1EXS 387 1“Sliding headfirst is the safest way to get to the next base, I think, and the fastest. You don't lose your momentum, and there's one more important reason I slide headfirst, it gets my picture in the paper.”PETE ROSEEXS 387 - BiomechanicsDr. MoranTuesday March 6, 2007Spring 2007Linear KineticsImpulseMomentumImpact2EXS 387 3Lecture Objectives• Momentum• Principle of Conservation• Example Problem• Impulse• Impacts• Perfectly Elastic• Perfectly Plastic• Coefficient of Restitution EXS 387 4• A 83 kg man runs on a treadmill with the incline set at 60. – What is the frictional force between his sneakers and the treadmill if the coefficient of friction is 0.34 between the surfaces. – Is this frictional force making it harder OR easier for the man to maintain his pace?3EXS 387 5Momentum• Def: “quantity of motion that a body possesses”– If a body has MASS and VELOCITY, then it has momentum• LINEAR MOMENTUM (M) =UNITS OF MEASUREMENT ( )EXS 387 6Momentum(con’t)• Momentum ∆  due to ∆ OR ∆•• VECTOR quantity so magnitude and direction are required4EXS 387 7MomentumSport Manipulations• By manipulating momentum in a sport setting we can produce different desired effects• Baseball: swing for fences VS. lay down a bunt• Volleyball: • Soccer: trap a ball VS pass a ball• Basketball: EXS 387 8MomentumUnderstanding Collisions• Sasha Cohen and Michelle Kwan have a head-on collision with Sasha skating 8 m/s to the right and Michelle skating 9 m/s to the left. If Michelle had a mass of 41 kg and Sasha 43 kg, then what would happen after the collision? – Sasha’s Pre-collision Momentum• M = m v• M = – Kwan’s Pre-collision Momentum• M = – Resulting Post-Collision Momentum• M = ASSUMPTIONS PRESENT1.) Both skaters stay on feet2.) No entanglement3.)5EXS 387 9Conservation of Momentum• “In the absence of external forces, the total momentum of a given system remains CONSTANT”• Pre-collision Momentum = Back to the skater example – what was the resulting velocity of Kwan-Cohen after the collision?M = m · vEXS 387 10Impulse• Def: Product of a force and the TIME in which it acts• UNITS OF MEASUREMENT: • When an impulse acts on a system  ∆ MOMENTUM IMPULSE =6EXS 387 11Impulse-Momentum RelationshipDerived from Newton’s Second LawMFtmvmvFttvvmFmaF∆=−=−==1212)(EXS 387 12Impulse Manipulation• If Impulse equals the FORCE times TIME, then how can Impulse be increased?• INCREASE • INCREASE DURATION • In baseball setting, why would a coach instruct a player to follow through? Who would this change the system’s momentum?7EXS 387 13Determining Impulse Graphically• The graphs represent the VERTICAL GRF during for vertical jump test for two trials• Area = • Impulse = AreaABEXS 387 14Relationships Between Ground Reaction Force Impulse and Kinematics of Sprint-Running Acceleration Hunter et al. Journal of Applied Biomechanics Feb 2005: Vol. 21 Issue 1. p. 31-43 13p• The literature contains some hypotheses regarding the most favorable ground reaction force (GRF) for sprint running and how it might be achieved. This study tested the relevance of these hypotheses to the acceleration phase of a sprint, using GRF impulse.• Thirty-six athletes performed maximal-effort sprints from which video and GRF data were collected at the 16-m mark. Results showed that relative propulsive impulse accounted for 57% of variance in sprint velocity. Relative braking impulse accounted for only 7% of variance in sprint velocity. In addition, the faster athletes tended to produce only moderate magnitudes of relative vertical impulse. • In conclusion, it is likely that high magnitudes of propulsion are required to achieve high acceleration. Although there was a weak trend for faster athletes to produce lower magnitudes of braking, the possibility of braking having some advantages could not be ruled out. Further research is required to see if braking, propulsive, and vertical impulses can be modified with specific training. This will also provide insight into how a change in one GRF component might affect the others.8EXS 387 15Impact• A collision characterized by the exchange of large force over a small time frame• Types of Impact• Perfectly Elastic: • Perfectly Plastic: at least one body deforms, does not regain original shape and bodies remain stuck togetherEXS 387 16Spectrum of ImpactsPerfectly ELASTICPerfectly PLASTIC9EXS 387 17Coefficient of Restitution (e)• “describes the relative elasticity of impact between objects”• Unitless Number• ELASTIC (1)  PLASTIC (0)• Relationship Governing Impact Velocities-e = (relative velocity after impact) / (relative velocity before impact)EXS 387 18Coefficient of RestitutionDetermining Experimentally• A basketball is dropped from a height of 2m and bounces to a new height of 1.6m. Determine the coefficient of restitution between the basketball and wooden floor.droppedbouncedhhe =droppedbouncedhhe =10EXS 387 19Review Questions• Introductory Problems: p415 #6-8• Additional Problems: p416 #6• Give two examples of how momentum can be increased?• How does the impulse-momentum relationship influence vertical jumping performance?• For a baseball catcher, why would they want to extend there arm prior to catching a pitch – explain in terms of impulse.• Explain the two types of impacts and give an example of each.• Conservation of linear momentum is based on what