Introduction to Sports Biomechanics: Analysing Human Movement ...

CAUSES OF MOVEMENT – FORCES AND TORQUES
examples from sport or exercise, other than the examples in this chapter, of the
application of each law.
Hint: You may wish to reread the sections on ‘Forces in sport’ (pages 164–80)
and ‘Momentum and the laws of linear motion’ (pages 183–5) before undertaking
this task.
2 Download a force–time Excel spreadsheet for a standing vertical jump from the
book’s website. The sample times (t) and magnitudes of the vertical ground reaction
forces (F) are shown in the first two columns of the spreadsheet.
(a) Obtain the vertical accelerations (a) in the third column by noting the jumper’s
weight (G) when standing still at the start of the sequence and using a = g F/G,
where g = 9.81 m/s 2 .
(b) Use a simplified numerical integration formula for the change in the magnitude
of the vertical velocity from one time interval, i, to the next, i+1, over sampling
time ∆t: ∆v = (a i + a i+1)∆t/2, and noting v = 0 at t = 0. Put your velocities in the
fourth column of the spreadsheet.
(c) Using a similar numerical integration formula for the change in magnitude of
the centre of mass vertical displacement (y) from one time interval, i, to the
next, i+1, over sampling time ∆t: ∆y = (v i + v i+1)∆t/2, and defining y = 0 at t = 0.
Put your displacements in the fifth column of the spreadsheet.
(d) Plot the time series of vertical force, and centre of mass vertical acceleration,
velocity and displacement. Compare your answers with Figure 5.12.
(e) What was the jumper’s take-off velocity and what was the maximum height
reached by the centre of mass?
Hint: You should reread the section on ‘Force–time graphs as movement patterns’
(pages 186–8) before undertaking this task. If you are unfamiliar with performing
simple calculations in Microsoft Excel, go to their online help site, or see your tutor.
3 Photocopy Figure 5.13(a) or download it from the book’s website. Measure the
x and y coordinates of each of the segment end points. Then use a photocopy of
Table 5.1, or download it from the website, to calculate the position of the ski
jumper’s whole body centre of mass in the units of the image. Assume that the joints
on the right side of the body have identical coordinates to those on the left side.
Finally, as a check on your calculation, mark the resulting centre of mass position on
your figure. If it looks silly, check your calculations and repeat until the centre of
mass position appears reasonable. Then repeat for Figure 5.13(b).
Hint: You may wish to reread the section on ‘Determination of the centre of mass of
the human body’ (pages 189–91) before undertaking this task.
4 Carry out the inclined plane experiment, mentioned on pages 167–8, to calculate
the coefficient of friction between the material of a sports surface and a training
shoe and other sports objects. You only need a board covered with relevant material,
a shoe and a protractor.
Hint: You may wish to reread the subsection on ‘Friction’ (pages 166–7) before
undertaking this task.
5 Obtain a video recording of top-class diving, trampolining or gymnastics from
your university resources or from a suitable website. Carefully analyse some airborne
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