Q4E Case Study 1  Impulse
Proposed Subject usage:
Mathematics / Physics (A/AS level)
Sports Science (Degree Yr 1/2)

AQA
Physics ALevel 2009 Specification 


11.1.7
Momentum, conservation of linear momentum
Recall and use of p = mv
11.1.8 Newton’s laws of motion. Candidates
are expected to know and to be able to apply the three
laws in appropriate situations.
Force as the rate of change of momentum:
F = D(mv) /Dt
For constant mass: F = ma 

Introduction
Impulse is a measure of what is required to
change the motion of an object and is a product of the force
applied and the time over which this force is applied.
Impulsemomentum relationship : this relationship relates the momentum of
an object to a force and the time over which the force acts.
Impulse = change in momentum.
 Momentum = mass x velocity: p = mv
 Newton’s second law states:
 F = m x a
 As a = dv/dt F = m(dv/dt)
 And further: F = d(m x v)
 If each side is multiplied by dt: F x dt =
d(mv)
 Or: F dt = mvfinal  mvinita
Using video footage of a sprinter leaving the blocks the impulse
applied by the athlete to the blocks and the athlete’s momentum
leaving the blocks can be demonstrated. Quintic software allows
a variety of kinematic and kinetic variables, such as velocity,
acceleration, impulse, momentum and force, to be calculated.
Methods
The video has been digitised and calibrated
and still images have been captured from the video to show the
stages of the sprint start in detail. The data has been exported
into excel and force, momentum and impulse have been calculated
(see spreadsheet provided).
Functions of the Quintic Software used:
Results


Front
foot 
Rear
foot 


Initial
Velocity (ms1) 
0.11 
0.19 


Final
Velocity (ms1) 
7.43 
6.27 


Initial
Momentum (kgms1) 
9.02 
15.58 


Final
Momentum (kgms1) 
609.26 
514.14 


Change
in Momentum (kgms1) 
600.24 
498.56 


Impulse
Time (s) 
0.36 
0.28 


Maximum
Force (N) 
607.84 
515.12 


Maximum
Acceleration (ms2) 
74.13 
62.82 


Impulse
(Ns) 
600.52 
498.01 

The results demonstrate that the front foot
produces a higher velocity, acceleration, and therefore momentum
than the rear foot and consequently the impulse produced by
the front foot is also greater. This increase in acceleration
from back to front (following the athlete’s centre of mass (COM))
helps to propel the sprinter away from the blocks. Notice that
(bold in the table):
Impulse = Change in momentum F Dt = mvfinal
 mvinitial
As the impulse produced by the athlete is closely
related to the velocity and acceleration with which the athlete
leaves the block a large impulse is necessary for greater acceleration
from the block. Maximum impulse would therefore be obtained
by producing a maximal force for a long period of time, therefore
obtaining maximal speed from the blocks. However, in a sprint
start the reaction time is a major variable in the start efficiency.
Thus, in order to remain on the blocks for only a short time
the greatest force possible needs to be produced. Performance
therefore is determined by the ability of the athlete to generate
maximal forces quickly and achieve the optimal impulse output. Forces produced by the feet are illustrated
in the graph below:
Conclusion
Coaches working on improving the sprint start
can measure impulse using this method and use training principles
and programmes to improve the athlete’s rate of force development,
thus increasing their impulse from the block. This will improve
their overall performance in the event. Each of the variables
in the table above can be analysed and improved, aiming to achieve
the optimal impulse for the athlete.
Teachers may use this method of calculating
performance kinetics to engage students’ interest whilst applying
sporting situations to this area of the syllabus. This study
can be adapted to compare different athletes or by manipulating
the calculations (allowing for different levels of study) to
apply this idea to the lesson.
Downloads
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Case Study 
Video avi.
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