4. Hammer a tee nut into the hole on one end of each 15 cm piece.
Standard:# 3600-06 Students will analyze relationships between Earth's crust and other Earth systems.
Category:Inquiry
Learning Objectives:
Materials, equipment and/or facilities:
For each small group of students:
Sequence and duration of each part of lesson:
Teacher Preparation:
Build the BOSS model by following the directions on Master 4.3a. Practice with your model until you've got a feel for each frequency and you can get any of the rod aassemblies to resonate. One technique is to use a firm push first, then watch the number you want and wiggle the base very lightly at its natural frequency to get resonance.
Introduction
Find out what students already know about the concepts of amplitude, frequency, and resonance. If they are not familiar with these terms, introduce them by building on what students already know from other areas. They may know, for example, that resonance and frequency are used in describing the tone of musical instruments and the quality of sound produced by different recording techniques and players. The phenomenon of resonance also accounts for laser light and for the color of the sky.
Lesson Development
1. Direct students' attention to the BOSS model, and explain its name. Ask the students to predict which numbered rod assembly will oscillate the most when you wiggle the base. Have them hold up 1, 2, 3, or 4 fingers to indicate their prediction. (They will probably say number 1 because it is the tallest.)
2. Oscillate the BOSS model so that some rod assembly resonates other than the one most students predicted. This will baffle the students, so let them predict again. Again make the rod resonate for an assembly they did not predict. Finish this demonstration after several tries making the rod resonate for the assembly most of the students did predict, so that they get it right. Invite discussion.
3. Relate the blocks and rods to buildings of various heights in an earthquake. Ask students if they think buildings would oscillate like this in an earthquake. (They always do, and in some earthquakes the effect is especially pronounced. In the 1985 Mexico City earthquake, the ground shaking resonated with the natural frequencies of 8 to 10 story buildings. The effect was severe damage to medium-height buildings that had the same frequency as the ground shaking and resonated with it. Higher and lower buildings were hardly damaged.) Use the BOSS model as a visual aid when describing this event. You may also want to draw attention to the photos or books you used in Lesson 1 of this unit.
4. Divide students into seismic engineering teams (SETs) and distribute one copy of Master 4.3b, BOSS Worksheet, to each group. Tell students that they will take turns performing an experiment with the model, recording their data, and providing the answer asked for on the data sheet. Give these directions:
b. Practice until you can get almost the same swing each time, then repeat the measurement four times. Calculate the average of these four times. Now calculate the natural frequency of the number by dividing 10 cycles by the average time. Record it. Repeat this procedure for the other three numbers.
c. Measure the height of each assembly from the base to the top, and record it.
d. Plot height versus natural frequency on the graph provided. (Students should come up with a hyperbola, a curve representing an inverse relationhip in which, as the height of the structure increases, its natural frequency decreases.)
e. Ask the class: From what you have learned, do the earthquakes with the highest numbers on the Richter Scale always do the most damage? (Students should already know that the amount of damage has to do with population density and other factors, but now they will be aware of something new. To illustrate the relationship of frequency and resonance, use the example of someone pushing a child in a swing. The person pushes a little at a time, over time, and soon the swing goes very high without a big push. Each small push is at the right frequency. Similarly, a building may vibrate with a great amplitude without big earthquake vibrations because the smaller vibrations came at that structure's natural frequency.)
5. Ask the SETs to share and discuss their results. Again point out the connection between the experimental results and the way real buidlings resonate. Other things being equal, taller buildings have lower natural frequencies than short buildings.
Conclusion
Review the terms and concepts introduced in this lesson. Explain that seismic waves caused by earthquakes produce oscillations, or vibrations, in materials with many different frequencies. Every object has a natural rate of vibration that scientists call its natural frequency. The natural frequency of a building depends on its physical characteristics, including the design and the building materials. Resonance is a buildup of amplitude in a physical system that occurs when the frequency of an applied oscillatory force is close to the natural frequency of the system. In the case of an earthquake, the ground shaking may be at the same frequency as the natural frequency of a building. Each vibration in the ground may come at or dangerously close to the natural frequency of the structure.
Ask the class to hypothesize what would happen when buildings of two different heights, standing next to each other, resonate from an earthquake. Wiggle the BOSS model so that assemblies 2 and 3 vibrate greatly, and let students see how buildings hammer together during powerful earthquakes. If you have some images of this effect from actual earthquakes, show them now.
Entice students to further investigation by leaving them with the question: "How could you add structural elements to reduce resonance in a building?"
Adaptations and Extensions
1. Tell students that one way to protect a building from resonating with an earthquake is to isolate its foundation, or base, from the ground with devices much like wheels. This technique is called base isolation. Structural engineers are now developing the technology to place buildings on devices that absorb energy, so that ground shaking is not directly transferred to the building.
Invite students to add standard small wheels from a hardware store to their models as an illustration of one of the many base isolation technologies, or add wheels to your own BOSS model, then shake the table. Better yet, place the model in a low box or tray and shake it. Then take out the model, fill the box with marbles or BBs, and replace the model on this base. Now shake the box. Challenge students to come up with other base isolation techniques.
2. If any of your students have studied harmonic motion in a physical science or physics class, challenge them to explain how the BOSS model is an example of an inverted pendulum.
3. To help students connect the numbered rod assemblies to actual buildings, make paper sleeves and decorate them to resemble buildings in your area. At some point in the lesson, slide the sleeves over the rod assemblies to show how buildings can collide, or hammer against each other, during an earthquake.
Evaluation:
Student assessment will be evaluated by their comprehension of vocabulary terms and their understanding of accompanying scientific principles.
1. Cut one of the meter long threaded rods down to 75 cm, leaving the other full length.
2. Cut one of the 61 cm threaded rods down to 45 cm, leaving the other full length.
3. Drill a .63 cm (1/4 in.) hole through the center of one of the short sides in each of the 15 cm pieces of wood (See assembly diagram)
4. Hammer a tee nut into the hole on one end of each 15 cm piece.
5. Countersink four 3/4-in. holes about 1/8 in. deep into the 45 cm 2 x 4 at 12 cm intervals, as marked on the diagram. (This will allow you to countersink the nuts so they don't scratch the surface where the model rests.)
6. Drill four 1/4-in. holes in the 45 cm. 2 x 4 in the countersunk holes.
7. Hammer a tee nut into each countersunk hole. Turn the board over so the tee nuts are on the bottom.
8. Assemble the rods and the base as shown on the diagram.
9. Use the permanent marker to label the 15 cm pieces of wood in four different colors. When they are dry, number them with the white paint.
Date
Cooperative Group
Scientist
Technician
Coordinator
Engineer
Record oscillation times in the data table below in the appropriate places for each rod assembly. These times are measured in seconds per 10 cycles. Repeat the measurement four times to minimize human error, then record.
Caution: Start the stopwatch as a numbered block reaches its maximum swing and start counting with zero, otherwise you will end up timing only nine swings. Practice this until your times for 10 oscillations are fairly close to each other.
Calculate the average time for each oscillation by adding four measurements and dividing by four. Record.
Calculate the natural frequency. Divide 10 cycles by the average time (do not simply move the decimal point). Frequency is measured in hertz, or cycles per second. Record.
A. Data Table: Oscillation Times
| Rod Assembly | Oscillation Time (sec/10 cycles) | Avg. Oscillation Times (sec/10 cycles) | Natural Frequency Hertz (cycles/sec) | |||
| Trial 1 | Trial 2 | Trial 3 | Trial 4 | |||
| #1 | ||||||
| #2 | ||||||
| #3 | ||||||
| #4 | ||||||
| Rod Assembly | Height (cm) |
| #1 | |
| #2 | |
| #3 | |
| #4 |
| Rod Assembly | Oscillation Time (sec/10 cycles) | Avg. Oscillation Times (sec/10 cycles) | Natural Frequency Hertz (cycles/sec) | |||
| Trial 1 | Trial 2 | Trial 3 | Trial 4 | |||
| #1 | 11 | 0.9 | ||||
| #2 | 6.7 | 1.5 | ||||
| #3 | 5 | 2.0 | ||||
| #4 | 3 | 3.3 | ||||
1. How much variation do you notice among the four trials?
Oscillation times vary by less than 10 percent.
2. What relationship do you notice, if any, between the height of the rods and their natural frequencies?
The shorter the rod, the higher the natural frequency. The taller the rod, the lower the natural frequency.
B. Heights of the Rod Assemblies
1. Measure the height of each rod assembly from teh base to the top of the block and record it.
| Rod Assembly | Height (cm) |
| #1 | 89 |
| #2 | 73 |
| #3 | 57 |
| #4 | 42 |