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Linear Impulse – Momentum Relationship Ft = m  v = m(v2-v1)

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)

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Linear Impulse – Momentum Relationship Ft = m  v = m(v2-v1)

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  1. 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

  2. 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 Vv2 Vh1 Vh2 t Ft = mv = m(v2-v1) = mv2 - mv1

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

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

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

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

  7. Take-Off mVh1 mVh2 Fht Impulse-Momentum Relationship Ft = HI = m(V2-V1) Touchdown H GRF V GRF Time (s) after contact

  8. H GRF V GRF Time (s) after contact Impulse-Momentum Relationship Ft = HI = m(V2-V1) Take-Off Touchdown mVv1 mVv2 Fvt

  9. H GRF V GRF Time (s) after contact Calculating Net Linear Impulse Using Geometry Take-Off Take-Off Touchdown mVv1 mVv2 mVh1 mVh2

  10. Back Somersault: Take-off Phase Vv Vh Backwards Rotation Push Tip Load Plate Departure Needs: Vertical Impulse (net positive), Horizontal Impulse (net negative), Backward-directed Angular Impulse How?

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

  12. time prior to take-off time prior to take-off take-off take-off Generation of Linear Impulse During a Back Dive BACK Somersault VRF FH FH FV FV FR

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

  14. Linear Impulse – Momentum RelationshipFt = mv = m(v2-v1) F=ma linear acceleration of the athlete’s center of mass is determined by the sum of forces acting on the center of mass Vertical Fv= FBW(-) + Fv(+) Fv = mav Fv = m (v/t) Fvt = m (v) Free Body Diagram Mass-Acceleration Diagram av FBW ah Fh Fv

  15. Linear Impulse – Momentum RelationshipFt = mv = m(v2-v1) F=ma linear acceleration of the athlete’s center of mass is determined by the sum of forces acting on the center of mass Horizontal Fh = Fh(+) Fh = mah Fv = m (v/t) Fvt = m (v) Free Body Diagram Mass-Acceleration Diagram av FBW ah Fh Fv

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

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

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

  19. Projectile motion Impulse Momentum Transfer 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.

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

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

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

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