Thinking about Biomechanics
NEWTON’S LAWS: WHAT’S THE BIG ATTRACTION? This is the second article in a regular series in which Steve Stanley of Siliconcoach explores various aspects of biomechanics. Some people, when asked who Sir Isaac Newton was, will reply that he was the person who had an apple fall on his head and at that moment invented gravity. Luckily for everyone at the time, apple growers included, gravitational attraction was already there and he just described its influences. Sir Isaac Newton is most famous for his breakthrough 1686 publication De Philosophiae Naturalis Principia Mathematica. It is the manuscript that challenged the mechanical views of Greek philosopher Aristotle, which had been believed for thousands of years (Knudson 2003). At the time Newton's Laws of Motion, together with his law of universal gravitational attraction and the mathematical techniques of calculus, provided a unified explanation for a wide range of physical phenomena (www.wikipedia.org). The importance of all his achievements cannot be overestimated. Most are still relevant today for objects not travelling near the speed of light. Although we may remember approaching such speeds on our youth, his three laws of motion are very relevant to our interest in human motion for the slower modern student. Whilst often described slightly differently in different references, they are basically the Law of Inertia, the Law of Acceleration and the Law of Reaction and will be briefly outlined below along with some applications. Newton’s First Law is called the Law of Inertia and is described by Knudson (2003, pg 132) as “objects tend to stay at rest or in a uniform motion unless acted upon by an unbalanced force”. This means that objects continue in their present manner, which may even be stationary, until some force changes that state. When designing practical activities to explain the Law of Inertia, the variables of interested are force and mass.
Find a slight downhill slope of 5 – 10 m that ends on a long flat surface. Have a student roll down the hill on a skateboard or bike and see how long it takes the force of friction to slow the rider down (air resistance is minimal at slow speeds). Now add weights to a backpack and repeat and then compare how far they rolled. The larger mass should have resulted in a longer roll before stopping because of the increase resistance to change.
Have a student perform a side-step as fast as they can and video them front on. Add extra mass to a backpack, have them repeat the manoeuvre and video that action. Analyse the changes in technique using video analysis software. You should notice in the heavier condition that the student is slower to change. Inertia (Mass) is a hindrance when speeding up or changing direction (also see Newton’s Second Law) but can be beneficial when the movement progresses towards an impact.
The rotational equivalent of inertia is called Moment of Inertia which involves the mass of the object plus the distribution of that mass. To minimise complexity, this will be the focus of another article, as we explore the aspects of moving our limbs quickly in sprinting and throwing.
Newton’s Second Law is called the Law of Acceleration and is described by Ozkaya (2003) as “if the net or resultant force acting on a body is not zero, then the body will accelerate in the direction of the resultant force”. The familiar expression for this law is: Force equals mass multiplied by acceleration (F = m.a). Rearranging this equation also illustrates that the magnitude of the acceleration is directly proportional to the force in the same direction, and inversely proportional to the mass. Basically, if you want to accelerate quickly you either need a large net force acting in the direction you want to go, or a small mass, or both. For those in sprint related sports there is a trade off. They want to generate large forces so need to have a large, well-trained muscle mass, although they also don’t want to be too heavy. The caveat is not just as simple as having big legs and a very light upper body; the distribution of the muscle mass is also important as track sprinters need powerful arms to counter the drive of the legs (see Law of Reaction below). To create learning scenarios for the students you should think about manipulating either the force or the mass.
An easy classroom demonstration: Place a block on a smooth table. One end of a string should be tied to the block, and the other is tied to a bag hanging over the edge of a table. Repeatedly add weights to the bag and measure the time it takes to move the block some set distance.
For a more interactive example: one way to alter the mass is to have the students wear a backpack while performing timed maximum-effort sprints over a distance of 15 – 20 m. Alter the mass of the sprinter by adding or removing weights from the backpack and observe the changes in time. Given they had the same strength and assuming they were generating the same force, any changes in acceleration should be due to the changes in mass. It is important to note that you are not actually measuring acceleration. However, a shorter time means they covered the distance with a greater average velocity, and as they would probably not have reached full speed in 15 m, time taken is a pretty good indicator of acceleration. You can also use video analysis software to measure the change in velocity and therefore acceleration.
To alter force you need to be a bit more creative: A timed 20 m sprint on the flat compared to the same distance on a slight downhill means you are using the force of gravity to alter sprint time from which changes in acceleration can be inferred. Similarly you could use a stretched-out bungee cord to aid their acceleration.
Newton’s Third Law is founded on the observation that there always appear to be two sides when it comes to forces (Ozkaya 2003). It is called the Law of Reaction and has been described by many including Carr (2004) as “every action has an equal and opposite reaction”. The two forces hard to observe as often one of the objects doesn’t appear to move any measureable amount, especially if that object is the earth! The following practical examples may help students better understand the concept of Action - Reaction.
On a very smooth surface have one skateboard rider push against a wall; observe that the push in one direction (action) sends them in the opposite direction (reaction). Now try two skate boarders pushing away from each other. Also try riders of different masses and you should see the influence of the Law of Acceleration as the rider with the larger mass will not move away as fast. Note that this can be influenced by technique so try to keep this consistent.
To observe the effects of removing the ‘reaction’ input from the arms in sprinting, have the students sprint normally and time them over a set distance. Repeat the task, but with their arms tied to their sides. The change in time is usually attributed to the inability to generate a sufficient ‘reaction’ to the legs ‘action’, consequently the force generated by the legs has to drop.
Ground Reaction Force (GRF) is incredibly important as it allows us to jump, and accelerate when sprinting and its ‘down force’ influences friction. GRF is a hard concept for student to grasp as often times they cannot understand how the ground is pushing back. When you explain to them that the ground pushes back by the same amount, they may ask how does the ground know how hard to push back? One way of simulating expensive biomechanical force plates is to use a set of bathroom scales; usually the ones with the rotational dial are easier to read than the digital ones. Make sure you have one that goes up over 200kg. What the scales are indicating is the downward force of the person standing one it. Note that you actually need to multiple the number on the scales (kg) by about 10 (actually 9.8) to get the true force. Have the student try a vertical jump using just their arms and read the maximum load off the dial. Have them repeat this just using their calf muscles, then again using their whole legs, then again using both legs and their arms. Have them keep increasing effort until they actually jump off the scales. What you have shown here is the ‘force’ they are generating (action) and the ground resisting and ‘pushing’ back (reaction). When that force gets large enough you will get a flight phase and therefore will have observed the force needed to jump. Now you have also introduced them to Sequential Sequencing. If you capture the jumping activity on video and review it in frame by frame slow motion, you can talk about the techniques used to generate the forces required to perform a jump.
The Law of Reaction is basically the same concept for rotational motion as it is for linear motion. However, the linear forces are now forces acting at a distance from an axis which cause rotation (Torques or Moments). For example, have someone sit on a swivel chair and counter rotate their arms and legs forcefully. The arms will rotate one way and the body, legs and chair will rotate the other. The interrelation between these laws (and most of the laws and principles of motion) may have become apparent while reading this brief overview. It is crucial to remember that every person and every situation are so different, they must be analysed on their own merits. These suggestions should help you deliver the knowledge and tools to the students, thus giving them the ability to analyse human motion for themselves. Bibliography Carr. G. (2004). Sport mechanics for coaches (2nd edition). Champaign: Human Kinetics. Knudson, D. Fundamentals of biomechanics. (2003). New York: Kluwer Academic/Plenum Publishers. Ozkaya, N., & Nordin, M. (1999). Fundamentals of biomechanics: Equilibrium, motion and deformation (2nd edition). New York: Springer-Verlag. www.wikipedia.org (accessed January 2008) Steve Stanley is a graduate of the School of Physical Education at Otago University and has a background in research and education. He now works for siliconcoach Ltd designing software and creating video analysis resources for education, sports, clinical and retail. He can be contacted on
[email protected].
