Linear Impulse – Momentum Relationship

Ft = mv = m(v2-v1)Impulse (Ns)Product of a force applied over a period of

time (Ft)Momentum (kg m/s)Quantity of motion. Product of mass * velocity

(mv)Positive (negative) changes in Linear

Momentum are created by Net positive (negative) Linear Impulse.

Course Reader: Kinetics, p 48 - 53; Linear Impulse 53-61

LINEAR IMPULSEWhy? • 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

Ft = mv = m(v2-v1)= mv2 - mv1

t

Net Linear Impulse (F*t) Generation

-800

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-200

0

200

400

600

800

0.000 0.040 0.080 0.120 0.160 0.200 0.240

Time (s)

Ground Reaction Force (N)

Horizontal

Vertical

Positive Impulse

Negative Impulse

Linear impulse magnitude = area under the force-time curve, is dependent upon …1) Ground reaction force magnitude (F)2) ground contact duration (t)

Free BodyDiagram

FFvv

FFhh

BWBW

Net Vertical Force = Fv(+)+BW(-)

touchdown take-off

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-600

-400

-200

0

200

400

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800

0.000 0.040 0.080 0.120 0.160 0.200 0.240

Time (s)

Ground Reaction Force (N)

Horizontal

Vertical

Positive Impulse

Negative Impulse

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)

Gro

und

reac

tion

forc

e (N

)

Ft = mv = m(v2-v1)= mv2 - mv1

V1V2

Free BodyDiagram

FFvv

FFhh

BWBW

-500

-250

0

250

500

750

1000

0.000 0.100 0.200 0.300

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

Hor

izon

tal G

RF

(N

)

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-250

0

250

500

750

1000

1250

0.000 0.050 0.100 0.150 0.200 0.250

time (s) after contact

Hor

izon

tal G

RF

(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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0

200400

600800

1000

120014001600

1800

0.000 0.050 0.100 0.150 0.200 0.250

H GRFH GRF

V GRFV GRF

Time (s) after contactTime (s) after contact

TouchdownTouchdown

Impulse-Momentum Relationship Impulse-Momentum Relationship FFt = HI = m(Vt = HI = m(V22-V-V11))

mVmVhh11

FFhhtt

Take-OffTake-Off

mVmVhh22

-400-200

0

200400

600800

1000

120014001600

1800

0.000 0.050 0.100 0.150 0.200 0.250

H GRFH GRF

V GRFV GRF

Time (s) after contactTime (s) after contact

TouchdownTouchdown

Impulse-Momentum Relationship Impulse-Momentum Relationship FFt = HI = m(Vt = HI = m(V22-V-V11))

mVmVvv11

Take-OffTake-Off

mVmVvv22

FFvvtt

-400-200

0

200400

600800

1000

120014001600

1800

0.000 0.050 0.100 0.150 0.200 0.250

H GRFH GRF

V GRFV GRF

Time (s) after contactTime (s) after contact

TouchdownTouchdown

Calculating Net Linear Impulse Using GeometryCalculating Net Linear Impulse Using Geometry

mVmVvv11

Take-OffTake-Off

mVmVvv22mVmVhh11

Take-OffTake-Off

mVmVhh22

Push Tip Load

Plate Departure

Back Somersault: Take-off Phase

Vv

Vh

BackwardsRotation

Needs: Needs: Vertical Impulse (net positive), Vertical Impulse (net positive), Horizontal Impulse (net negative), Horizontal Impulse (net negative), Backward-directed Angular ImpulseBackward-directed Angular Impulse

How?How?

BACK Somersault

FFVV

FFHH

FFRRFFVV

FFHH

time prior to take-off take-off

Generation of Linear Impulse Generation of Linear Impulse During a Back DiveDuring a Back Dive

Near Zero Initial Near Zero Initial TBCMTBCM

Momentum (mv)Momentum (mv)

Net Positive Vert. mvNet Positive Vert. mvNet Negative Horiz. Net Negative Horiz. mvmv

InitiationInitiation Take-OffTake-Off

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0

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1000

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-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1

Time Prior to Take-off (s)

Force (N)

Horizontal RF

Vertical RF

VRF

BACK Somersault

time prior to take-off take-off

FFVV

FFHH

FFRRFFVV

Generation of Linear Impulse Generation of Linear Impulse During a Back DiveDuring a Back Dive

time prior to take-off take-off

FFHH

QuickTime™ and aDV/DVCPRO - NTSC decompressor

are needed to see this picture.

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

F=malinear 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

FFvv

FFhh

FFBWBW

Vertical

Fv = FBW(-) + Fv

(+)

Fv = mav

Fv = m (v/t)Fv t = m (v)

ah

aavv

Linear Impulse – Momentum RelationshipFt = mv = m(v2-v1)

F=malinear 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

FFvv

FFhh

FFBWBW

Horizontal

Fh = Fh(+)

Fh = mah

Fv = m (v/t)Fv t = m (v)

ah

aavv

Linear Impulse – Momentum RelationshipFt = mv = m(v2-v1)

Verticalforce

Horizontalforce

BWBW

HGRFHGRFVGRFVGRF

BWBWBWBW

V GRFV GRF == BWBW V GRFV GRF >> BWBW

Linear Impulse – Momentum Relationship

Ft = mv = m(v2-v1)

V GRFV GRF = 0= 0

Verticalforce

Horizontalforce

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0

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-0.500 -0.400 -0.300 -0.200 -0.100 0.000

Bodyweight

Time (s) prior to departure

GroundReaction

Forces(Newtons)

BWBW BWBWBWBW

HGRFHGRFVGRFVGRF

-600

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0

200

400

600

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1200

-0.500 -0.400 -0.300 -0.200 -0.100 0.000

Body weight

Time (s) prior to departure

GroundReaction Forces

(Newtons)

Net Impulse = Change in Momentum( Force) *(time) = (mass)*(velocity)

Increase in the positive vertical velocity

Increase in the negative horizontalvelocity

(+) verticalimpulse

(-) horizontalimpulse

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

Momentum Transfer

Mechanical Objective of the Shot PutMaximize the horizontal distance traveled by the shot

Projectile Motion

How does the shot become a projectile?

Total body momentum is generated and passed on to the shot

Take-Home Message

Each foot (ground) contact is an opportunity to:

a) increase, b) decrease, or

c) maintain your total body momentum.