Lesson: Simple Machines Conceptual Physics: Paul Hewitt Chapter 9, Section 9.8 Machines Support provided by:
Context of Lesson This lesson is a one or two day, teacher-led and demonstrated, structured inquiry that will reinforce the student’s knowledge of a common simple machine family--the lever. The focus of this lesson will be the seismometer models in the Harris Loan Experience Box: Simple Machines. One of the models functions as a horizontal pendulum and includes most of the important functional components of all mechanical seismometers with one exception: it does not include any device that would magnify the ground motion of an earthquake. A second model in the kit will function as a lever and will be used to show how this simple machine can magnify the record produced by the seismometer. Students will predict how many times larger will be the sweep of the pen in the lever-type seismometer. Then, students will identify the parts of a lever, measure lever arms and finally, compare the ratio of the lever arms to the magnification of the pen movement. The lesson will teach or reinforce observation skills, data collection and analysis, and making a conclusion based on experimental results. This lesson will further reinforce students’ knowledge of force and displacement, studied in chapter 2 of Conceptual Physics. The skills and knowledge gained in this lesson will show how simple machines can be important parts of complex measuring devices. Also, the student will learn that concepts of force and displacement are integral to understanding earthquakes and their measurement. Main Goals/Objectives Students will be able to: • • •
Describe how earthquakes occur. Explain how the seismometer model works and how it compares to an actual mechanical seismometer. Identify the lever system parts in another seismometer, locating the fulcrum, the lever arm(s), and explaining how the machine can amplify displacement. Students will relate the magnification of displacement to the magnification of force that they have learned from their textbooks. Explain the function of levers in seismometers. Collect, analyze, and interpret data.
General Alignment to Standards Mathematics State Goal 7. Estimate, make and use measurements of objects, quantities and relationships and determine acceptable levels of accuracy. A. Measure and compare quantities using appropriate units, instruments and methods. ILS 7.A.4b Apply formulas in a wide variety of theoretical and practical real-world measurement applications involving perimeter, area, volume, angle, time, temperature, mass, speed, distance, density and monetary values. Mathematics State Goal 8. Use algebraic and analytical methods to identify and describe patterns and relationships in data, solve problems and predict results. A. Interpret and describe numerical relationships using tables, graphs, and symbols. ILS 8.B.5 Use functions including exponential, polynomial, rational, parametric, logarithmic, and trigonometric to describe numerical relationships. Mathematics State Goal 10. Collect, organize and analyze data using statistical methods; predict results; and interpret uncertainty using concepts of probability. A. Organize, describe and make predictions from existing data. ILS 10.A.4a Represent and organize data by creating lists, charts, tables, frequency distributions, graphs, scatter plots and box plots ILS 10.A.4b Analyze data using mean, median, mode, range, variance, and standard deviation of a data set, with and without the use of technology. Science State Goal 11. Understand the processes of scientific inquiry and technological design to investigate questions, conduct experiments, and solve problems. A. Know and apply the concepts, principles and processes of scientific inquiry. ILS 11.A.4c Collect, organize and analyze data accurately and precisely. Science State Goal 12: Understand the fundamental concepts, principles and interconnections of the life, physical and earth/space sciences. C. Know and apply concepts that describe properties of matter and energy and the interactions between them. ILS 12.C.3a Explain interactions of energy with matter including changes of state and conservation of mass and energy D. Know and apply concepts that describe force and motion and the principles that explain them. ILS 12.D.5a Analyze factors that influence the relative motion of an object (e.g., friction, wind shear, cross currents, potential differences).
E. Know and apply concepts that describe the features and processes of the Earth and its resources. ILS 12.E.3a Analyze and explain large-scale dynamic forces, events and processes that affect the Earth’s land, water and atmospheric systems (e.g., jet stream, hurricanes, plate tectonics). Overview of the Lesson • • • • • • • •
Students will learn how an earthquake occurs and why there are large and small quakes by performing an experiment with the lateral fault model included in the Experience Box. Students will observe the function of the model seismometer in the Simple Machines Experience Box. Students will understand that most earthquakes that occur are very small tremors, and that the equipment used to analyze these small quakes must include some way to magnify the motion of the detector. Students will measure the sweep, or wiggle, of the pendulum model’s recording pen. Students will measure the sweep, or wiggle, of the lever model’s recording pen. Students will write a ratio of the lever arms in the lever seismometer. Students will compare the displacement of the base to the displacement of the recording device and then note the similarity to the ratio of the lever arms. Students will compare the lever systems used in actual mechanical seismometers to the lever system of their model. (Optional, time permitting) Students will investigate other components of the Experience Box, particularly the slip-strike fault model and related activities.
Vocabulary and Equation Used Lever Fulcrum Inertia Mass Displacement Pendulum Seismometer (seismograph) Seismogram Fault Earthquake
Longlever arm displacement Short lever arm displacement
Length of longlever arm Length of short lever arm
Modifications/Accommodations If you are worried about the class losing their focus (or interest) as you disassemble the pendulum model and assemble the lever model, you should assemble the lever model before the lesson begins. You can introduce the lesson with only a few modifications. Then, as you mention the parts of a seismometer, you’ll refer to the lever model. Demonstrate its function, and then proceed to measure and record data. While students are working at calculations and answering questions, you can disassemble the lever model and assemble the pendulum model. A major problem with the seismometers is their size. Students may have trouble seeing what you are doing and seeing the seismometer itself. Try to position your worktable, or, if possible, position the students for maximum visibility. While students are working on calculations or questions, you might allow small groups to come to the worktable to manipulate the apparatus. Teachers with large classes may also want to consider assigning this activity as an out-ofclass research project to a small team of students. These students will collect the data, analyze the results, and answer questions under the supervision of the teacher. As a part of their assessment, students will give a presentation on the entire experiment to their class. Assessment There are three main areas of assessment: A) Students should be able to explain how a lever system can magnify variables other than force, especially displacement, and to use this explanation to explain the function of the lever seismometer model. The discussion questions prompt students for these explanations and can be used to assess student understanding. B) Students should be able to use a diagram of a lever with lever arm lengths clearly marked and calculate not only the mechanical advantage of the lever but the relative displacement of the ends of the lever arms. C) Students should be able to make a list of experimental errors that changed the expected outcome of the experiment.
Materials from the Harris Educational Loan Program’s Simple Machines Experience Box: o Model seismometer kit: horizontal pendulum model, with instructions for assembly o Metal lever rod, hanging mass, copper wire support, stop tabs, felttipped marker, sticky tack: for the lever model seismometer o Ruler o Hall’s car mechanics cart o “Spaghetti” slip-strike lateral fault model
Other materials (teacher supplied): o If you would like to perform the demonstration using rulers or pencils, as noted in the Lesson Outline, you will need to provide those items. o Pieces of dry spaghetti for the slip-strike lateral fault model. o Calculator o Chalk or tape
Teacher Lab Preparation The Harris Loan Experience Box contains the materials to construct the seismometers you’ll need for a teacher-led demonstration of the effect of levers on the output of a seismometer. You can copy the data page and project it on an overhead for your students. They can then copy the table into their laboratory notebooks. As an alternative, you can describe the table to students and have them create it in their laboratory notebooks. Or, if the resources and technology are available, you can make a copy for each student. Copy the “Discussion Questions” page and project it on an overhead, or make a copy for each student. In the Experience Box, find the seismometer model parts. There are only enough parts to assemble one seismometer at a time. There are instructions included in the Experience Box for the assembly and operation of one of the models. This seismometer functions as a horizontal pendulum. In this lesson, this model will be referred to as the pendulum model. In the pendulum model, a curved hanger-wire is attached to a metal and plastic support at two points. A pair of washers, a screw, and a wing nut constitutes the pendulum “bob”. There is a marking pen attached to the bob. The pen and bob form an inertial mass—that is, they would remain stationary during an earthquake while the rest of the seismometer—the support and the recording paper—would shake. Since there is relative 5
motion between pen and paper, the pen creates a back-and-forth drawing on the paper, and this drawing is called the seismogram. This back and forth motion of the pen relative to the paper will be referred to as a “sweep” or a “wiggle” in the rest of this lesson. The paper can be pulled through the seismometer to show the degree of shaking over time. In addition to the seismogram parts mentioned above, you will find an aluminum rod, hanging mass, 18 gauge copper wire, and an additional marking pen. These items will be used to assemble the seismometer that functions as a lever. This model will be referred to as the lever model throughout this lesson. Once assembled (instructions appear below), the modified seismometer will have a hanging mass that serves as the inertial mass and also as the lever fulcrum. The physics of both seismometers are similar. Both are horizontal pendulums, and the pendulum bob is an inertial mass that resists changes in motion while the seismometer shakes around it. However, one model is also a lever, as well as a horizontal pendulum. The pen in the lever model will move through a much larger distance for a small quake than the pen in the horizontal pendulum model. A short lever arm between the mass and support and a long lever arm between the mass and the pen creates the magnified pen sweep. Small amounts of shaking at the support end are recorded as large wiggles on the seismogram. What would have been a small, even imperceptible drawing on the seismogram of the horizontal pendulum seismometer is magnified to the point where it becomes a large, very noticeable drawing. There might be some confusion as to the definition of “lever” at this point. A lever is a class of simple machine. Students have learned that a lever is a bar that turns about a fixed point, and that a simple machine is a device that is used to multiply force or to change the direction of force. The lever in this experiment does not magnify a force. In fact, the force of the earthquake is being reduced. The job of the machine in this case is not to adjust a force, but instead to adjust a displacement. By this time, students should have learned that machines can magnify a force, but at the expense of the distance over which the force is applied. For example, you can use a lever to lift a 100N weight to a height of 1m by applying a force of 10N over a distance of 10m. In the lever seismometer model, the lever is taking a large earthquake force acting over a small distance and producing a smaller force that acts over a larger distance. In complex machines, the function of levers is often used to magnify (or reduce) displacement. The two seismometers should be assembled and operated before the lesson. This will allow you to become an expert at making adjustments to the models while you lead a discussion with your class. The models are both simple, but require some familiarity if you are going to lecture and demonstrate simultaneously. Because there is only one support in the box, this lesson is best performed as a demonstration and structured inquiry. Practice step 7 and 8 of the Lesson Outline--the steps that lead to measurable output from the seismometers. 6
The experiment calls for the seismometers to be placed onto and held to a mechanics cart during the experiment. This requires a little hand-eye coordination and a stable connection between cart and seismometer. You might want to attach the seismometer to the cart with tape, sticky-tack, or rubber bands. Or, you might want to hold the seismometer with both hands, pressing down securely as you move the cart back and forth. You should find a location in your room where the class can see the models and can see how you are manipulating the materials. The lever model is assembled as follows: 1) Remove the inertial mass and wire hanger along with the paper roll from the pendulum model, if you haven’t already. This will leave a plastic base and metal support. This is the support for the lever model. You will not use any other part of the pendulum model. 2) Straighten the copper wire. (Note that the copper wire is looped through the hanger on the mass. If the wire has been undone, loop it through the mass hanger and twist-tie it.) 3) Remove the protective cork cover from the end of the aluminum rod. Be careful of this needle end of the rod, as it is very sharp. 4) Notice that there are two small vinyl (or rubber) disks on the rod on either side of the mass. These are the “stops” that hold the hanging mass in place. You can slide them to adjust the position of the mass. To start, position the mass about 5cm from the needle end. Push the stops together so that the hanging mass is secured and won’t slide along the rod. (If the mass has been removed from the rod, hang the mass on the rod between the two stops.) 5) Put the needle end of the rod in the small hole of the metal support near the plastic base. 6) While you hold the rod, slide the length of copper wire through the hole at the top of the support. 7) Pull the wire taught through the hole. 8) Bend the wire down on the other side of the hole. For a picture of the setup, see figure 1. You may have to loosen the wire or you may have to pull it through the hole so that the aluminum rod is horizontal and the mass hangs freely above the plastic base. 9) Attach the pen to the end of the rod as shown in figure 1, using the sticky tack included in the Experience Box. The model is now assembled and ready for use. Once the model has been assembled (either one), the base of the support may be placed on a mechanics cart with the wheels aligned perpendicular to the aluminum rod (lever model) or to the wire support (pendulum model).
Test this seismometer by moving the cart back and forth (away from you and toward you) through a very small distance—about 0.50 cm is recommended. Again, the inertial mass will resist the motion, staying essentially in one position and creating the pivot point for the system. This is the fulcrum of this lever. The end of the shorter lever arm moves through the 0.50 cm displacement you are creating. The longer lever arm moves through a much larger distance. The table you are working on should be level and stable, or the aluminum rod may lean to one side. If you are having problems with the aluminum rod staying close to center in the model, try the following: 1) 2)
3) 4) 5) 6) 7) 8)
Turn the metal support until the rod is centered and tighten the screw holding it to the plastic base, if necessary. This will usually solve the problem. Twist the metal rod a little in the hole of the support. For brand new seismometer models, the hole might need to be “worked in” by twisting the rod around in the hole until all tiny burrs have been removed. This might be a problem for the horizontal pendulum model too. Straighten out any bent components—these result from improper storage and handling. This might be a problem for the horizontal pendulum model. Rotate the cart and seismometer model so that it is moving back and forth in a different direction. Make sure that the rod is horizontal. Adjust the length of the copper wire. Make sure that the hanging mass is not sitting on the plastic base. Check to make sure that the needle end of the rod did not fall out of the hole in the support. Move the cart in a gentle manner through very small distances. The lever model is made to work with very small displacements of the cart.
The mechanical problems you encounter during your demonstration provide a good opportunity for problem solving. Allow your students to identify the problems and to suggest solutions. Lesson Outline 1) Ask students about their experience with earthquakes. Have any of them heard of nearby quakes or have any of them felt a tremor from an earthquake? Students may know about recent quakes in Illinois. You may hear stories involving pets (birds squawking, dogs barking, etc.), rattling dishes, or stories of relatives who live close to an earthquake’s epicenter and who have experienced severe tremors or even property damage. Tell students about the Friday, April 18, 2008, earthquake that had a magnitude of 5.2, and which shook southern Illinois in the early morning. People as far as 900 8
miles away felt the tremor. Some people in Chicago noticed it and others slept through it. Tell students that many quakes in Illinois and Missouri originate around the Mississippi River and Ohio River valleys in the Southern part of Illinois, Southeastern Missouri, and Northwest Kentucky. This area has many fault lines and seismic lines. (For a map of the most common earthquake locations in Illinois and the surrounding areas, see “Earthquake Facts: Earthquake Occurrence in Illinois, by the Illinois State Geological Survey (ISGS): http://www.isgs.uiuc.edu/research/earthquake-hazards/pdf-files/qk-fct-occur.pdf) Most of these earthquakes are very mild, and many go unnoticed in Illinois. For more information on the frequency and severity of Illinois earthquakes, see the ISGS fact sheet “Damaging Earthquakes in Illinois” at: http://www.isgs.uiuc.edu/research/earthquake-hazards/pdf-files/qk-fct-damag.pdf At this point, mention that scientists need a device so sensitive that it can detect and record even the smallest tremor. This might spark questions about the model from the Harris Loan Experience Box. Would it record a small quake in Illinois? Tell students that the pen sweep of this pendulum model is only about as large as the ground motion itself. The displacement of the ground during a small quake will be a small fraction of a millimeter. (Remind students of how small a millimeter is, if necessary, by showing them the markings on a ruler.) In the case of a small quake, a seismometer without some means of magnification wouldn’t produce a noticeable pen sweep. This horizontal pendulum model would need something to magnify the pen sweep if it were to produce a noticeable seismogram. Modern seismograms can magnify the motion of the ground many thousands of times. These machines are anchored into the bedrock so that they will vibrate only when the rock far below the surface vibrates. These machines are so sensitive that they are positioned in a way so that they don’t pick up ground vibrations from traffic or other human activity. If interest in seismometers and their construction has been stimulated, be flexible and proceed to a discussion of seismometers, starting with #4 below. You may return to other parts of the discussion later. 2) Ask students if they know how earthquakes are created. If their answers are incorrect or if they do not know, explain the basics of earthquakes along a lateral fault, which they will be studying in the next part of the lesson. Tell students that an earthquake originates when parts of the earth move past each other along a crack in the earth’s crust, called a fault. Huge rocks get trapped between the moving slabs of Earth and the pull on them creates enormous stress. 9
When the rocks finally overcome the force of friction holding them, they become unstuck, and like a stretched rubber band being snapped, motion energy is released. The ground surrounding these slabs begins to vibrate back and forth. This vibration radiates in all directions. In other words, a matter wave is generated. We call this an earthquake. More information is given in #3 below. A large amount of information about earthquakes, including lesson plans, maps, FAQ, historical facts, animations, diagrams of seismometers, and photos, may be found at http://earthquake.usgs.gov/ 3) Ask students the following question: What might happen to cause an earthquake with a lot of energy—one in which the ground really shakes? If time permits, perform the activity involving the “spaghetti” slip-strike model. Instructions, data sheets, and questions are included with this model in the Experience Box. Since there is only one model in the box, you can perform this activity as a structured inquiry demonstration, allowing students to come to their own answer to the question as they complete the experiment. A fault is a crack in the earth with relative motion between the sides of the crack. In a strike-slip fault, the motion of the plates relative to each other is side-to-side, or horizontal, with little or no vertical movement. This is the type of crack that runs along the Western edge of California called the San Andreas fault. There is a map of this fault on the slip-strike model. Along the San Andreas fault, the pieces of earth that are rubbing against each other are not smooth, but rather are very jagged, with large chunks of rock the size of cities or even larger jutting out of one side and sticking into another. As the sides of the fault move relative to each other, the stuck boulders are placed under huge stress (rock does not stretch very well!). Eventually, the forces get so large that the city-sized boulders break free, sending a huge jolt throughout the landmasses on each side of the fault. It is as though an enormous spring has been stretched to the maximum and then released. There is movement everywhere and this motion is vibratory. There are shakes, rattles, and rolls felt throughout the land on each side of the fault. How much back and forth movement there is depends to a large extent on the strain built up in the enormous rock that is stuck between the moving blocks of earth. In the strike-slip model, you will be investigating the movement, or displacement, that results from different strains on the caught rock. The strikeslip fault model has a map of California, and the moving piece in the model is in the approximate geographic location of the San Andreas Fault. Also in this model, caught rock will be represented with small pieces of spaghetti. As more rock gets caught up in the sides of the fault, more strain builds and the displacement of the land is greater when the rock breaks free.
As this activity is performed, students will come to realize that along a lateral fault, enormous sections of rock that are embedded on one side of the fault can get stuck in the other side. The rocks are put under enormous stress as the two landmasses on either side of the fault continue to slide past each other with the rocks locked in position. Eventually, the rocks give way, and enormous vibrations are sent out in all directions. The vibrations—horizontal and vertical— are waves that constitute an earthquake. The model presents a study of the amount of rock that is stuck and the resulting displacement of the ground when the rocks break free. Remind students that ground movement during the wave or vibration of an actual earthquake is very small. 4) Have students observe the pendulum seismometer in the Experience Box, taking note of its parts. Move the model back and forth on the cart. Ask students if they see what is moving and what is “staying put”. Ask them to determine how the seismometer works and what it measures. Students should understand that any seismometer is strongly attached to the ground (bedrock), often with strong metal bars that extend far below the earth’s surface. Because of this, a seismometer would shake as hard as the ground it is attached to. It is important that some part of the machine remain motionless while the rest of the machine shakes. In this way, the shaking can be compared to the motionless piece and the degree of displacement can be recorded. This is where the inertial mass comes in. The inertial mass gets its name from its resistance to movement (inertia). The inertial mass, since it is attached to the seismometer in a way that allows it to move freely, wouldn’t move during an earthquake. This part of a seismometer is a very large mass, and by definition of mass, greatly resists any change in its position. Its free-swinging support allows it to stay put while the rest of the machine sways back and forth. This is a pendulum, but is moving opposite to the way a pendulum is expected to move. Tell students that to an observer standing fixed on the shaking ground, the inertial mass (or pendulum bob) appears to be swinging back and forth. To an observer removed from the shaking ground, it is the bob that stays put while the support sways back and forth. There is a video of a modern seismometer’s recording device in action during a Southern California earthquake at http://cbs13.com/video?id=26614 The seismometer was invented to record the magnitude of the shaking that occurs during an earthquake.
Here are reproductions of three seismograms recorded during the earthquake on April 18, 2008. These come from three different recording stations, the bottom being closest to the epicenter, while the top is farthest away.
You should redraw at least two of these reproductions on your blackboard and use them to show students how strong tremors produce a large wiggle, while smaller tremors produce smaller wiggles on the seismograms. Also note that the pendulum seismometer has no way of amplifying the shake of an earthquake. The displacement of the ground should be equal to the size of the wiggle on the seismograph. 5) Define seismometer, seismograph, and seismogram, so that students can use these terms in their discussion and writing. Seismometer and seismograph are interchangeable terms for the machine that records the intensity of an earthquake by measuring the amount of displacement of the ground as it shakes back and forth. The seismogram is the output of the seismometer, the zigzag recording of the tremor. The range of the markings on a seismogram is related to the intensity of the earthquake and can be used to calculate a number related to the energy or damage-causing ability of the quake. Students may want to research the Richter scale or Mercalli scale to learn what the relative numbers mean. There is information about both scales in the Experience Box. 6) Create a seismogram with the pendulum seismometer. (Note: if you have modified this experiment to use the lever model first, you should skip to step “8” and return to this step after you are finished with that model.) Put two chalk marks or pieces of tape on the table 0.5 cm apart. Pull the recording paper through the seismometer base and attach it to the end with the
rubber band. Open the pen cap and place the pen in its holder. It should just be touching the paper. The seismometer should now be placed on the mechanics cart and moved back and forth between the marks or pieces of tape--a very small displacement of 0.5cm. Ask for a student volunteer to pull the paper slowly and gently through the seismometer as you move the mechanics cart back and forth. Show the students the seismogram and the wiggle you have created. Note that with such a small displacement, there won’t be much range in wiggle of the seismogram. This artificial quake you are creating represents a small tremor, which is very common. 7) Now you are ready to begin recording measurements with the pendulum model. Note: the “pen” referred to is actually a lightweight felt-tipped marker. A) Make sure that your two marks made on the table and 0.50 cm apart are clearly visible to you. Tell students that you have made these marks so that the “earthquake tremors” that you create will be the same every time and that the seismometer will be “shaking” consistently through a distance of 0.5 cm. Tell students that this amount of displacement would actually be related to a major earthquake and could result in quite a bit of damage. B) During these measurements, you won’t be pulling paper through the seismometer. All you will need is a side-to-side sweep of the pen. Cut off a piece of paper from the roll and tape it to the bottom of the seismometer. One end of the paper can be held down with the rubber band. C) Remove the recording pen from its holder. Move the cart perpendicular to the length of the seismometer and make the maximum back and forth distance traveled 0.5cm each time. Practice this so that you can get a consistent shake each time. Do not move the cart too quickly but create a steady back and forth rocking motion. When you have the technique mastered, move on to the next step. D) Put the pen back in the holder. Make sure the pen is lightly touching the paper. Repeat the back and forth motion that you practiced in “C”, keeping the cart moving between the marks you made. E) Measure the maximum sweep or wiggle of the pen mark on the seismogram. Remove the pen, and cap it. Pass the seismogram to your students and have them measure the size of the wiggle. 8) Disassemble the pendulum model and assemble the lever model. Put the hanging mass 5 cm from the end of the support. Use the “stops” to fix its position. Tell students that you have now made a seismometer that will amplify the ground movement by using a lever. Ask students what they know about a lever. Ask them: “What are the main parts of a lever? How does a lever work?”
A lever is a category of simple machine. A simple machine can magnify force (or change the direction of force) and make a task easier. Remind students that the same amount of energy will go into the task. The two main parts of a lever are the lever bar and the fulcrum. The lever bar can be divided into two sections, one on each side of the fulcrum. In the diagram below, the lever bar sections are labeled “A” and “B”. The sections are called lever arms. A force applied at the end of the long lever arm “A” will be magnified at the end of the short lever arm “B”. For example, you could lift a 10 N weight at the end of “B” by applying a downward force of 1 N at the end of “A”. The end of the longer lever arm “A” moves through a greater distance than the shorter lever arm, “B”. For example, if a 10 N weight at the end of “B” is lifted by 1.0m, a 1 N force at the end of “A” moves through 10m. Students should be familiar with an equation that describes the input force and distance moved with the output force and distance moved:
(Force x distance) input = (Force x distance) output A first-class lever magnifies a force by a certain factor, X.
(Force) output (Force)input
This factor X, is also related to the distances that each end of the lever moves.
(distance)input (distance) output
or, from the diagram,
(distance) A (distance) B
X is also equal to the ratio of the lever arms. In other words
where “A” and “B” are the lengths of the respective lever arms in the diagram.
€ B A Fulcrum
9) Ask students how the lever seismometer works. Ask them: “Where is the fulcrum? What are the lever arms?” The fulcrum is the hanging mass in the model. This is the inertial mass of the seismometer. It is the part of the seismometer that “stays put” during an earthquake while the rest of the machine shakes. The hanging mass divides the lever bar into two lever arms. The lever arm that is closest to the support is the short lever arm, similar to “B” in the above diagram. The lever arm on the side of the inertial mass away from the support is the longer lever arm, similar to “A” above. 10) Ask students how the seismometer magnifies the ground motion. The support is attached to the end of the short lever arm, and it moves this arm through the same distance that the ground moves. The other end of the lever bar moves through a much greater distance. The end of the longer lever arm moves through a distance “X” times greater than the shorter lever arm. (“X” is defined above.) This is how the ground movement is magnified. You can demonstrate this very simple principle by taking a ruler or a pencil and holding it between your thumb and forefinger. Hold it so that there is a long end and a short end protruding from your fingers. Wiggle the ruler or pencil so that it moves in a vertical plane. Point out to students the difference in movements
along the ruler or pencil. The end of the short lever arm moves through a small distance. The fulcrum (or pivot point) doesn’t move at all. The end of the longer lever arm moves through a much greater distance.
Thumb and forefinger
(You can even have students do this with their laboratory rulers [half-meter sticks work well] and take measurements. They can calculate the ratio of the wiggle distance at both ends of the meter stick. Then, they can calculate the ratio of the lever arms. The ratios should be approximately equal.) Tell students that levers have been used to magnify the shaking ground of an earthquake since the very earliest seismometers were created to produce a seismogram. Some of these early seismometers employed “optical levers”, where light from a candle fixed to the seismometer was reflected off of a mirror attached to the inertial mass. The recording device on the seismometer was light sensitive paper that would be exposed with the reflected candlelight hit it. This recording paper was much further from the mirror than the candle, making the wiggle of the reflected light at the paper much greater than the wiggle of the candle. Gottfried Wagener constructed one of the first successful horizontal pendulum seismometers that employed a mechanical lever (similar to the one in the Harris Box) in 1880. A top-down view of this seismogram is shown below, with the lever marked.
The drawing on the right is a simplification of the actual model, shown at left. Looking down on the model, you can see the support (which would be fixed to the ground) connected to the lever at point B. The bearing at point B allowed the lever to pivot here. Thus, B was the fulcrum. The inertial mass is marked as M. The short lever arm was the distance from B to the inertial mass, M. T represents the long lever arm. You may want to copy and project the diagram to show how the lever system was employed. In this seismometer, the fulcrum (pivot point) moved during an earthquake. The large inertial mass stayed behind and swung what would have been the recording pen through a large sweep. It is interesting to note that the tip of this lever arm did not have a recording instrument attached. Rather, as the end swung back and forth, it would pull string from a spool. The amount of string removed would be proportional to the ground motion. More information on the history and development of seismometers may be found at: http://earthquake.usgs.gov/learning/eqmonitoring/eq-mon-6.php 11) Now you are ready to make measurements with the lever seismometer. A) Use the same two marks you made on the table (0.50 cm apart). Remind students that you have made these marks so that the “earthquake tremors” that you create will be the same every time and that the seismometer will be “shaking” consistently through a distance of 0.5 cm.
B) Cut off a piece of paper from the roll as before and tape it to the bottom of the seismometer. One end of the paper can be held down with the rubber band. C) Remove the pen from the end of the metal rod. Move the cart perpendicular to the length of the seismometer and make the maximum back and forth distance traveled 0.5cm each time. Practice this so that you can get a consistent shake each time. Do not move the cart too quickly but create a steady back and forth rocking motion. The inertial mass should hang straight and the end of the metal rod, furthest from the support, should be wiggling through a distance greater than the 0.5 cm you are moving the cart. When you have the technique mastered, move on to the next step. D) Remove the cap from the pen and attach it to the end of the metal rod with the sticky tack provided. Make sure the pen is lightly touching the paper. Repeat the back and forth motion that you practiced in “C”, keeping the cart moving between the marks you made. Continue making marks until you have a good sweep recorded. If the pen creates too much friction, repeat from step B, but attach the pen so that it very lightly touches the new piece of paper. E) Measure the maximum sweep or wiggle of the pen mark on the seismogram. Remove the pen, and cap it. Pass the seismogram to your students and have them measure the size of the wiggle. F) Assign a student to measure the length of the lever arms. Tell the student to carefully measure from the end to the middle of the hanging mass. Report these measurements to the students and have them record them in a data table entitled “Experiment #1” in their laboratory notebooks. G) Repeat this experiment, but move the hanging mass to a distance 8.0 cm from the support. Place the information in a second data table entitled “Experiment #2”. H) Have students calculate the ratios to complete the data tables. Note that the movement of the cart is called “ground movement”. Tell students that you have created an artificial earthquake with a specific amount of shaking—0.50cm. I) Assign the “Discussion Questions” for homework or for class work and future discussions.
Data Page Size of the pen sweep for the pendulum model seismometer: _________________ cm
Length of shorter lever arm (cm)
Length of longer lever arm (cm)
Experiment 1 Ratio of lever Width of pen arms sweep or “wiggle” (cm)
Length of shorter lever arm (cm)
Length of longer lever arm (cm)
Ratio of pen sweep to “ground movement”
Experiment 2 Ratio of lever Width of pen arms sweep or “wiggle” (cm)
Ratio of pen sweep to “ground movement”
Simple Machines and Seismometers Discussion Questions Teacher Annotated Copy 1. How do the ratio of the lever arms compare to the ratio of the pen sweep to ground movement? Was this what you were expecting? Ideally, the ratio of the lever arms should be the same as the ratio of the pen sweep to the ground movement. Remind students that the “pen sweep” is the size of the wiggle in the seismogram. The purpose of using the lever was to magnify this wiggle. Students should be able to articulate in words or writing the following: the magnification of the wiggle over the ground motion is equal to the mechanical advantage of the lever. Also, the mechanical advantage of the lever is equal to the ratio of the lever arms: longer lever arm divided by the shorter lever arm. In reality, the magnification might be greater or less than the expected. See the answer to the next question. 2. What are some reasons why your expected result might be different from the actual result? In other words, what are the sources of error in this experiment? A few sources of error include: 1. There are several points in the lever model where friction would reduce the magnification. Any point of attachment where there are parts moving would be a point where friction could alter the results. If you discuss this question in class, tell students that scientists would build seismometers to minimize friction by using lubricated bearings between moving parts, using the smallest contact points possible (needle point and knife-edge contact points, for example), or by using light instead of mechanical parts, as in the optical lever used in early seismometers. Modern seismometers mostly overcome the problem of friction during magnification by using electrical components. 2. The inertial mass is actually not very large compared to research quality mechanical seismometers, where the inertial mass might be hundreds of pounds or more in weight. When the inertial mass is as small as this one, it eventually will start to sway back and forth, and this can be dramatic if you move the cart in time to the natural resonance frequency of the system. Once the inertial mass starts swaying, the pen can move wildly beyond the bounds of the paper. Modern seismometers are constructed so that the natural frequency of the pendulum is very different from possible earthquake frequencies. 3. The 0.5 cm displacement of the cart is so small that occasional deviations from this distance are possible throughout the experiment. If you move the cart too
much, the sweep will be “too large” in response, and if you move the cart too little, the sweep will be “too small”. 4. There is friction between the pen (marker) and the paper. This will produce a sweep that is too small. In modern seismometers, the recording pen has a very small tip, and the force between pen and recording paper is very small. Alternatively, the research grade seismometer might record the ground motion as a computer file. You could tell students about the interesting research being done in California, where citizens are being recruited to record earthquake tremors with certain laptops. Read more at the Quake Catcher Network homepage: http://qcn.stanford.edu/ 5. There are balance problems with the lever model: the pen could tip during the experiment, the model might slip on the mechanics cart since it is hand-held, etc. 3. Describe how the lever works as part of a seismometer to magnify the motion of the ground. Lever systems are constructed in two ways: 1) The seismometer support is at the end of the short lever arm and the inertial mass is the fulcrum, or 2) The seismometer support is at the fulcrum and the inertial mass is at the end of the short lever arm. In either case, ground motion is represented by the relative motion of the short lever arm. A seismometer that uses a lever will have the recording device at the end of the long lever arm. The long lever arm moves through a greater distance than the short lever arm. Thus, ground movement has been magnified. 4. Did the lever model seismometer work? Would this seismometer be better for measuring the intensity of small earthquakes than the pendulum model seismometer? Although the model seismometer worked, it would not be used in an actual earthquake. There are too many sources of error that would need to be minimized, and the magnification is only 2 to 4 times. Actual seismometers magnify the ground movement by many thousands of times to record small tremors.
5. After you have investigated ground displacement along a lateral fault using the slipstrike fault model, explain how earthquakes of large magnitude originate. There are many factors that affect the size of an earthquake. The slip-strike model investigated the amount of rock that was stuck between two slabs of earth moving past each other. The greater the amount of trapped rock, the greater the total strain, and the greater the potential energy. Once the trapped rocks slip, this potential energy is released as kinetic energy—the earth surrounding the fault vibrating and sending wave-like vibrations in all directions.
Simple Machines and Seismometers Discussion Questions 1. How do the ratio of the lever arms compare to the ratio of the pen sweep to ground movement? Was this what you were expecting? 2. What are some reasons why your expected result might be different from the actual result? In other words, what are the sources of error in this experiment? 3. Describe how the lever works as part of a seismometer to magnify the motion of the ground. 4. Did the lever model seismometer work? Would this seismometer be better for measuring the intensity of small earthquakes than the pendulum model seismometer? 5. After you have investigated ground displacement along a lateral fault using the slipstrike fault model, explain how earthquakes of large magnitude originate.