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Kinematics, Impulse, and Human Running

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Kinematics, Impulse, and Human Running Kinematics, Impulse, and Human Running Kinematics, Impulse, and Human Running Purpose This lesson explores how kinematics and impulse can be used to analyze human running performance. Students will explore how scientists determined the physical factors that allow elite runners to travel at speeds far beyond the average jogger. Audience This lesson was designed to be used in an introductory high school physics class. Lesson Objectives Upon completion of this lesson, students will be able to: ஃ describe the relationship between impulse and momentum. ஃ apply impulse-momentum theorem to explain the relationship between the force a runner applies to the ground, the time a runner is in contact with the ground, and a runner’s change in momentum. Key Words aerial phase, contact phase, momentum, impulse, force Big Question This lesson plan addresses the Big Question “​What does it mean to observe?” Standard Alignments ஃ Science and Engineering Practices ஃ SP 4​. Analyzing and interpreting data ஃ SP 5​. Using mathematics and computational thinking ஃ MA Science and Technology/Engineering Standards (2016) ஃ HS-PS2-10(MA)​. Use algebraic expressions and Newton’s laws of motion to predict changes to velocity and acceleration for an object moving in one dimension in various situations. ஃ HS-PS2-3.​ Apply scientific principles of motion and momentum to design, evaluate, and refine a device that minimizes the force on a macroscopic object during a collision. ஃ NGSS Standards (2013) HS-PS2-2. ​Use mathematical representations to support the claim that the total momentum of a system of objects is conserved when there is no net force on the system. Kinematics, Impulse, and Human Running 1 ஃ Common Core Math/Language Arts Standards CCSS.ELA-LITERACY.RST.11-12.7.​ Integrate and evaluate multiple sources of information presented in diverse formats and media (e.g., quantitative data, video, multimedia) in order to address a question or solve a problem. Misconceptions Addressed ஃ This lesson addresses misconceptions about forces and impulse, including: ஃ The object with a larger mass exerts more force in an action-reaction pair. (Question 3) ஃ A change in momentum only happens due to a change in the force of the impact, not the change in time. (Question 9) ஃ Further information about student misconceptions on this topic can be found ​here​ and ​here​. Primary Sources ஃ Bite ​“​What Limits How Fast You Can Run?​” based on​: Weyand, Peter G., Deborah B. Sternlight, Matthew J. Bellizzi, and Seth Wright. 2000. “​Faster top running speeds are achieved with greater ground forces not more rapid leg movements​.” ​Journal of Applied Physiology​ 89(5): 1991–1999. ஃ Misconceptions ஃ Hestenes, David, Malcolm Wells, and Gregg Swackhamer. 1992. "​Force concept inventory​." ​The Physics Teacher ​30(3): 141–58. doi:10.1119/1.2343497. ஃ Singh, Chandralekha, and David Rosengrant. 2003. "​Multiple-choice test of energy and momentum concepts​." ​American Journal of Physics​ 71(6): 607–17. doi:10.1119/1.1571832. Materials Copies of the student handout and Science Bite for each student Time This lesson should take approximately one or two 50-minute class periods. Student Prior Knowledge Prior to conducting this lesson, students should be able to provide conceptual definitions of linear motion, perform quantitative analysis of kinematics, momentum, and impulse, relate forces to velocity and acceleration, and describe impulse as related to force and time, and to momentum. Instructions and Teacher Tips ஃ General Procedure ஃ Ask students students to brainstorm where the act of running may occur in their lives. As Kinematics, Impulse, and Human Running 2 students offer suggestions record them on the board. Have students work together to rank which activities require the fastest running motion. For example, a list may include, being late to class, playing sports, running outside, moving through an airport, etc. ஃ Have students read the Introduction and answer Questions 1–6 in groups. ஃ Review the answers to the questions with the class. In your discussion, make sure to review the information in the paragraph after Question 6. Students may accidentally skip this part, but it is important in understanding why a runner traveling at a constant velocity experiences an impulse with each step. ஃ As you discuss human running, you may want to call up a volunteer to model the different phases of running and what differences in stride frequency, stride length, contact time, aerial time, and maximum force applied to the ground would look like. ஃ You could also show the video “Slow motion running - side view” by EMU Running Science Laboratory, posted 2015. ​https://youtu.be/Jd8Jijb7jZY​ in order to aid your discussion. ஃ Have students read the Bite and answer Questions 7–11. ஃ Review the answers with the class. ஃ Tips, Extensions, and Variations ஃ You could have students collect their own data and compare it to the researchers’ plots. In order to do this groups of 2–4 students must make a video recording of themselves running on a long piece of paper with wetted shoes or bare feet. They will also need to measure the total distance they ran and the time it took them to run that distance (the time could be determined from the video or measured separately using a stopwatch). ஃ To determine stride length, students can measure the distance between one left (or right) footfall and the next left (or right) footfall. It is recommended that they measure multiple stride lengths and then average them. ஃ Students will then need to use video analysis software such as that available on Vernier’s LoggerPro or the free software Tracker to determine aerial time and contact time. They can do this by analyzing the time of the frames when their foot is in contact with the ground and those when their feet are not in contact with the ground. In order to get an accurate contact time, students must multiple the time they determine by 0.85. This factor accounts for the fact that the video doesn’t necessarily record the precise moments where a runner’s foot starts and finishes force delivery to the ground (due to shoe cushioning, etc). Scientists studying runners have simultaneously a) used force plates to measure exactly when forces are being applied to the ground by the foot and b) used videos like in this exercise to identify when the foot strikes and lifts off the ground. When they compared the estimates of contact time from video (b) to real contact time measured by force plates (a), they found that we consistently overestimate contact time from video. Real contact time was ~85% of the values predicted from video analysis, and therefore, students should adjust their video-derived contact time accordingly. Kinematics, Impulse, and Human Running 3 ஃ Students can then use the equation below to calculate maximum force scaled by body weight. This “scaling” means that the value students calculate here equals the force their runner created in newtons divided by their body weight in newtons. Therefore the number they calculate here has no units. This equation was determined by scientists who have studied the relationship between maximum force applied and running speed. In order to determine the maximum force, students first must determine running speed by dividing their total distance by their total time. Maximum force = [1.26 + (0.101 × running speed)] ஃ The class can then plot all of the data in order to make graphs like those in ​Figure 2 in the Student Handout. Each group will contribute one point on each graph. Hopefully the class will see similar trends to the researchers. If not, a discuss possible errors with the students. Example errors include: students not running normally, because of the odd situation, difficulty identifying the first and last frames of contact phase, difficulty measuring the stride length due to the runner not running in a straight line, etc. ஃ Newton’s laws of motion can help explain the concept of walking around in everyday life. The various different surface contacts between feet/shoes and ground affects the frictional coefficient, which in turn works against motion. The current field of sports science engages questions like these to study human performance analysis, making runners faster. You may consider the following prompts in order to push student thinking further: ஃ Walking on ice versus pavement, then running on ice versus pavement. Why does motion on smoother surfaces lead to slipping? ஃ Various styles of athletic footwear such as ballet slippers, cleats, bowling shoes, track shoes, spikes, flip flops, etc. Why do different sports use different shoes? How does friction impact athlete performance? Direct student conversation to blend from shoe style to corresponding leg motion needed to perform activities for respective shoes. Note the comparison of leg mechanics versus desired motion outcome. ஃ If students are interested, the impulse-momentum theorem can be derived quickly from Newton’s second law of motion and the equation for acceleration: Δv Δv F = ma and a = Δt , substitute Δt for acceleration Δv F = m Δt , rearrange F Δt = mΔv Big Question Discussion This lesson plan addresses the Big Question​ “What does it mean to observe?”​ In particular, why do scientists collect data on things that don’t seem to actually matter? If you choose to delve into the Big Question, consider the following ideas: Kinematics, Impulse, and Human Running 4 ஃ Make a class list of times that students observed something they didn’t think was important, but later was key. If students can’t think of examples in their own lives, discuss examples of television or movie detective shows. Connect their examples to the experiment described in the Bite. ஃ Make a class list of times that students wished they had made note of an observation.
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