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Linear Impulse – Momentum Relationship F t = m v = m(v2-v1) Impulse (Ns) Product of a force applied over a period of time ( F t) Momentum (kg m/s) Quantity of motion. Product of mass * velocity (m v) Positive (negative) changes in Linear Momentum are created by Net positive (negative) Linear Impulse. Course Reader: Kinetics, p 48 - 53; Linear Impulse 53-61

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LINEAR IMPULSE Why? Mechanism for controlling linear velocity of the total body center of mass Necessary for successful completion of general locomotion tasks, and athletic movements Vv1 Vh1 Vv2 Vh2 F t = m v = m(v2-v1) = mv2 - mv1 tt

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Net Linear Impulse ( F* t) Generation Linear impulse magnitude = area under the force-time curve, is dependent upon … 1) Ground reaction force magnitude ( F) 2) ground contact duration ( t) Free Body Diagram FvFvFvFv FhFhFhFh BW Net Vertical Force = Fv (+) + BW (-) touchdown take-off

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Net Linear Impulse, the sum of negative and positive linear impulse generated during the entire ground contact phase (touchdown – take-off) time=0 touchdown force=0 take-off time (s) Ground reaction force (N) F t = m v = m(v2-v1) = mv2 - mv1 V1 V2 Free Body Diagram FvFvFvFv FhFhFhFh BW

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How do you generate large Horizontal Impulse (force*time)? – force, time, or a combination of force & time The mechanical goal of the task influences how Impulse is generated e.g. sprinters need to generate horizontal impulse quickly Time (s) after ground contact Horizontal GRF (N)

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time (s) after contact Horizontal GRF (N) Vh = 1.30 m/s Vh = 1.29 m/s Similar net changes in linear momentum can be achieved with different force-time linear impulse characteristics

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H GRF V GRF Time (s) after contact Touchdown Impulse-Momentum Relationship F t = HI = m(V 2 -V 1 ) mV h 1 FhtFhtFhtFht Take-Off mV h 2

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H GRF V GRF Time (s) after contact Touchdown Impulse-Momentum Relationship F t = HI = m(V 2 -V 1 ) mV v 1 Take-Off mV v 2 FvtFvtFvtFvt

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H GRF V GRF Time (s) after contact Touchdown Calculating Net Linear Impulse Using Geometry mV v 1 Take-Off mV v 2 mV h 1 Take-Off mV h 2

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Push Tip Load Plate Departure Back Somersault: Take-off Phase VvVv VhVh Backwards Rotation Needs: Vertical Impulse (net positive), Horizontal Impulse (net negative), Horizontal Impulse (net negative), Backward-directed Angular Impulse Backward-directed Angular ImpulseHow?

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BACK Somersault FVFVFVFV FHFHFHFH FRFRFRFR FVFVFVFV FHFHFHFH time prior to take-offtake-off Generation of Linear Impulse During a Back Dive Near Zero Initial TBCM Momentum (mv) Net Positive Vert. mv Net Negative Horiz. mv Initiation Take-Off

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VRF BACK Somersault time prior to take-offtake-off FVFVFVFV FHFHFHFH FRFRFRFR FVFVFVFV Generation of Linear Impulse During a Back Dive time prior to take-offtake-off FHFHFHFH

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Mechanical objective of the shot put: Vertical Impulse (net positive) Horizontal impulse (net negative - translate backward)

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F=ma linear acceleration of the athlete’s center of mass is determined by the sum of forces acting on the center of mass Free Body Diagram Mass-Acceleration Diagram FvFvFvFv FhFhFhFh F BW Vertical F v = F BW (-) + F v (+) F v = ma v F v = m ( v/ t) F v t = m ( v) ahah avavavav Linear Impulse – Momentum Relationship F t = m v = m(v2-v1)

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F=ma linear acceleration of the athlete’s center of mass is determined by the sum of forces acting on the center of mass Free Body Diagram Mass-Acceleration Diagram FvFvFvFv FhFhFhFh F BW Horizontal F h = F h (+) F h = ma h F v = m ( v/ t) F v t = m ( v) ahah avavavav Linear Impulse – Momentum Relationship F t = m v = m(v2-v1)

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Vertical force Horizontal force BW HGRF VGRF BW BW V GRF = BW V GRF > BW Linear Impulse – Momentum Relationship F t = m v = m(v2-v1) V GRF = 0

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Vertical force Horizontal force Body weight Time (s) prior to departure Ground Reaction Forces (Newtons) BW BW BW HGRF VGRF

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Body weight Time (s) prior to departure Ground Reaction Forces (Newtons) Net Impulse = Change in Momentum ( Force) *( time) = (mass)*( velocity) Increase in the positive vertical velocity Increase in the negative horizontal velocity (+) vertical impulse (-) horizontal impulse

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Mechanics of each phase influence the mechanics during the next phase. Impulse generation during the unseating phase will influence initial conditions of the blocking phase. Impulse Projectile motion MomentumTransfer

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Mechanical Objective of the Shot Put Maximize the horizontal distance traveled by the shot Projectile Motion

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How does the shot become a projectile? Total body momentum is generated and passed on to the shot

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Take-Home Message Each foot (ground) contact is an opportunity to: a) increase, b) decrease, or c) maintain your total body momentum.

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