectra from the bulbs of various wattages and the fluorescent lights both partially and fully turned on, do you believe it is possible to determine the temperature of a star just by looking at its spectra? C. As you have seen, a hot gas gives off an emission spectrum or bright line spectrum. However, when
white light, which contains all of the colors in the rainbow, passes through a cool gas, the gas absorbs certain colors of light. When viewed through a spectrometer, the remaining light looks like a continuous spectrum of colors with vertical black lines streaking through it in various places (see your instructor’s overhead). This spectrum is called an absorption spectrum or dark line spectrum.
Observe the emission spectra for hydrogen and helium on your instructor’s chart. Also observe the absorption spectra for hydrogen and helium on the overhead. Record your observations. Observe the absorption spectra on the overhead of hydrogen, helium and lithium. Based on your observations, what element(s) is(are) contained in the spectra from stars 1 and 2? D. What is the name of the nearest star to our planet? The nebular theory states that our star began as a huge cloud of dust and gas (which is called a nebula) in outer space. Gravity pulled the nebula together into a hot, rotating ball of gas. As the protons, neutrons and electrons became hotter, they collided more frequently and with greater speeds. At low speeds, two positive protons repel from one another because of the repulsive electric force (like charges repel). However, at extremely high speeds protons and neutrons can collide so hard that their nuclei can get close enough for an attractive force, called the strong nuclear force, to overpower the repulsive force and hold them together. Obtain several magnetic spheres. Put a piece of tape on half of the spheres and mark them as +1 (protons). Mark the other half as 0 (neutrons). Simulate the collision of the protons and neutrons inside of a hot, spinning nebular cloud that is developing into a star. Demonstrate this process for your instructor. Record your observations.
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Use your periodic table to identify what you formed. Record your results. Which element, beyond hydrogen, would be the easiest to form inside of a star? Explain your reasoning. Use the element that is most likely to be formed after hydrogen to form the next most likely element to be formed. In other words, hydrogen nuclei (protons) and neutrons collide to form element #2. Element #2 collides with other protons and neutrons to form element #3. Demonstrate this process for your instructor. Use your periodic table to identify element #3. Record your results. If the only matter present in the universe were nebulae (mostly hydrogen) and stars, where do you think the heavier elements like iron, calcium and uranium came from? E. What is the name of the process where atoms collide and form a new element? Have you ever wondered why stars are so hot? A pretty simple calculation can show us why. Suppose the following nuclear reaction took place within a star,
p + p + n + n 42He Table 1- Nuclear reaction #1
p p n n 42He
The laws of conservation of mass and energy tell us that matter and energy cannot be created or destroyed. Based on these laws, what do you expect the relationship to be between the total mass of the reactants (two protons and two neutrons) and the total mass of the product (helium atom)? Use Table 2 below to fill in the values in Table 1 above. Summarize the result of your calculation. Table 2 – Isotope Mass data1
Isotope Symbol Mass (amu) Neutron n 1.008665 Proton p 1.007825
Hydrogen 11H 1.007825
Deuterium 21H 2.01410
Tritium 31H 3.01605
Helium-4 42He 4.00260
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The nuclear reaction above can be rewritten in a form that allows both sides to be equal. The reaction becomes,
p + p + n + n 42He + Δm Table 2- Nuclear reaction #1 with missing mass
p p n n 42He Δm
Here, ‘Δm’ represents the missing mass. What happened to the missing mass? Write the value of the missing mass and the other masses in Table 2 above. Albert Einstein showed that matter can be converted into energy and vise versa (E = mc2, where ‘E’ is energy, ‘m’ is mass, and ‘c’ is the speed of light). What do you think happened to the missing mass? From Einstein’s equation, E = mc2, we know that 1 amu of matter can be converted into about 930 MeV. Remember, a proton and a neutron each have masses of about 1 atomic mass unit (amu). The unit ‘MeV’ or million electron volts is a very small energy unit (1 eV = 1.60 x 10-19 J). An electron volt is the amount of energy an electron would gain as it accelerates through a voltage drop of 1 volt. How much energy would be released by the nuclear reaction above if the missing mass was converted into energy (Show your work)? (Hint: 1 amu = 930 MeV) This type reaction occurs trillions of times each second within a star. Why do you think stars are so hot and bright? F. The formation of heavier elements up to iron from lighter elements releases energy. The tremendous
amount of electromagnetic radiation energy released by the nuclear reactions within a star push the star’s gases outward with explosive force. However, our star has not exploded (become a supernova). Think about the forces acting on a star. What force is responsible for preventing our star from exploding?
The formation of elements beyond iron requires energy rather than releases energy. For this type of nuclear reaction, do you expect the reactants to be more massive than the products or vice versa?
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Use a yellow balloon to demonstrate the likely change in a young star’s size once nuclear reactions begin inside its center or core. Also use the balloon to show what would happen to the star if the nuclear reactions were to stop. Finally, use the balloon to show what would happen if an outward force on the star continued to overpower the inward force. What is the name of the star process you just demonstrated? During this process in a star’s life cycle, the star becomes so hot that it supplies the energy needed to form elements heavier than iron. These heavy elements are then spewed into outer space where gravity can pull them together with other elements to form planets. Describe your balloon after this star process. Also compare the size of the balloon after this process to its size before the process. What do you think happens to the star’s matter that is still near its original position in space after this star process? How would this star matter compare in size to the star before the process took place? G. Describe how stars produce energy.
Describe how a star produces all of the elements on the periodic table.
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Extension Activity: 1. Research the relative sizes of the planets and sun and make a mobile that can be permanently displayed
in the classroom. Photos of the planets and sun may be found in text books and on the Internet. 2. Gather four to six relatives at home and discuss the following situation with them. Suppose scientists on
Earth detect the distress signal sent by an extremely intelligent, technologically advanced and peaceful race of large, lizard-like creatures. Their sun is going to explode (supernova) in 3 months and they need to find a temporary planet or planets in which to relocate while they search for a new home. They have the technology to transport their entire population of 2 billion “people” to any planet that will send an answer signal into space in the form of a radio wave. As payment for the emergency assistance, this race will share their technological advances in the fields of medicine, transportation, power, galaxy mapping and architecture. Each of your relatives is to represent a continent or continents. Discuss whether or not the Earth should reply. Give your family’s final decision and explain why you made that decision.
3. Consider the nuclear reaction below that might take place within a star. Using Table 2 above, calculate
the missing mass and the amount of energy produced by this reaction in MeV.
21H + 31H 42He + n + Δm
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Physical Science Gravitational Forces and Kepler’s Laws
Ohio Benchmark and Indicators Supported by These Activities: Earth and Space Sciences Benchmark C: Explain the 4.5 billion-year-history of Earth and the 4 billion-year-history of life on Earth based on observable scientific evidence in the geologic record. 9-3 Explain that gravitational forces govern the characteristics and movement patterns of the planets, comets and asteroids in the solar system. Science and Technology Benchmark A: Explain the ways in which the processes of technological design respond to the needs of society. 9-9 Identify a problem or need, propose designs and choose among alternative solutions for the problem.
Scientific Inquiry Benchmark A: Participate in and apply the processes of scientific investigation to create models and to design, conduct, evaluate and communicate the results of these investigations. 9-10 Construct, interpret and apply physical and conceptual models that represent or explain systems, objects,
events or concepts. 9-11 Decide what degree of precision based on the data is adequate and round off the results of calculator
operations to the proper number of significant figures to reasonably reflect those of the inputs. 9-12 Develop oral and written presentations using clear language, accurate data, appropriate graphs, tables,
maps and available technology. 9-13 Draw logical conclusions based on scientific knowledge and evidence from investigations.
Scientific Ways of Knowing Benchmark A: Explain that scientific knowledge must be based on evidence, be predictive, logical, subject to modification and limited to the natural world. 9-1 Comprehend that many scientific investigations require the contributions of women and men from different disciplines in and out of science. These people study different topics, use different techniques and have different standards of evidence but share a common purpose – to better understand a portion of our universe. 9-3 Demonstrate that reliable scientific evidence improves the ability of scientists to offer accurate predictions. Benchmark B: Explain how scientific inquiry is guided by knowledge, observations, ideas and questions. 9-14 Recognize that scientific knowledge and explanations have changed over time, almost always building
on earlier knowledge.
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Benchmark C: Describe the ethical practices and guidelines in which science operates. 9-5 Explain how support of ethical practices in science (e.g., individual observations and confirmations,
accurate reporting, peer review and publication) are required to reduce bias. Benchmark D: Recognize that scientific literacy is part of being a knowledgeable citizen. 9-15 Illustrate that much can be learned about the internal workings of science and the nature of science from
the study of scientists, their daily work and their efforts to advance scientific knowledge in their area of study.
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Physical Science Gravitational Forces and Kepler’s Laws
Name: __________________________ Group: ____________________________ ____________________________ ____________________________ ____________________________ Materials: Styrofoam ball, portable light source, optical bench, 2 double convex lenses, nail, hammer, wood surface, loop of string, a pencil, a piece of paper, ruler, a large circular bowl or wide oil funnel, a marble, and a calculator. Time: 2 hours
A. Imagine that the Styrofoam ball represents the moon. You are to be an observer of the moon from your location on the Earth. The incandescent light bulb in the front of the classroom represents the sun. After the room lights are turned off, you’re your instructor will slowly move the “moon” around the room (see Figure 1). Each time the instructor pauses, observe the shape of the phase of the moon and sketch it in the boxes below.
#1 #2 #3 #4 #5 #6
#3 light source #2 student #1 #4 #5 #6
Figure 1
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Did any of these phases involve a straight line? If yes, explain how the Earth’s shadow could have created this straight line. What causes the moon to have the various phases throughout the month? B. Galileo improved upon the invention of the telescope and was very excited when he saw Jupiter and its
moons; Saturn, Venus and sun spots on the Sun (Never look directly at the sun! Galileo went blind as a result of this mistake.). During Galileo’s time most people believe that the sun and the other heavenly bodies orbited around the Earth (Geocentric Theory). Why would people think the Sun orbited the Earth?
Galileo was a careful observer and he noticed that Venus had phases similar to the moon. Did the discovery of Venus’ phases support the Geocentric Theory (Earth centered solar system) or the Heliocentric theory (Sun centered solar system)? Explain. C. Discover if you can make a simple telescope (like Galileo) by adjusting the positions of two double
convex lenses on the optical bench. Where you successful? How do you know if you were successful? D. Which of the forces that you discovered earlier could be responsible for planets, asteroids, and comets
orbiting the sun in the heliocentric theory? Explain. E. What can affect the strength of the force that you identified in the previous question? F. Johannes Kepler was a mathematician who used very precise data on the positions of Mars throughout
the year to plot its path in space. In other words, he discovered the shape of Mars’ orbit! Let’s have a little plotting practice.
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Plot the points in Table 1 on graph A. After plotting the points, connect the points smoothly and not with short straight line segments (connect the dots). Next, plot the points in Table 2 on graph B and repeat the process. y-axis x-axis 1 2 3 4 5 6 7 8 9 10 Graph A Graph B Table 1- Orbit A Table 2- Orbit B
x y -12 0 -11 3 -11 -3 -9 5 -9 -5 -7 6 -7 -6 -3 7 -3 -7 0 7 0 -7 3 7 3 -7 7 6 7 -6 9 5 9 -5 11 3 11 -3 12 0
The shapes you have made represent possible orbits for planets, asteroids, and comets. What is the name of the shape in graph A?
x y -10 0 -9 5 -9 -5 -7 8 -7 -8 -3 10 -3 -10 0 10 0 -10 3 10 3 -10 7 8 7 -8 9 5 9 -5 10 0
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What is the name of the shape in graph B? The amount of “ovalness” of the shape below can be measured by calculating its eccentricity (e). 2a = longer length of ellipse b 2b = shorter length of ellipse e = eccentricity = (a2 – b2) a a Focal Points 0 < e < 1 (range of values) Use this process to calculate the eccentricity value for the shapes in graphs B and A (graph A is a little tricky). Make a table and record your values here.
G. Obtain a large circular bowl or wide oil funnel and a marble. You are going to roll the marble around the bowl or funnel in a way similar to the way your donated coins roll around the large funnels in some stores and museums. Roll the marble toward the center of the bowl or funnel while missing the center so that it will roll around the center or hole several times before fill into the hole or stopping in the center. Move the bowl or funnel to continue the process without allowing the marble to stop.
After you have practiced creating sustained circular and elliptical orbits, test your skills by getting nine marbles of various sizes to orbit simultaneously. Demonstrate your skills for your instructor. Carefully observe the marble’s motion during circular and elliptical orbits. What observations can you make about motion of these marbles that may apply to the motion of the planets? How does the motion of the marble model the motion of a planet? Consider the orbit of a planet. What is located at one of the focal points? H. Devise a way to use a nail, hammer, wood surface, loop of string, a pencil and a piece of paper to draw a
near perfect circle. You have 5 minutes. I. Now replace the single nail with two nails placed several centimeters apart. Repeat your “circle making
process” with both nails remaining inside the loop at all times. What is the name of the positions of the nails?
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J. Repeat the previous step with the nails a different distance apart. Calculate a quantity for both of these
shapes that will distinguish them from one another. Record your values here.
K. How does the shape change as the eccentricity increases from 0 to 1? L. Table 3 lists the eccentricities of the planet’s orbits in our solar system. What is the general shape of the
orbits of the planets? Table 3- Planetary orbit eccentricity data1
Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto Eccentricity 0.206 0.0068 0.0167 0.0934 0.0485 0.0556 0.0472 0.0086 0.250 (1- Halladay and Resnick, “Fundamentals of Physics 2nd Ed.”, 1986, John Wiley and Sons Inc., Appendix C. )
Imagine that Kepler had data on all of the planets and plotted their orbits. Use Table 3 to determine which planet’s orbit would have been the easiest to determine that it was not a perfect circle? Record your answer and explain your choice. M. Suppose that when Kepler plotted the orbital data on Mars’ position each month it made the diagram
below. Carefully observe the diagram. What conclusions can you make about Mars’ motion? November October December September August June May April February
March
July January
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N. The data in Table 4 represents a simplified form of some of the data Kepler was able to calculate for a particular planet. In Table 4, ‘R’ represents the distance the planet is from the sun in meters and ‘V’ represents its speed at a particular distance in meters per second.
What observations can you make about this data? (Hint: Use arithmetic to discover a relation between ‘R’ and ‘V’.) Table 4 – Planet position and speed data
R (m) V(m/s) R + V R - V R x V R / V 1 10
3 3.33
7 1.43
9 1.11
11 0.91
12 0.83
O. Many years after discovering this relationship, Kepler noticed another relationship in his data. In Table
5, ‘T’ represents the period or time it takes a planet to orbit once around the sun in years and ‘R’ is the average or mean distance the planet is from the Sun compared to the distance Earth is from the Sun.
Table 5 – Planet period and average distance from Sun1
R* T (yr) T/R T2/R T/R2 T2/R3 Mercury 0.39
0.24
Venus 0.72
0.62
Earth 1.00
1.00
Mars 1.52
1.88
Jupiter 5.19
11.9
Saturn 9.53
29.5
(1- Halladay and Resnick, “Fundamentals of Physics 2nd Ed.”, 1986, John Wiley and Sons Inc., Appendix C.) * Measured as planet’s actual distance from the Sun divided by the distance Earth is from the Sun. What observations can you make about this data?
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P. Congratulations on retracing Kepler’s footsteps! Summarize what you have learned below about Kepler’s Laws.
Kepler’s 1st Law (see Step L): Kepler’s 2nd Law (see Steps M-N): Kepler’s 3rd Law (see Step O): What force keeps the planets, asteroids and comets in orbit? Describe the shape of the orbits of planets, asteroids and comets that regularly travel around the sun.
Extension Activity: 1. View animations or diagrams of Kepler’s laws on the following websites: http://home.cvc.org/science/kepler.htm (Laws 1-3) http://www.glenbrook.k12.il.us/gbssci/phys/mmedia/circmot/ksl.html (Law 2) http://library.thinkquest.org/04apr/00533/Text-Only/kepler's_laws.htm (Laws 1-3) Choose or locate a website that gives an account of Johannes Kepler’s and Tycho Brahe’s contributions to astronomy. After reading the accounts on Johannes Kepler and Tycho Brahe, answer the following questions:
A. What was unique about Tycho Brahe’s data on Mars? B. Compare and contrast Johannes Kepler’s and Tycho Brahe’s abilities as scientists. C. Summarize what you have learned about the scientific discovery process after reading about
Johannes Kepler and Tycho Brahe.
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D. Tycho Brahe did not give his data on the positions of the planets to Johannes Kepler before he died.
The individual who inherited Brahe’s data also did not want Kepler to have it. As a result, Kepler tricked him and obtained the data. Using this data, Kepler developed his three famous laws. In your opinion, was it right or ethical for Kepler to take Brahe’s data? Explain.
E. Name and sketch the shape of a comet’s path around the sun when it enters our solar system with a
speed that is so fast that it does not continue to orbit around the sun. F. There is a large ring or belt of asteroids that orbit the sun. Between what two planets is the asteroid
belt located?
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References:
a. Paul G. Hewitt, “Conceptual Physics 7th Edition”, 1993, Harper Collins Publishers, New York, NY, p.629.
b. Mark Grayson, “Holt Science Spectrum”, 2001, Holt, Rinehart and Winston, Austin. c. Shipman, Wilson and Todd , “An Introduction to Physical Science 7th Edition”, 1993, D. C.
Heath and Company, Lexington.
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