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Perilous Plunge Activity Guide Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Science Activity – Give ’em the Hooke! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Exploring Hooke’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Technology Activity – Stretching the Choices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Choosing the Right Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Mathematics Activity – Scatter My Bones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Predicting Using a Scatter Graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Engineering Challenge – Build It, They Will Jump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Teacher Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

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Introduction As legend goes, bungee jumping originated as a modern-day imitation of “vine jumpers” of Pentecost Island. These jumpers tied vines from the jungle to their ankles and leapt off of wooden towers more than 80 feet high. The natural elasticity (stretchiness) of the vines provided enough give for the jumpers to slow their descent and survive the force of the fall. Modern-day bungee jumpers use rubber bungee cords to slow their fall, and the cords attach to a durable harness around their ankles, rather than just being tied. These cords are very similar to rubber bands – only much stronger. Many amusement parks now have these types of activities available, but they use body harnesses to be even safer. In bungee jumping, the length and strength of the bungee cord must be matched to the mass of the jumper and the height of the jump. Great care is taken to get the right combination before an actual jump. Most often, a dummy is used in place of the jumper to determine if the right combination has been used.

The dummy (loaded with sand to the proper mass) is attached to the bungee cord and thrown off the platform – and observers watch to determine how close the dummy comes to the ground (or water) underneath the platform. Changes are made to the length of the cord or to the thickness of the cord to vary the amount of drop. After the right combination is found, the jump is made. In most cases, everything goes as it should and the jumper is safe and exhilarated. However, as with most things, there are possible unexpected outcomes. The key is to minimize the possible negative outcomes to give the best chance for success. In this activity, you are going to experience bungee jumping in a little different way – from the perspective of the jump manager, the person responsible for making the jump safe and successful. You will need to bring a doll or action figure from home that is between 5" and 12" tall. If you are successful, there will be no dolls or action figures harmed in doing these activities.

Making a Rubber Band Chain In the following activities, you will need to know how to make a rubber band chain. 1. Take two rubber bands. Thread one through the other and pull the ends of the first rubber band away from the second rubber band (Figure 1).

2. Thread one of the ends of the first rubber band through the other end (Figure 2) and pull it tight. 3. Add a third rubber band to either end of the two-band chain in the same manner. Continue to add rubber bands until the chain is as long as desired.

Figure 2

Figure 1

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Science Activity – Give ‘em the Hooke! Understanding Hooke’s Law Elasticity is defined as a material’s ability to return to its original shape. Most materials are not very elastic, but what comes to mind most often to show or describe elasticity is a rubber band. It can be stretched out, but when it is released, it returns to its original shape or length. The amount of stretch that a rubber band has is dependent upon its length, width, and thickness. This amount of stretch is known as the elastic constant and is specific to each rubber band combination of length, width, and thickness. Note: Rubber bands are not springs and do not act exactly as springs do. However, for the purposes of these activities, they provide a reasonable and inexpensive alternative. Robert Hooke, a scientist during the 1600s, determined that the amount of elasticity of a material was connected to the amount of distance the material would stretch and the force required to make it stretch. This connection is the law of elasticity, which is commonly referred to as Hooke’s law.

For example, if a certain rubber band has a elastic constant of 1.25 N/cm (1.25 newton per centimeter; a newton is a metric measure of force), the amount of force needed to stretch that rubber band 5 cm would be:

F = kx



F = 1.25 N/cm · 5 cm



F = 6.25 N

So, the amount of force required would be 6.25 newtons. You can also rearrange this formula to determine k from the stretched length and force applied:

k = x/F

Using the above formula, if you have 10 cm of stretch produced by a force of 2 N, then:

k = 10 cm/2 N



k = 5 cm/N

Essentially, Hooke’s law says that the amount of distance of stretch of a material is proportional to the force causing that stretch. Hooke’s law can be written as a mathematical formula:

F = -kx

Where F is the amount of force, k is the elastic constant of the material, and x is the distance of stretch. So, the amount of force is equal to the elastic constant times the distance of stretch. In this equation, the minus sign is an indication that the force (F) is in the opposite direction of the stretch. For calculation purposes, we will remove the minus sign from the equation.

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Science Activity – Give ‘em the Hooke! Exploring Hooke’s Law In this activity you will determine the elastic constant of several different rubber bands. It will work best if you work with someone to obtain your data. Your teacher will determine if you will both report the same data or if you will each have your own data.

Materials • • • • •

4. Using the ruler, determine the length of the stretched rubber band. 5. Record this length in the data table. 6. Repeat Steps 1-5 for the second and third rubber bands. Complete the data table as directed.

Ruler Hooked masses (200, 500, and 1,000 grams) Rubber bands (1/16", 1/8", and 1/4" widths) “Exploring Hooke’s Law” worksheet Pencil or pen

Procedure 1. Determine the length of the first rubber band by laying the rubber band on top of the ruler and compressing the “circle” of the rubber band on both sides to make it more like a line (Figure 3).

Figure 3

2. Place the 200-gram mass on a flat surface and hook the first rubber band into the hook of the mass. 3. Pull up on the rubber band until the mass is just barely in contact with the surface.

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Science Activity – Give ‘em the Hooke! Exploring Hooke’s Law Worksheet 1. Follow the procedure to determine L1 (the original length of the rubber band) and L2 (the stretched length of the rubber band attached to the corresponding mass) and record that data in the proper columns of the data table below. 2. After all data is recorded, calculate m2 (the number of kilograms of each mass) by dividing m1 (the mass in grams) by 1,000. Do this calculation to determine all m2 values. 3. Calculate F (the amount of force) by multiplying m2 by 9.8 (the acceleration due to gravity). 4. Calculate x (the amount of stretch) by subtracting L1 from L2. 5. Calculate k (the elastic constant) by dividing the amount of stretch (expressed as a negative number) by the force: k = -x/F. Mass (g)

Mass (kg)

Force (N)

Original Length (cm)

Stretch Length (cm)

Amount of Stretch (cm)

Elastic Constant

m1

m2

F

L1

L2

x

k

measured

measured

x = L2 – L1

k = x/F

1/16"

200 g 500 g 1,000 g

1/8"

200 g 500 g 1,000 g 200 g

1/4"

Rubber Band Width

m2 = m1/1,000 F = m2 • 9.8

500 g 1,000 g

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Science Activity – Give ‘em the Hooke! Analyzing the Results 1. As heavier masses are added to the rubber bands, what happens to the amount of stretch measured? 2. What happens to the value of the elastic constant as heavier masses are added to the rubber bands? 3. What happens to the value of the elastic constant as the rubber band width increases? 4. About what value would you expect the elastic constant of a 1/2" width rubber band to be?

Inquiry Questions 1. If you had three 1/8" rubber bands chained together (Figure 4), what stretched length would you expect with a 500-gram mass? _______ Figure 4

2. If you had five 1/16" rubber bands chained together, what would you expect the elastic constant to be? _______

3. If you had two 1/4" rubber bands attached to a 1,000-gram mass as shown (Figure 5), what would you expect the amount of stretch of the rubber bands to be? _______

4. Set up the three scenarios above and determine the values experimentally. For each scenario, explain any differences in your predicted results and your experimental results. a. Experimental value for Question 1: _______ b. Experimental value for Question 2: _______ c. Experimental value for Question 3: _______ Figure 5

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Technology Activity – Stretching the Choices Understanding Materials In this activity, you will make a logical choice for a bungee material based on the comfort level of the action figure. This activity is best done in teams of two students. One will pull the action figure to the ceiling and drop it; the other will determine the amount of drop. An important factor in the design of an amusement park ride or any such entertainment is the comfort of the person on the ride. If the circular motion of Figure 6 the ride is too tight, is too fast, or accelerates or 2. Chain 15 of the 1/16" rubber bands together. decelerates too quickly, then the ride will not be enjoyable, and in some instances, not safe. 3. Attach one end of the rubber band chain to the ankles of the action figure.

The Activity – Choosing the Right Material In the case of the bungee jump, deceleration (the rate at which the velocity is decreasing) is of primary concern to the comfort of the rider. Through observation and measurement, you will determine which bungee material (the thickness of the rubber bands) would provide the most comfort to the rider.

Materials • Rip Cord Parachute Drop (Pitsco product 32863) • Action figure • Rubber bands (1/16", 1/8", and 1/4" widths) • Paper clip • Measuring tape • Binder clip • “Choosing the Right Material” worksheet

Procedure 1. Secure a paper clip to the feet or ankles of the action figure using a rubber band wrapped tightly around the ankles (Figure 6). 8

4. Attach the other end of the rubber band chain to the ceiling or drop stand arm about six inches from the Rip Cord Parachute Drop. A binder clip works well for this. 5. Attach the paper clip around the action figure’s ankles to the slot in the Rip Cord’s chute clip. Close the two arms over the slot, securing the paper clip in the slot. 6. Raise the chute clip by pulling on the twine. Stop pulling before the chute clip reaches the bumper ring. 7. One team member should be prepared to watch and determine the lowest height that the action figure reaches. 8. The other team member will pull the chute clip up into the bumper ring to release the action figure. Measure the distance the action figure drops and record it on the “Choosing the Right Material” worksheet. 9. Repeat Steps 5-8 to obtain two more trials. 10. Repeat Steps 2-9 using 1/8" rubber bands. 11. Repeat Steps 2-9 using 1/4" rubber bands. 12. Complete the “Choosing the Right Material” worksheet. Perilous Plunge Activity Guide 59779 V0708

Technology Activity – Stretching the Choices Choosing the Right Material Worksheet 1. Follow the procedure on the previous page to determine values in the table below for the drop distance for each of three trials for the three rubber band widths. 2. Calculate and record the average for the drop distance for each rubber band width. 3. Assign one of the following descriptions for the speed at which the action figure slows as it descends to its lowest point: slowly, quickly, very fast. 4. Assign one of the following descriptions to the appearance of how the action figure changes from downward motion to upward motion: gradual, semi-smooth, abrupt. 1/16" Rubber Band Trial 1 Trial 2 Trial 3

Avg.

1/8" Rubber Band Trial 1 Trial 2 Trial 3

Avg.

1/4" Rubber Band Trial 1 Trial 2 Trial 3

Avg.

Drop Distance (m) Rate of Deceleration (observed) Change in Motion (observed)

Inquiry Questions If you were the action figure: 1. Which of the rubber band widths would have given you the smoothest, most comfortable ride? 2. Which of the rubber band widths might have given you the worst neck ache? 3. If the goal of the ride is to provide both thrill (measured by the rapid change in acceleration) and enjoyment (least amount of neck and back aches), which of the rubber band widths might meet the goal?

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Mathematics Activity – Scatter My Bones Graphing Data Part of the function of mathematics is to provide various methods to look at data in useful ways. In this activity, you will collect data for your action figure, graph that data, and then predict how many rubber bands would be needed to have your action figure come just to the level of the floor when dropped.

2. If a paper clip hook has not been attached to the feet/ankles of your action figure, use a separate rubber band around the ankles to attach the paper clip hook (Figure 7).

The Activity – Predicting Using a Scatter Graph While this activity could be done using simple proportions, the accuracy of your prediction can be better if more data is used. After the points are plotted on a scatter graph, a line of best fit (also known as a trend line) is added to the graph. Extending this line and reading the graph at the exact drop distance will provide a prediction of the number of rubber bands needed.

Materials • Action figure • Rubber bands – all the same size and width • Rip Cord Parachute Drop (Pitsco product 32863) • Measuring tape • Paper clip • Binder clip • “Scatter My Bones” worksheet

Procedure Note: This activity is best done in teams of two. 1. Chain six rubber bands of equivalent length and width to each other.

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Figure 7

3. Attach the end of the chained rubber bands to the ceiling or rod about six inches away from the Rip Cord Parachute Drop. A binder clip works well for this purpose. 4. Attach the other end of the chained rubber bands to the paper clip hook of the action figure. 5. One team member should slowly pull the action figure upward toward the ring bumper of the Rip Cord. The other team member should be in position to watch for the lowest height that the action figure reaches. Record that measurement on the “Scatter My Bones” worksheet. 6. Add three more rubber bands to the chain and repeat Step 5. 7. Keep adding three more rubber bands at a time, repeating Step 5 each time until a total of 21 rubber bands are chained together. 8. Complete the “Scatter My Bones” worksheet.

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Mathematics Activity – Scatter My Bones Scatter My Bones Worksheet 1. Follow the procedure on the previous page and complete the data table below. 2. Plot the data on the graph below. This type of graph is called a scatter graph, as the data points are scattered on the graph.

No. of Rubber Bands

1.75

Lowest Height (m)

1.5

6 1.25

12 15 18 21

Lowest Height (m)

9

1

.75

.5

.25

0

5

10

15

20

25

30

35

Number of Rubber Bands

3. Using a ruler or other straight edge, draw a line through the data that best fits the general trend of the data. Some points should be above the line and some below the line. This line is called the line of best fit, and it represents the data as a linear function. 4. Extend the line until it crosses the horizontal axis of the graph. This is the point at which the lowest height is zero, or the action figure is just at the floor level when dropped. 5. Determine, to the nearest whole rubber band (partial rubber bands do not work well), how many rubber bands the graphed data predicts will work to get your action figure to drop exactly to floor level. This number will be the whole number value on the horizontal axis where the line of best fit intersects the horizontal axis. Perilous Plunge Activity Guide 59779 V0708

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Mathematics Activity – Scatter My Bones 6. Your predicted number of rubber bands required is _______ 7. Add additional rubber bands to the chain so that you have the predicted number of rubber bands in the chain. 8. Hook the action figure to the rubber bands and to the Rip Cord and pull the action figure up to the bumper ring to release it. 9. How close did the action figure come to bumping its head? 10. Do you need to add to or subtract from the number of rubber bands used? If so, how many do you estimate you will need to add or remove? _______

Inquiry Questions 1. How far would your action figure be from the floor if you used 16 rubber bands? _______ 2. If the ceiling were only 1.55 meters tall, how many rubber bands would you chain together to have your action figure barely survive? _______ How did you arrive at this answer?

3. If you switched to rubber bands twice as wide as the ones you used, estimate the number of rubber bands it would take to drop your action figure to floor level. _______ Explain your answer.

4. If your action figure weighed 1.5 times as much, how many rubber bands would you estimate you would need? _______ Explain your answer.

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Engineering Challenge – Build It, They Will Jump Understanding the Challenge Engineering pulls the three disciplines – science, technology and mathematics – together to provide a solution to a problem. That problem may be designing a bridge to cross a river, determining what the most efficient shape would be for an airplane wing and what materials would be best for the construction, or designing and building a bungee jump ride at an amusement park.

The Challenge Note: This challenge should be done in teams of two. Given the information and data from the previous activities, determine the appropriate width and number of rubber bands to use for a special tag team bungee jump that combines your and your partner’s action figures. You must predict the width and number of rubber bands that it will take for a safe jump before you try the jump with the action figures. The action figures should be fastened together back-to-back using rubber bands or string. They should have a paper clip hook at their boundtogether ankles for attachment to the Rip Cord Parachute Drop.

Scoring Rubric Within 5 cm of the floor – 100 points Within 5 to 10 cm of the floor – 90 points Within 10 to 20 cm of the floor – 80 points Within 20 to 40 cm of the floor – 70 points More than 40 cm from the floor – 60 points

Procedure You are on your own. Use what you have learned to this point and write your prediction below. Rubber band width: _______ Number of rubber bands: _______ After recording your prediction, drop the pair of figures using the number and width of rubber bands you predicted. Distance to the floor of the dropped tag-teamed action figures using the numbers above: _______ Perilous Plunge Activity Guide 59779 V0708

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Teacher Notes Equipment

Activities

Included in the Perilous Plunge package from Pitsco are six Rip Cord Parachute Drop devices. These devices can be shared by student teams as they work through the activities.

All activities are best done in teams of two: one student controlling the Rip Cord and the other observing and measuring the drop distance.

The Rip Cord is best used with a suspended ceiling of heights of seven to 10 feet for these activities. Connectors come with the Rip Cord for easy connection to the suspended ceiling grid work. To keep the rubber band bungee cord from being tangled with the Rip Cord or the action figure, the end of the cord (the rubber bands chained together) should be attached about five to six inches away from the Rip Cord. The best way to accomplish this is by using binder clips to attach the cord to the ceiling grid. About 100 feet of twine is supplied with the Rip Cord to allow the device to drop objects from gymnasium ceilings and other tall places. This is not recommended for the Perilous Plunge activity, and much of the twine can be cut and removed for easier maneuvering by students. A fairly weighty object, such as a large washer, can be tied to the free end of the twine to keep it from getting loose and becoming disconnected from the Rip Cord.

Materials If desired, you can provide action figures for the students rather than having them bring them from home. In this manner, the students would have the same action figure to work with.

All the activities are stand alone, with the exception of the Engineering Challenge, which draws on the experiences from the other activities. The activities can be done in any sequence – with the noted exception of the Engineering Challenge, which would be an obvious final activity. Time requirements for each activity will vary with class size and maturation. In general, you will need one class period per activity.

Measurement Systems Students may use customary units or metric units at your discretion.

Other Any pages of this document can be photocopied for use in your classroom. They should not, however, be photocopied for distribution to other teachers or parents who wish to do the activity. Many videos and photos of real live bungee jumping can be found on the Internet and can provide an exciting introduction for the activities.

Rubber bands of specific sizes are supplied with the Perilous Plunge activity. Other lengths and widths of rubber bands may be used, but you are encouraged to try them out before providing them for students.

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Answer Keys Exploring Hooke’s Law Worksheet Answer Key Analyzing the Results 1. As heavier masses are added to the rubber bands, what happens to the amount of stretch measured?

It increases.

2. What happens to the value of the elastic constant as heavier masses are added to the rubber bands?

It remains about the same.

3. What happens to the value of the elastic constant as the rubber band width increases?

It increases.

4. About what value would you expect the elastic constant of a 1/2" width rubber band to be?

It would be a value twice as big as the value computed for the 1/4" rubber band.

Choosing the Right Material Worksheet Inquiry Questions If you were the action figure: 1. Which of the rubber band widths would have given you the smoothest, most comfortable ride?

1/16"

2. Which of the rubber band widths might have given you the worst neck ache?

1/4"

3. If the goal of the ride is to provide both thrill (measured by the rapid change in acceleration) and enjoyment (least amount of neck and back aches), which of the rubber band widths might meet the goal?

1/8"

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Answer Keys Scatter My Bones Worksheet Inquiry Questions 1. How far would your action figure be from the floor if you used 16 rubber bands?

Answers will vary.

2. If the ceiling were only 1.55 meters tall, how many rubber bands would you chain together to have your action figure barely survive? _______ How did you arrive at this answer?

Answers will vary.

3. If you switched to rubber bands twice as wide as the ones you used, estimate the number of rubber bands it would take to drop your action figure to floor level. _______ Explain your answer.

Answers will vary.

4. If your action figure weighed 1.5 times as much, how many rubber bands would you estimate you would need? _______ Explain your answer.

Answers will vary.

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