Science of NHL Hockey: Projectile Motion Subject Area: Physical Science Grade Level: 5–8 (Physical Science) Lesson Title: Projectile Motion National Science Education Standards: Science as Inquiry: 5–8 Motions and Forces: 5–8 Suggested Prior Knowledge: concepts of velocity and angles; lab techniques of measuring velocity and angles. Note that students might more easily grasp the concepts in this video if they have already viewed the video Newton’s Three Laws of Motion. Purpose and Introduction: This video uses the hockey technique of a wrist shot to give students an understanding of the relation between uniform linear motion and uniform angular motion, and how a projectile moves. Key Vocabulary: angular motion—movement of an object around a fixed point or axis. angular velocity—the number of rotations an object makes around a fixed point or axis per unit of time. linear motion—movement of an object along a straight line. motion—change in the position of an object with respect to time. projectile motion—movement of an object through space along a path determined by an initial velocity and the effect of gravity and air resistance. Objectives: 1. Students will differentiate among three common kinds of motion in two dimensions. 2. Students will design and carry out an investigation to measure linear and angular velocity. 3. Students will design and carry out an investigation to determine the shape of a projectile’s path. Materials: - safety goggles - 2 stopwatches - tape measure - small flexible tubing - adapter to faucet - nozzle - catch pan (or sink) - ring stand Projectile Motion (Middle School) 1 - clamps - clear plastic sheet - erasable marker - paper - pencil Procedure: 1. Before students watch the video, ask them what projectiles are and how they might describe the path of a projectile. Most will likely describe something like a bullet and a path that shoots straight out, and keeps going. After students watch the video, lead a discussion in which they can correct their own thinking about projectile motion. Have volunteers describe the other kinds of motion in the video and compare and contrast them. Use questions such as these to prompt discussion: What is an example of linear motion? What is an example of angular motion? What is a projectile? What path does a projectile follow? 2. Lab protocols should be followed incorporating safety equipment. Goggles must be worn at all times. 3. Guide students to design an investigation that will allow them to observe the connections among linear, angular, and projectile motion. Questions such as the following can help focus students’ plans and guide them: What are the units of linear velocity? How do you measure linear velocity? If an object rotates around its axis once per second, what is its angular velocity in rotations/second? How do you measure angular velocity? How can you record the path of a projectile? How can you measure the velocity of a projectile? Comparing Linear and Angular Speed 4. One way students might explore linear and angular speed is with one student spinning slowly in the center of an open space (a football field, for example). The student should make one complete rotation every 12 seconds (one quarter of a rotation in 3 seconds, or 0.083 rotation/second). Make sure he or she does not get dizzy. 5. Then two students could link arms with the spinning student, one on each side, and walk in small circles. Expand the line of students by having more pairs of students link arms, while the student at the center spins at the same rate. One student with a stopwatch measures the angular velocity of rotation. (Make sure that all parts of the line move with the same angular speed f.) Projectile Motion (Middle School) 2 6. More students could link arms until the circle grows too large for the outermost students to keep up easily (or no other students are available). Students should make two complete circles at maximum size. The two outermost students should then break away from the others and walk in a straight line at the same speed. (They may need to follow one of the lines marked on the field.) A second student with a stopwatch measures the time they need to cover a predetermined distance. 7. Measure the radius of the circle traveled by the students at the end of the line. Calculate the speed of the outermost students using their angular speed, the radius of the circle, and the formula v = 2πrf. Students compare the speed calculated for the outermost students walking in a circle to the linear speed measured directly. (They should be equal). Graphing Projectile Motion 8. Brainstorm ways with students that they might be able to document the path of a projectile so that they could then transfer the patterns to graph paper. One possibility students might envision is to connect tubing to a faucet to fashion a hose and clamp it to a ring stand near its base. They can adjust the tubing so that it is pointed upward and produces an arc of the size that would fit on a regular sheet of graph paper (about 20 cm wide and about 30 cm high). Elicit from students where the speed of the water is greatest (at the bottom of the arc) and where it is least (at the top of the arc). 9. Students could then clamp a plastic sheet vertically and align it close to the stream of water. This allows them to trace the path of the water on the dry side of the plastic with the marker. plastic sheet ring stand with clamps tubing connected to water spigot arc of water catch pan 10. With the water off, students could attach a sheet of graph paper to the dry side of the plastic, making sure that the paper is vertical. They trace the arc onto the graph paper. By folding the graph paper students should be able to recognize that it is symmetrical. If they do not know the name of the figure, remind them that the video identified the path of a projectile as a parabola. Projectile Motion (Middle School) 3 11. To follow up this investigation, have students determine what initial angle for the stream of water produces the greatest horizontal range. Have each group sketch all the paths they try on a single piece of paper and compare its sketch to sketches by other groups. Then ask the groups what angle a hockey goalie should use in order to get maximum range when throwing a puck (The puck should leave his hand with a path 45 degrees from the vertical). Additional Resources: http://www.korpisworld.com/Mathematics/diversions/activity_for_angular_velocity.htm http://www.uwstout.edu/physics/upload/UNIFORM-CIRCULAR-MOTION.pdf http://www.srri.umass.edu/sites/srri/files/mop_samples/ActAT016.pdf http://teachingphysics.wordpress.com/2009/03/01/projectile-motion-activity/ http://www.srri.umass.edu/sites/srri/files/mop_samples/ActAT009.pdf http://jersey.uoregon.edu/vlab/Cannon/ http://pdgusers.lbl.gov/~aerzber/aps_motion.html#projectile http://www.livestrong.com/article/447525-projectile-motion-of-golf-balls/ http://mrfizzix.com/basketball/index.htm Projectile Motion (Middle School) 4 Student Worksheet for Projectile Motion Experiment Title: _____________________________Date: __________Name: _____________ Student Hypothesis: _____________________________________________________________ Materials: _____________________________________________________________________ ______________________________________________________________________________ Wear safety goggles for all lab work. ____________________________________________________________________________ ____________________________________________________________________________ ____________________________________________________________________________ ____________________________________________________________________________ ____________________________________________________________________________ ____________________________________________________________________________ ____________________________________________________________________________ ____________________________________________________________________________ ____________________________________________________________________________ ____________________________________________________________________________ Data and Observations: Projectile Motion (Middle School) 5 Analysis of Data: _______________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ Conclusion: ___________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ Projectile Motion (Middle School) 6