SCIENCE AND ENGINEERING OF THE 2014 OLYMPIC WINTER GAMES: Physics of Figure Skating - Integration Guide (Grades 7-12) Print

Objective:

Students synthesize science, technology, engineering design, and math concepts involved in the the role of center of mass in figure skating and apply their understanding to other curricular areas.


Introduction Notes:

SCIENCE AND ENGINEERING OF THE 2014 OLYMPIC WINTER GAMES

Physics of Figure Skating

 

INTEGRATION GUIDE

Middle School Focus / Adaptable for Grades 7–12

Lesson plans produced by the National Science Teachers Association.

Video produced by NBC Learn in collaboration with the National Science Foundation.

 

Background and Planning Information.............................................................. 1

About the Video....................................................................................................................... 1

Video Timeline ........................................................................................................................ 2

 

Promote STEM with Video................................................................................ 2

Connect to Science................................................................................................................... 2

Connect to Technology............................................................................................................ 3

Connect to Engineering........................................................................................................... 3

Connect to Math...................................................................................................................... 4

 

Incorporate Video into Your Lesson Plan........................................................... 5

Integrate Video in Instruction................................................................................................. 5

            Bellringer...................................................................................................................... 5

            Explain.......................................................................................................................... 5

            Homework.................................................................................................................... 6

            As Part of a 5E Lesson Plan.......................................................................................... 6

Connect to … History............................................................................................................... 6

Connect to … Geography......................................................................................................... 6

Connect to … Physical Education............................................................................................ 7

Use Video as a Writing Prompt............................................................................................... 8

 

Connect Video to Common Core ELA................................................................ 8

Common Core Standards for ELA............................................................................................ 8

Facilitate Inquiry through Media Research............................................................................ 8

Make a Claim Backed by Evidence.......................................................................................... 9

Present and Compare Findings............................................................................................... 9

Reflect on Learning.................................................................................................................. 9

Inquiry Assessment................................................................................................................ 10

 

 

 

Background and Planning

 

About the Video

Physics of Figure Skating discusses the important concepts of center of mass and projectile motion in figure skating. Featured athletes are Olympic medalist and former world champion

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Evan Lysacek and Ashley Wagner, who will be competing at Sochi as a first-time Olympian. Also

featured is Brad Orr of the Physics Department at the University of Michigan. The video points out that a skater’s center of mass must remain above the point where the skates contact the ice. The video also explains that, when the skater is airborne (and thus described as a projectile), the center of mass moves in a parabolic path, because of the independence of the horizontal and vertical parts of this motion. The horizontal component of the velocity is constant, while only the vertical part is affected by gravity.

 

Video Timeline

0:00     0:14     Series opening

0:15     0:50     Introducing Lysacek, Wagner, and Gold

0:51     1:04     Making figure skating look effortless requires an understanding of physics

1:05     1:40     Introducing Orr and center of mass

1:41     1:56     Finding the center of mass of a figure skater and why it is unstable

1:57     2:35     Importance of keeping center of mass above point of support

2:36     3:42     Projectile motion and figure skating

3:43     4:28     Demonstration of importance of vertical and horizontal motion

4:29     4:55     Summary

4:56     5:08     Closing credits

 

Language Support: To aid those with limited English proficiency or others who need help focusing on the video, click the Transcript tab on the side of the video window, then copy and paste the text into a document for student reference.

 

 

 

Promote STEM with Video

 

Connect to Science

Science concepts described in this video include the idea that the different (perpendicular) components (or parts) of a projectile’s velocity are independent of each other; the horizontal part is uniform but the vertical part is accelerated downward by gravity. The uniform horizontal component of the motion is a good example of Newton’s First Law; since there is no horizontal force (except perhaps a small amount of air resistance), the speed remains constant. The vertical part, where the initial upward speed decreases and then becomes downward, is a good illustration of Newton’s Second Law; a constant downward force (gravity) produces a constantly changing vertical speed (that is, a constant acceleration).

 

Related Science Concepts

       inertia

       force

       velocity

       acceleration

       component

       projectile motion

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Take Action with Students

       Have students work in pairs, with one student practicing tossing a tennis ball (or similar object) straight up a few feet and then catching it, while the other student watches before switching roles. Have students predict what will happen if a student throws the ball up while walking. (Some might think the ball will land behind the thrower.) Then, have one thrower walk at a brisk pace in a straight line and execute the exact same motions, tossing the ball straight up and then catching it while walking. Each partner can watch the ball’s path against a background, and then describe the path’s shape (a parabola). Elicit from students that the ball’s horizontal motion during the flight did not change.

       Give students the scenario of one ball rolling off the end of a level table and another being dropped from table height at the same time. Have students predict which will hit the ground first. Then have students work in pairs to conduct the test. Elicit from students why the balls hit the floor simultaneously and ask them to explain why. Students should note that the horizontal motion had no effect on the vertical motion of falling.

 

Connect to Technology

Many years ago, ice skating was possible only outdoors, in winter, in cold climates. Often, these outdoor surfaces were uneven because of irregularities caused by weather and environment. Now, indoor ice skating rinks are common. They are also a large consumer of electricity. A typical ice rink consumes approximately 1185 MWh/year. That is equal to the average energy consumption of 109 households!

 

Take Action with Students

       Ask students how they think an indoor ice-skating rink could be made more energy efficient. They might work in groups to identify the separate uses for which electricity is consumed in an ice arena and then propose ways to make each use more energy efficient. After they have presented their ideas, have them do research on the Internet to find how ice skating rinks really are being made more energy efficient. An interesting resource can be found at: http://inhabitat.com/energy-efficient-liege-ice-rink-serves-up-a-whale-of-a-good-time-in-belgium/belgium-ice-rink-lead/. Then, have students compare and contrast their own ideas with actual practices before sharing with the class.

 

Connect to Engineering

The engineering design process uses human ingenuity to draw from science, math, and technology to solve a problem. The belt hanger demonstration at http://www.oapt.ca/resources/Demonstration Corner Archives/DC 01 Mechanics/2010-07 Belt Hanger Centre of Mass (McFarland).pdfoffers a simple demonstration that will quickly get students interested in center of mass. Many types of machines, vehicles, and structures must be designed with center of mass in mind. Cars are designed so that they don’t easily tip over when rounding turns. Passenger airplanes must be capable of stable, controllable flight. Buildings must be structurally sound. All of these purposes require calculations of the location of the object’s center of mass.

 

 

 

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Take Action with Students

Have students work in groups, with each group choosing a particular engineered object for which they think center of mass might be an important design consideration. Ask students to brainstorm to come up with ideas about why the center of mass might be important and how it might affect the object’s design. Then, have them do research to find if and how center of mass is actually incorporated in engineering their object. Have them later present their findings to the rest of the class.

 

Connect to Math

The location of an object’s center of mass can be calculated as a sort of weighted average, which is a commonly used technique for many applications. Students may be familiar with simple averaging, in which numbers are added up and the sum then divided by the number of entries. They might not have thought about situations where the entries should be multiplied by some weighting factor first, and then the sum divided by the sum of the weighting factors.

Another idea discussed in the video is that of projectile motion and the resulting path, called a parabola. Parabolas are frequently encountered in mathematical applications and have many interesting properties and uses. They are part of a family of curves called conic sections.

 

Take Action with Students

       To explore weighted averages, suggest to students that you have three classes of a certain subject, and that you are thinking of curving the grades for a test, based on the average of all the scores. However, instead of calculating that, you have already found separate averages for each class, and of course you know the number of students in each class. Ask students to brainstorm a way to get the overall average score without having to go back and add up all the individual scores again. Lead a class discussion about exactly how such calculations can be made, and also ask students to think of other reasons for doing this procedure. An example might be accurately finding an annual (365 day) average of a quantity for which monthly averages have already been calculated (considering month lengths range from 28 to 31 days).

       Show students a conical object, preferably a wooden one already sliced into segments to illustrate the conic sections: circle, ellipse, parabola, and hyperbola or an image such as that at http://csep10.phys.utk.edu/astr161/lect/history/newtonkepler.html. Before showing the students the individual pieces, ask them to draw what they think these various slices will look like in cross-section when the cone is disassembled. Then take it apart and show the pieces, comparing them to the students’ predictions.

       To encourage more advanced students to explore parabolic shapes, have students make a rectangular grid, with a spacing of 0.1 centimeters, on a large piece of poster board (or as an alternative, display a similar grid using a projector). Let students use smartphones or other video recording devices to create video of a small ball being tossed close to and paralleling the grid. Have students play this back, either directly or on a computer, pausing the video to collect several data points of the ball’s position, measured in meters. Then suggest students enter their data (calling the horizontal coordinate x and the vertical one y) in a spreadsheet program to mathematically model a parabola. If students require further assistance, use the following steps (using Microsoft's Excel as a model).

 

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       Set up a spreadsheet with the following entries: A1: “x”, B1: “y”, C1: “y predicted”, D1: “error”, E1: “absolute error”, G1: “a”, H1: “b”, I1: “c”, G2: “-0.4”, H2:”4”, I2: “-4”,C2: “=$F$2*A2^2+$G$2*A2+$H$2”, D2: “=C2-B2”, E2: “=ABS(D2)”

       Students might then enter the first x and y values in A2 and B2, respectively, and then additional values below those, with the x’s in column A and the y’s in column B. Supposing they enter 5 pairs of data, they might then copy C2 through E2 and paste these down through row 6.

       Then, they might enter these additional values: C8: “averages”, D8: “=AVERAGE(D2:D6)”, E8: “=AVERAGE(E2:E6)”

       Now students might try changing the values of a, b, and c (in cells G2, H2, and I2) to try to get the average net and absolute errors (in cells D8 and E8) as small as possible.

Ensure students understand that what they are doing is finding the a, b, and c values in the equation for a parabola, of the form y = ax2 + bx +c. Students who have had algebra may have seen this already.

As an enhancement, have students insert a chart (using the program's help features, if needed) in which they plot both the y values and the predicted y values versus x. They may want to do this before starting the process of finding a, b, and c, to help visualize what they are doing. Finally, there is an option to add a trendline to the graph and display its equation. Students might do this (for the actual y values, not the predicted ones—or, optionally, for both) and compare the a, b, and c values the program thinks are best with the ones they came up with. They could also enter the program's values in the cells for a, b, and c, and see how small the errors are.

 

 

Incorporate Video into Your Lesson Plan

 

Integrate Video in Instruction

As Part of the Day

       Bellringer Show the video as students are getting settled for class. Direct them to determine how they might use the video to plot the path of the skater (a projectile) moving through the air. A difficulty with this is that the camera is more or less following the skater, so that some ingenuity may be required to determine her motion against the background. Have students brainstorm in groups to create a way to do this (e.g., something involving the background scenery). Another challenge might be deciding what point on the skater’s body to plot; it should be the center of mass, but how do we know where that is? They might then plot points and draw a smooth curve through them.

       Explain Project the video on a whiteboard and pause it at 0:41, or at another point that clearly shows a skater spinning, with the point of contact between the skates and ice visible. Have students trace the skater’s body and carefully make a cardboard cutout of it. Have them then draw a vertical line from the point where the skate touches the ice, through the cutout. The center of mass supposedly lies along this line. Students might then attach a string to the skate (at the point of ice contact), hang the cutout from it, and trace an extension of the string to see if it coincides with the vertical line representing the skater’s axis of rotation. If they coincide closely, students will have verified, confirmed, or

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corroborated (all good vocabulary words) the idea that the video presents about the center

of mass remaining over the point of contact. However, there may be a significant discrepancy. If so, ask students to think of possible reasons for this. A major one is that the cutout is a two-dimensional model of a three-dimensional person; for example, one leg may be hidden behind the other. Also, the skater does not have uniform density (i.e., hair is much less dense than bone).

       Homework Have students find two objects in their home which have interesting shapes, and which they can easily bring to class. While at home, students might try balancing the object on a point or hanging it from a string attached at different points to locate its center of mass. When they bring the objects to class, they might swap objects with a partner to see if the other person arrives at the same result.

 

As Part of a 5E Lesson Plan

If you use a 5E approach to lesson plans, consider incorporating video in these Es:

       Engage Encourage interest in the concept of center of mass by having students try to stand on one foot while holding a moderately heavy object with that arm extended. The student will find it necessary to extend some part of the body in the opposite direction to keep the center of mass over the foot. Encourage students’ interest in projectile motion by having them walk rapidly across the room, holding a small object, and try to drop it into a can (without slowing down). Some students may wait until they are directly over the can before they let go, thus overshooting the target. After some practice, students should realize that they must let go some distance before the target, because the object will continue to move horizontally during its fall.

       Explain The video points out the independence of the vertical and horizontal components of a projectile’s velocity. In particular, a projectile falls vertically just like one with no horizontal motion, and moves horizontally as it would even if it were not falling. Newton’s Laws of Motion provide the explanation for this behavior. Ask students to explain projectile motion in their own words. If they have learned Newton’s Laws, ask them to explain how they apply here.

 

Connect to … History

Projectiles and History The video shows how an airborne ice skater can be described as a projectile. People have been using projectiles for sport, hunting, or war for many thousands of years. Some scientists think that Homo sapiens outcompeted and outlived the Neanderthals partly because of the development of an understanding of projectile motion (e.g., spears and arrows) and Neanderthals stuck with direct contact hunting (resulting in many broken bones). Modern hunting and warfare through the ages, all the way up to concerns over nuclear-armed intercontinental ballistic missiles, rely heavily on our control and understanding of projectiles. Ask students to brainstorm about ways humans have used projectiles, and follow up with information from some of these sources:

       http://usnavymuseum.org/Education_LP0014.asp

       http://ffden-2.phys.uaf.edu/211.fall2000.web.projects/J.%20Gentry%20and%20D.%20Arnold/phys211.html

       http://www.augustana.ualberta.ca/~hackw/mp480/exhibit/ballisticsMP480.pdf

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       http://wiki.croomphysics.com/index.php?title=The_Physics_of_the_Mighty_Medieval_Siege_Weapons

       http://www.nbcnews.com/id/28663444 - .UuZhpnn0CiZ

 

Connect to … Geography

Geographic Center Very similar to the concept of center of mass is that of the geographic center of a continent or political entity (i.e., a country or state). In fact, it is calculated in essentially the same way and could be found by similar methods, using a uniform thickness cut-out map of the area, by hanging from strings at two points or trying to balance on a pencil point. Students might choose a state or country and then use tracing or projection to draw a map of it on cardboard. Before cutting it out, students might mark where they think the center of mass might be. As a second step, they might then cut out their map and try hanging it from a string at two separate points, and trace and extend lines along the strings across the object. Where these lines intersect locates the center of mass. Another method to use instead of or in addition to this is trying to balance the cardboard map horizontally on a pencil point. The point at which it is best balanced is the center of mass. Students might measure the distance from their guessed point to the actual one.

Also, students could use Google Earth or another mapping program, along with this site: http://geography.about.com/library/weekly/aa120699a.htm to see how close their determined center of mass is from the official center of the political entity. This activity can also be used to reinforce or introduce the ideas of latitude and longitude. Related informative and interesting resources can be found at: http://www.geomidpoint.com/ or http://en.wikipedia.org/wiki/Mean_center_of_the_United_States_population

 

Connect to … Physical Education

       High Jump and Pole Vault These two track and field events involve consideration of both center of mass and projectile motion. The main objective is to reach a considerable height, so emphasis is placed on achieving a large initial vertical (upward) velocity component, but there must be some horizontal motion as well, or the athlete will hit the bar on the way up! Center of mass is important because, in both events, it is possible for the athlete to clear the bar while his or her center of mass actually passes under it. Ask students how this is possible and why it is desirable. Some good internet sources for video and information about this include:

       http://www.huffingtonpost.com/2013/03/20/high-jump-physics-video-athletes-center-mass_n_2911308.html

       http://nrich.maths.org/2742

       http://www.real-world-physics-problems.com/Real_World_Physics_Problems_Newsletter-pole-vaulting.html

       Acrobatics and Center of Mass Acrobats, high-wire artists, and other circus performers must be very aware of where their center of mass is located, and like ice skaters, must keep their center of mass directly over a contact point to avoid falling. They also find it necessary to use arms, legs, or other objects (such as a balance bar) to make small corrections, because having the center of mass over (as opposed to under) a contact point is an inherently unstable situation. There are some useful internet sources for information and activities about these ideas, such as

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       http://www.pbs.org/opb/circus/classroom/circus-physics/center-mass/

       http://www.scientificamerican.com/article.cfm?id=bring-science-home-circus-balance

       http://www.csmonitor.com/Science/2013/0624/Grand-Canyon-tightrope-walk-What-was-that-huge-pole-for

       http://www.sciencebuddies.org/science-fair-projects/project_ideas/Sports_p017.shtml#summary

 

Use Video as a Writing Prompt

       Close your eyes briefly and imagine that you are an Olympic ice skater. Now apply what you know to explain the skills and knowledge that would be necessary for you to be the best you can be for at least one skating skill (jumps, spins, lifts, throws).

       During a toss or jump the skater exhibits projectile motion. Explain the phenomena of changes in motion in terms of the concepts of acceleration (speed increases and decreases, as well as changes in direction) and the force(s) acting upon the skater.

       Citing evidence from other sources, assess how each of Newton’s three laws of motion is demonstrated by figure skaters in the video.

 

 

Connect Video to Common Core ELA

Encourage inquiry via media research. Student work will vary in complexity and depth depending on grade level, prior knowledge, and creativity. Use prompts liberally to encourage thought and discussion.

 

Common Core State Standards Connections: ELA/Literacy –

RST.6-8.1 Cite specific textual evidence to support analysis of science and technical texts, attending to the precise details of explanations or descriptions

WHST.6-8.1 Write arguments focused on discipline-specific content.

WHST.6-8.7 Conduct short research projects to answer a question (including a self-generated question), drawing on several sources and generating additional related, focused questions that allow for multiple avenues of exploration.

WHST.6-8.8 Gather relevant information from multiple print and digital sources, using search terms effectively; assess the credibility and accuracy of each source; and quote or paraphrase the data and conclusions of others while avoiding plagiarism and following a standard format for citation.

 

Facilitate Inquiry through Media Research

Show The Physics of Figure Skating and encourage students to jot down notes while they watch. Elicit questions and problems from group members and help them determine which are better explored using print media or online resources. Then, students should brainstorm to form a list of key words and phrases they could use in Internet search engines that might result in resources that will help them answer a question or solve a problem. Review how to safely browse the Web, how to evaluate information on the Internet for accuracy, and how to correctly cite the information found. Suggest students make note of any interesting tangents they find in their research effort for future inquiry. Encourage students with prompts such as the following:

       Words and phrases associated with our question are….

       The reliability of our sources was established by….

       The science, math and engineering concepts that underpin a possible solution are….

       Our research might feed into an engineering design solution such as….

       To conduct the investigation safely, we will….

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Related Internet Resources

       The Science of Jumping and Rotating: http://btc.montana.edu/olympics/physbio/biomechanics/bio-intro.html

       See John Skate: http://www.udel.edu/udaily/2011/may/high-tech-skating-051211.html

       Recent trends and changes in figure skating: http://www.britannica.com/EBchecked/topic/206646/figure-skating/221988/Recent-trends-and-changes

 

Make a Claim Backed by Evidence

As students carry out their media research, ensure they record their sources and findings. Students should analyze their findings in order to state one or more claims. Encourage students with this prompt: As evidenced by… I claim… because….

 

Present and Compare Findings

Encourage students to prepare presentations that outline their inquiry investigations so they can compare findings with others. Students might do a Gallery Walk through the presentations and write peer reviews as would be done on published science and engineering findings. Students might also make comparisons with material they find on the Internet, the information presented in the video, or an expert they chose to interview. Remind students to credit their original sources in their comparisons. Elicit comparisons from students with prompts such as:

       My findings are similar to (or different from) those of the experts in the video in that….

       My findings are similar to (or different from) those of my classmates in that….

       My findings are similar to (or different from) those that I found on the Internet in that….

 

Reflect on Learning

Students should reflect on their understanding, thinking about how their ideas have changed or what they know now that they didn’t before. Encourage reflection, using prompts such as the following:

       I claim that my ideas have changed from the beginning of this lesson because of….

       My ideas changed in the following ways….

       When thinking about the claims made by the experts, I am confused about....

       One part of the investigation I am most proud of is….

 

 

 

 

 

 

 

 

 

 

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Inquiry Assessment

 

Assessment Rubric for Inquiry Investigations

Criteria

1 point

2 points

3 points

Initial question or problem

Question or problem had had a yes/no answer or too simple of a solution, was off topic, or otherwise was not researchable or testable.

Question or problem was researchable or testable but too broad or not answerable by the chosen investigation.

Question or problem was clearly stated, was researchable or testable, and showed direct relationship to investigation.

References cited

Group incorrectly cited all of the references used in the study.

Group correctly cited some of the references used in the study.

Group correctly cited all of the references used in the study.

Claim

No claim was made or the claim had no evidence to support it.

Claim was marginally supported by the group’s research evidence.

Claim was well supported by the group’s research evidence.

Presentations

Groups neither effectively nor cooperatively presented findings to support their stance.

Groups effectively or cooperatively presented findings to support their stance.

Groups effectively and cooperatively presented findings to support their stance.

Findings comparison

Only a few members of the group constructively argued their stance.

Most members of the group constructively argued their stance.

All members of the group constructively argued their stance.

Reflection

None of the reflections were related to the initial questions.

Some reflections were related to the initial questions.

All reflections were related to the initial questions.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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