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- 1. Physics 399 Research Presentation Impulse-Momentum Theorem Gavan Kaizawa Sam Campbell
- 2. HCPS III Physics standards Standard 1: Scientific Investigation – Discover, invent, and investigate using the skills necessary to engage in the scientific process. Standard 2: Nature of Science – Understand that science, technology, and society are related. Standard 3: Matter and Energy conservation Standard 4: Force and motion
- 3. Presentation Format follows the Scientific Method used for Lab Reports Physical Observation Research / Literature Review Hypothesis Experiment (safety, materials, procedures) Analysis (Data Table, Graphs, Sample Calculations, Error Analysis, Percent Error) Conclusions Peer Review
- 4. Physical Observations Students observe that various colliding objects will have a different time interval due to the impact Students observe that inelastic collisions stick together causing the time interval to be infinite Students observe that elastic collisions do not stick together but time interval do vary over a range of elasticity
- 5. Research & Literature Search Impulse is the integral of force over time measured in SI units of N.s Applying Newton’s 3rd law, every impulse has an equal and opposite impulse Deriving Impulse (J) from Newton’s 2nd Law Fnet = m.a = (m.∆v)/∆t Fnet ∆t = (m.∆v) Impulse (J) = change of momentum (p)
- 6. Research & Literature Search (cont’d) Unbalanced forces always accelerates an object In a collision, an object will experience a force resulting in a change of momentum The object will either speed up, slow down or change directions Impulse, as well as force and change in velocity, is a vector quantity
- 7. Research & Literature Search (cont’d) When calculating a quantity is a result from multiplying units measured by the y- axis and x-axis, you calculate the area under the graph for the relevant integral
- 8. Research & Literature Search Sources Baker, Martin John (2009), Physics – Impulse: On-line @ http://www.euclideanspace.com/physics/dynamics/collision/impulse.index Franklin, Bill (2005), Impulse and Momentum: An AAPT / PTRA Manual, AAPT: College Park, MD. Science Joy Wagon (2009), Impulse -When Push Comes to Shove: On-line @ http://regentsprep.org/Regents/physics/phys01/impulse/default.htm Spark Notes from Barnes & Nobles (2009), SAT Physics – Impulse: Online @ http://www.sparknotes.com/testprep/books/sat2/physics/chapter9section2 The Physics Classroom-comPADRE (2009), The Impulse- Momentum Change Theorem: On-line @ http://www.physicsclassroom.com/class/momentum/U4/1b.cfm
- 9. Hypotheses If the mass of an object is increased then the impulse created by the object will increase because of the greater force exerted by the object. If the elasticity of an object is increased then the impulse created by the object will increase because of the greater change in momentum of the object.
- 10. Impulse-momentum free fall lab In a nutshell: How mass affects impulse. Drop a solid wooden ball, racquetball, and tennis ball onto a force plate and record the impulse created by each. How elasticity affects impulse. Drop a frozen (“inelastic”) racquetball and frozen (“inelastic”) tennis ball on a force plate and compare to racquetballs and tennis balls at room temperature.
- 11. Safety precautions No horseplay! (Sam!) Clear area of trip hazards Potential electrical hazards when recharging Vernier LabQuest and laptop computers Clean up lab work area when finished
- 12. Materials Vernier LabQuest data collector Vernier Logger Pro software laptop computer Vernier force plate Wooden ball, tennis ball, racquetball Meter stick and hollow tube Freezer
- 13. Equipment set up
- 14. Procedures Set up free fall apparatus as shown in previous diagram. Collect various balls to test the effects of masses and degree of (in)elasticity. Connect the force plate to the LabQuest unit and set data collection parameters: 2 sec record time, 120 samples/s. Zero force plate.
- 15. Procedures (cont’d) Take individual runs for each ball on the force plate while recording force and time data through the LabQuest unit. Download data into a laptop computer and analyze with Logger-Pro. Analyze and present data as force, time interval of impact, and impulse in a data table and in graph form.
- 16. Sample Vernier graph: 2 bounces of a racquetball
- 17. Sample Vernier graph (cont’d) First racquetball bounce, zoomed
- 18. Sample Vernier graph (cont’d) Impact of first racquetball bounce, zoomed Demonstrates Integrate function to calculate impulse.
- 19. Analysis: Sample Calculations Impulse = FΔt We can’t just multiply the peak force (highest force recorded) by the time interval (Δt) because throughout the impact the force varies through time. Realize that the area under the curve is the impulse on the force plate by the ball. Vernier units contain a function called Integrate that calculates the area under the curve for you. Use Integrate to calculate the ball’s impulse.
- 20. Analysis: Data table Ball Type ∆t (sec) Force peak (N) Impulse (N*s) wood ball 0.0216 165.5 2.043 tennis ball 0.0216 73.5 0.9414 "inelastic" tennis ball 0.0242 65.3 0.9231 racquetball 0.022 65.1 0.6613 "inelastic" racquetball 0.0247 59.3 0.6481
- 21. Analysis: Data graphs Ball type vs. Impulse 2.5 2 1.5 1 impulse (N*s) 0.5 0 wood ball tennis ball "inelastic" racquetball "inelastic" tennis ball racquetball type Inelastic vs. elastic impulse differences (zoomed in) 0.92 0.87 0.82 0.77 c 0.72 impulse (N*s) 0.67 0.62 tennis ball "inelastic" tennis ball racquetball "inelastic" racquetball type
- 22. Error Analysis The free fall apparatus helped to maintain a consistent height for each drop The experimenter dropping the balls may had a parallax error when aligning each ball to drop The free fall apparatus was resting on the force plate and could have attributed to a dampening affect on the data
- 23. Error Analysis (con’t) The balls had to be perfectly aligned in the center of the free fall apparatus. If they touched the apparatus during the fall, friction could have affected the results The assumption that freezing the tennis ball and racquet ball over a period of time will cause the balls to become inelastic; or rather, become more inelastic
- 24. Percent Error -the affect of mass on Impulse- Since there was no standard impulse available for comparison (no control in the first experiment), the data presented shows a correlation of impulse to mass for ball dropped (see bar graphs!!!)
- 25. Percent Difference -comparing the affects of elasticity- The percent difference comparing the affects of elasticity to inelasticity for: Tennis ball % difference = [(0.9914 - 0.9231) / 0.9914] 100 = 1.943 % difference Racquet ball % difference = [(0.6613 - 0.6481) / 0.6613] 100 = 1.996 % difference
- 26. Conclusions If a ball’s mass is increased then it will have a greater impulse on the object it strikes. If the elasticity of an object is increased then the impulse created by the object will increase.
- 27. Focusing activity: clocking your fastball How can you figure out an object’s speed just by measuring how hard it hits another object? Students throw a racquetball with all their might against an immoveable force plate, as a LabQuest unit records force and time data.
- 28. Clocking your fastball calculations Impulse = FΔt = Δ mv. We want to solve for v into the plate, not Δv, so we need to use a highly elastic ball so that vfinal ~ vinitial. Δv = vfinal – vinitial. Therefore if the ball is perfectly elastic, Δv = 2v. “Bouncing.” We can get force and Δt readings from the force plate, and can measure the mass of the ball. v = (FΔt)/(2m) Students convert m/s to mph; compare to Roger Clemens’ fastball.
- 29. Other student extensions Using a GoMotion sensor, students can record data on a ball’s position as it falls. Along with force plate data, students can verify the velocity of the ball at impact using: 3) Kinematic equations: v = vo + gt 4) Impulse-momentum: v = (FΔt)/(2m) 5) Conservation of energy: v = sqrt(2gh)
- 30. Mahalo! Questions? “Damn it, Jim! The GoMotion detector is less than functional!”

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