# Earthquake Slip Classroom Exercise

Earthquakes can provide a useful context for teaching or reviewing many basic physics concepts, such as sliding and static friction, forms of energy and conversion from one form to another, and the elastic properties of materials. Conducting the following lesson provides an opportunity for students to work cooperatively together, develop and test a hypothesis, make measurements, and write a short report on the results with graphs.  This lab could be part of an earth science course, but could also be used in general science or physics.  Depending on the instructions given, this lesson could be made more "inquiry based" than what I describe below.  One possibility would be to spend one period in inquiry with the rubber bands and blocks of wood, and then a second one doing this more directed experiment.

I believe the level of this lab is about right for 7-9th grade, but it could be adapted for higher or lower grades as well.  In fact, there is a published version suitable for college students (Hall-Wallace, 1998; Abbreviated instructions based on the principal concept of her paper.)

Introduction

 Background Information Timing: Best time for students to do this investigation Discussion and research topics

The Activity

 Teacher preparation In-class inquiry Student instructions Quiz

Understanding the Results

 Histogram of the data Advanced histogram analysis of the data Answers to questions Scoring Rubric References Acknowledgements Links

## Introduction

### Background Information

The Earth's outer, hard shell is very thin as compared to the radius of the Earth, about 80 km as compared with 6380 km. That's similar to comparing the thickness of an apple's skin to its radius. During the past 35 years, scientists in the fields of geophysics, geology, and oceanography have discovered that this hard outer shell is broken into about a dozen major "plates" that are slowly sliding about with respect to each other.

Tectonic earthquakes are caused by a sudden slippage along the boundary (fault) between two plates. The type of motion that occurs between two plates is used to classify faults as strike-slip (one plate slides past another), thrust (one plate slides under another) or normal (plates that are pulling apart from each other). Although one might expect earthquakes at the base of the plates, where they slide over the materials of the Earth's mantle, the high temperature and material properties at 80 km depth are such that plates slide along without generating earthquakes on their lower surfaces.

Typical rates of plate motion are a few cm per year. Why then, might someone ask, do destructive earthquakes occur in which many meters of fault slip happen so quickly that the vibrations are recorded by seismographs all around the world and are sometimes strong enough to destroy nearby buildings and bridges? This is where friction and elasticity come into play. Since the shallow portions of the plates are relatively cool, two plates cannot flow past each other, but rather the faults that form their boundaries tend to stick or lock up for years or centuries at a time. Each year the portions of plates near locked faults deform elastically by a few more cm. The more the plates are bent and deformed, the greater the force is on the fault (shear stress). Eventually the force is sufficient to make the plates break free of one another and the elastic energy that has been stored up is released as frictional heating on the fault and ground vibrations. (seismic waves). This process of faulting is called stick-slip or elastic rebound.

The initial force on the fault must be able to overcome static friction. Once the fault starts slipping, then slip will continue until the force drops below the resistance of sliding friction. The force available to keep the fault slipping decreases as the distorted plates return to their original shape.

### Timing: Best time for students to do this investigation

Although this lab could be done after a unit on energy or friction, these topics could also be introduced following when a large earthquake has been reported in the news. At this time the students will be particularly interested in what causes earthquakes, and this curiosity would help them learn more about the basic science concepts of energy and friction, review their knowledge of plate tectonics, practice undertaking a guided inquiry, and writing a report on their results.

### Discussion and research topics

This topic could also lead to discussions and/or reports on the topic of earthquake hazards that contain elements of both science and social studies. These could include the spectrum from preparations that an individual or family could make, such as maintaining a supply of food and water, to government policy decisions, such as adopting and enforcing building codes or funding studies to assess earthquake hazards. Questions could be raised, such as, "should schools, hospitals, and fire stations be built to the same safety standards as homes?" "How about bridges and apartment buildings?" If the internet is available, students could try to look for answers to questions such as, "What is the largest earthquake that has occurred in this state?" or "How does the seismic hazard of my community compare with that of California?" or "Which were the largest 10 earthquakes to occur within the United States and how much damage did they cause?"

## The Activity

### Teacher preparation

In addition to gathering the materials needed for each group, as indicated in the next section, it is important to experiment with some of the blocks of wood and the table surfaces that the student will be using. If the surfaces are very smooth, then the block will tend to slide as the rubber band is stretched, rather than stick and then slip. There are places along the San Andreas fault where the fault creeps rather than sticking and then generating an earthquake, so this type of behavior is possible for faults as well as for blocks of wood. However, this lab would not be very interesting if the block moved by creep rather than by stick-slip motion.

Stick slip motion is more likely if the rubber bands are thin and the string of rubber bands is long. If the tables have very smooth tops, it may be necessary to purchase boards on which to slide the 2x4 blocks. The boards could be pieces of 1"x6" pine, or 1/4" plywood cut into 6"-wide strips. Boards that are 1 m long would be sufficient. It isn't necessary for the end of the string of rubber bands that is being pulled remain on the board, but just that the block does so. If a board is used, then sand paper can be attached to the 2x4 block to increase the friction (but don't scratch the table top!).

Another option to increase the friction is to cut a strip of elastic faberic (such as Spandex) that is a bit wider than the block and  1 meter long.  The faberic can be taped to the table to provide a runway for the block.

### In-class inquiry

Divide the class into groups of 3 or 4 students. Each group will need the following materials:

A piece of 2x4 wood, cut approximately 13 cm long.
10 thin rubber bands (looped together for a total length of about 16 cm)
A meter stick or tape measure

A flat working surface about 1.5-m long, such as a wooden tabletop. (If all of the tabletops are very smooth, such as plastic laminate, then a 1-m long 1"x6" pine board should be used as the sliding surface, because a very hard and smooth surface may not generate stick-slip events.  The Earth doesn't always generate stick-slip events either, such as in the creeping section of the San Andreas fault in Holister, California.)

Teachers making measurements at an IRIS workshop in 2004.

### Student instructions

Take a few minutes to make a string of rubber bands by looping them together. Loop one completely around the block of wood and try pulling the block along the table (or along the board if one is furnished) with the string of rubber bands. Test the effect of various pulling speeds on the motion of the block.

In this lab, one student will be the puller, one will be the observer, and one or two will take notes. The puller will start with the rubber bands pulled out so that there is almost no tension on the 2x4. This initial position on the meter stick of the leading edge of the block and the leading end of the string of rubber bands needs to be recorded by the recorder(s). Then when everyone is ready, the puller will move the end of the rubber bands 1 cm and then count slowly out loud, "one one one,"  move the end of the rubber bands 1 more cm and then count slowly out loud, "two two two," move 1 cm, count slowly out loud, "three three three" and so forth. The observer will read out loud the position of the 2x4 at its initial position and then after each movement that the puller makes and the recorder(s) will write these numbers down.

Below is a photo of my block, rubber bands, and measuring tape on my back deck and a video of the procedure.

 When I tested my block and rubber bands on a table, I found that the block tended to creep along slowly rather than slip suddenly.  I added another piece of 2x4 for added weight and also stretched out a strip of stretch fabric.  The block now moved in clear steps.  Click here for some added information and videos.

Using the notes of both recorders, make a graph of the position of the 2x4 versus the position of the end of the rubber bands that was being pulled. Did both recorders write down the same numbers? Now that you have an idea about how the lab works, discuss what you think is going on. How is friction related to the movement of the 2x4? Do you expect the motion of the block would be the same if the experiment were repeated? Repeat the experiment twice more, each time changing the puller, observer, and recorder assignments. Graph the additional two sets of data. Here is a sample set of data and graph, which is based on my observations of one trial.

### Quiz

Now, each student working alone, answer the following questions:

1) Trace the flow of energy. Describe the flow of energy through a complete cycle of stick and slip. Include the energy stored in your muscles.

3) How would the results be different if a string were used instead of a rubber band?

4) In what way does the force between the block and the rubber band vary as the rubber bands are stretched? Describe an experiment that could be conducted to test this relationship.

5) Does the probability that the block will slip during the next interval of time depend on the history of past block movements? Explain your answer.

6) Compare and contrast this lab with the elastic-rebound process that generates earthquakes in the Earth.

## Understanding the Results

### Histogram of the data

A histogram can be a useful tool for exploring physical processes. A simple histogram could be made in which the data from each group or from the entire class was combined together. The first step would be to define the slippage bins for the histogram. Something like:

0-1 cm, 1-2 cm, 2-3 cm, 3-4 cm, etc. Then decide the convention for slips that fall right on a boundary. In this case you would probably put a slip that equals a boundary value in the higher bin. In other words a slippage of 0 would go into the first bin and a slippage of 2 would go into the third bin.

Next count the number of events that fall within each bin. Plot this number versus the bin number to see how the number of events varies with the amount of slip in the event. I've made a table of my measurements and a histogram plot.

### Advanced histogram analysis of the data

In the study of earthquakes, a histogram of the number of earthquakes within narrow magnitude bands is often used. The relationship of the form log (N) = A - b*M is usually found, where the value of the constant b is about 1. This is called the Gutenberg-Richter magnitude distribution.  What this means is that for every magnitude 5, for example, there are 10 magnitude 4's and 100 magnitude 3's. Depending on grade and math level, this concept could be presented in different ways. See this page for plots of the global distribution of earthquake magnitudes.

To compare earthquakes with the sliding block experiment, the energy released by each slippage first needs to be computed. The first step needs to be finding the elastic constant of the rubber bands, k, where force = -k * extension. This could be done by hanging the rubber bands from the block and measuring their length while suspending varying amounts of weight. In a plot of length versus weight, the elastic constant k would be the slope of the line in units of force/length. The equation could be eliminated and the plot of force versus length used directly in the next step.

For each slippage of the block, the notes may be used to determine the length of the rubber band string just before and right after the slippage. Then the graph or the equation can be used to determine the force right before and right after the slippage. The average of these two forces would be the average force on the block during slippage. When multiplied by the distance the block moved, this would give the energy that the rubber band transferred to the block. This energy was in turn, converted into elastic vibrations that radiated away from the block and into heat due to friction between the block and the table surface. Convert the energy of each event to joules.

Next the energy may be converted to magnitude using the equation:

M = (log E - 4.8)/1.5

where E is the energy in joules. These events will be extremely small, so the magnitudes will be negative. Larger events will have less negative magnitudes.

It would probably be most interesting to combine the magnitudes from the entire class, so that there are a larger number of data points. Decide on the magnitude bins for the histogram and for each bin, count the number of events that occurred. Take the log of each count and plot this number against the lower magnitude limit of each bin. Then compare the slope of this line to that of real earthquakes, which generally have a slope near 1.0.

1) Trace the flow of energy. Describe the flow of energy through a complete cycle of stick and slip. Include the energy stored in your muscles.

The body uses chemical energy to cause the muscles to contract, thus stretching the rubber bands. Some of this chemical energy is also converted to heat within muscles. The rubber bands store this energy as elastic potential energy. The more the rubber bands are stretched, the more energy they store and the harder they pull on the 2x4 block. When the force on the block exceeds the static friction force, the block begins to slide, converting the elastic energy of the rubber bands into kinetic energy of the block. As the block slides, it's kinetic energy is transformed into heat energy on the sliding surfaces and elastic wave energy as vibrations radiate away from the sliding block. The block stops sliding when the force is reduced the about the level of sliding friction. The elastic waves become weaker as they move away from the block, both because they spread out and because during each cycle of motion some of their energy is converted to heat. Eventually all of the elastic energy that was given up by the rubber bands is converted to heat energy.

Yes, energy is conserved. The original source of energy, which was chemical potential energy within muscles, was converted to heat, both in the muscles, in the block, in the table surface, and in the surrounding area where the elastic waves traveled. If, during a given interval of time, the rubber bands became more stretched, then energy was also stored as elastic potential energy.

3) How would the results be different if a string were used instead of a rubber band?

The string would not stretch very much, so the block would just move the same amount as the end of the string that is being pulled. No measurable amount of energy would be stored in the string, so large "earthquakes" would not occur.

4) In what way does the force between the block and the rubber band vary as the rubber bands are stretched? Describe an experiment that could be conducted to test this relationship.

The more the rubber bands are stretched, the more energy they store and the harder they pull on the 2x4 block. The block could be positioned so that the rubber bands hang down from the table. Then the length of the string of rubber bands could be measured with various amounts of weight hanging from them. A plot of length versus weight should be linear, with a slope equal to the elastic constant of the rubber bands.

5) Does the probability that the block will slip during the next interval of time depend on the history of past block movements? Explain your answer.

Yes. The more the rubber bands have been stretched from past movement of their free end, the greater the force on the 2x4 block and the greater the chance that the block will slip during the next interval of time. This is similar to the situation with the Earth's faults. If a fault is known to be active, then the longer it has resisted slip, the more dangerous is becomes. Unfortunately, if this time interval is 100 years or more, people that live near the fault tend reduce their concern for future earthquakes, even as the concern should be increasing year by year. Seismologists today can not predict exactly when or where an earthquake will occur, but they can make decade-long* forecasts about the probability of earthquakes within a given region.

6) Compare and contrast this lab with the elastic-rebound process that generates earthquakes in the Earth.

The block in this lab is connected by an elastic element to a point that is moving at a uniform velocity, and yet it moves in rapid slips rather than with a uniform velocity. This is similar to the way that the rocks at a plate boundary move rapidly past each other during earthquakes, even though the bulk of the plates move at a constant velocity. One difference is that in the case of earthquakes the elastic element is the plate itself, which can bend to store energy and then return to its original shape during earthquake fault rupture. Another difference is that it's the block lower surface that is sticking on the tabletop. In the case of the Earth, the high temperature and material properties at 80 km depth are such that creep rather than stick-slip motion takes place on lower surfaces. The motion is stick-slip only along the shallower and cooler upper portions of the boundaries between plates.

*For an example of a long-term forecast, see:

http://quake.wr.usgs.gov/study/wg99/

Revised long-term quake prediction expands Bay-area danger zone

October 16, 1999

Web posted at: 10:34 AM EDT (1434 GMT) (AP) --
Just two days before this weekend's magnitude 7.0 earthquake in Southern California, the U.S. Geological Survey released a grim prediction: There is a 70 percent chance of a major earthquake in the San Francisco Bay area in the next 30 years.

The U.S. Geological Survey said its estimate is for an earthquake at or above a magnitude of 6.7 -- the strength of the 1994 Northridge quake that killed 67 people and caused \$20 billion in damage in the Los Angeles area.

The forecast, which comes with an uncertainty factor of plus or minus 10 percent, is different from earlier predictions because it expands the danger zone from the Pacific Ocean to the Sacramento Delta, about 40 miles inland.

Another report released Thursday, by the Association of Bay Area Governments, said hundreds of thousands could be left homeless if a large quake hit.

### Scoring Rubric (100 points total)

Question 1) Trace the flow of energy. Describe the flow of energy through a complete cycle of stick and slip. Include the energy stored in your muscles.

10 points: The answer indicates an understanding that energy is stored in the rubber bands for later release when the block slips.

5 Points: The block gains kinetic energy.

5 Points: The block's energy is converted to heat and vibration energy.

5 points: The answer is yes.  Energy is conserved but converted to heat and elastic potential energy.

Question 3) How would the results be different if a string were used instead of a rubber band?

10 points: The answer indicates an understanding of the role of the elasticity of the rubber bands in storing energy for later release.

5 points: The block would always move when the string was pulled.

Question 4) How does the force between the block and the rubber band vary as the rubber bands are stretched? Describe an experiment that could be conducted to test this relationship.

10 points: The force increases as the rubber bands are stretched.

5 points: The increase in the force is directly proportional to the increase in length of the rubber bands.

5 points: The answer suggests a reasonable method of measuring the elastic constant of the rubber bands.

Question 5) Does the probability that the block will slip during the next interval of time depend on the history of past block movements? Explain your answer.

10 points: The answer is yes.

10 points: The explanation indicates an understanding that the more the rubber bands are stretched the greater the probability that and further stretching will cause the block to slip.

Question 6) Compare and contrast this lab with the elastic-rebound process that generates earthquakes in the Earth.

10 points: The answer indicates an understanding that elastic-rebound involves slow storage of elastic energy followed by rapid release.

10 points: The answer indicates that the rubber bands in the lab are analogous to the elastic deformation of the Earth's plates.

5 points: The answer includes the fact that the Earth's plates creep on their lower surfaces and stick-slip on their boundaries, whereas the block was stick-slipping on its lower surface.

### References

Lahr, John, 1999, Table-Top Earthquakes, USGS Open-File Report 98-767.
This report describes a more elaborate demonstration that can be built to generate "earthquakes." Included is a sensor and AD computer interface so that the waves that are generated by the "earthquakes" can be monitored.

Hall-Wallace, M.K., 1998, Can earthquakes be predicted?, Journal of Geoscience Education, v. 46, p. 439-449.
This paper describes a sliding block experiment that can be conducted to explore whether either the time of the next earthquake or the amount of slip in the next earthquake can be predicted.  There is a version of this lab that uses this concept with the blocks and rubber bands described above.

USGS Information on Earthquake Hazards and Preparedness:
http://quake.wr.usgs.gov/hazprep/

The Gutenberg-Richter Magnitude Distribution is described in more detail on this web site published by the Southern California Earthquake Center:
http://www.scecdc.scec.org/Module/s2act08.html

### Acknowledgements

This report was prepared for a Colorado State University class entitled "Science Assessment: Tools and Strategies" that was given by Nancy Kellogg and Karen Hunter on January 26-27, 2000.  This was an excellent class and I've attempted to apply some of the things I learned to this earthquake exercise.  The report has also benefited from suggestions offered by Nancy Kellogg.