Monday, April 19, 2010

Physics - Newton's Law of Gravity

Recently because of the injury to my knee, I cannot stunt as much, but I had not been slacking by going to the gym to work out more often. Going to the gym more makes me more conscious about the amount of weight I can lift or press, and this sets me thinking about an old yet current issue that has sort of puzzled me for some time.

How come it feels so different when people stunt a 40 kg flyer and a 45kg flyer? The difference is only a mere 5kg. And for that matter, how about the difference of stunting a 44kg flyer and a 45kg flyer, which is only 1kg difference?

To solve this puzzle, I did some homework and tried to put things into perspective.

We know that in the sport of cheerleading, most of times we are fighting against the forces of gravity. So what is gravity? It is the downward force exerted on any object which can be given by:

F=mg (F = Force of gravity, m = Mass of object & g = Gravitational constant=9.81m/s2)

So whenever we toss a flyer into the air, we are exerting a force (F) = m(flyer’s mass) X g(gravitational constant)

Ok now we all know the concept of Force, but it is still not enough to quantify the full picture for cheerleading. We need to take into consideration of another variable that is the Height, or distance travelled against gravity. So putting Height into the equation, we have Work Done(W) or Energy (E) = Force (F) X Distance moved or Height (d), simply put it as:

E =F X d (E = Energy exerted, F = Force against gravity & d = Height travelled)

Now back to my question of the difference in stunting a 44kg flyer and 45kg flyer (only 1kg difference); how does these equation put things more into perspective?

Let’s do a scenario study:

Before we start, let’s qualify things a little. In the study, it is assumed that all flyers have the same build, same size, same vertical leap, same locking, same techniques and all else same except the weight. Also for simplicity of calculations, g(gravitational constant) will be taken as 10m/s2.

So let us take the scenario of tossing a flyer to extension. Let’s take the average height of an extension to be 2metres, from the palms holding the flyer’s feet to the ground. What it means in physics terms of tossing a flyer to extension is to work against gravity and bring the flyer to travel a distance of 2m.

Therefore for a flyer of 45kg, the Energy used to toss her to extension can be given as:

Energy = F X d
= mg X d
= 45kg X 10m/s2 X 2m
= 900 Joules

So assuming this energy of 900J is your threshold or limit you can produce in a toss (means no matter how hard you try, you can only give 900J). So your full strength is 900J and if you were to put this Energy into tossing a flyer of 44kg, what outcome will you get?

Energy(E)= F x d(Height)
Height = E/F
= E/mg
= 900/(44 X 10)
= 2.05m

So from the equation, you can see that if you use the same amount of strength to toss a flyer of 44kg, you can actually toss her higher by about 5cm (take out your ruler and see how much it is if you must). Now 1kg of difference may not seemed a lot, but to see it from another angle, it is actually worth 5cm of difference, and this 5cm is usually the difference of having the float at the end of the toss that we are always talking about.

Now to amplify things a little more and take a flyer of 40kg:

Energy(E)= F x d(Height)
Height = E/F
= E/mg
= 900/(40 X 10)
= 2.25m

You can actually toss a flyer of 40kg 25cm more than a flyer of 45kg (of course considering all other variables the same as assumed above) and 25cm is almost about the length of 1 foreman of the base! If you continue to play around with the mathematics, you will realize that for every 1kg, it is approximately representative of 5cm in toss.

Now that we have seen things from another perspective and angle, we can appreciate what a mere 1kg difference or even 500grams signify. And when performing at the peak, near our threshold, every centimeters counts to whether stunt stays up or comes down.

Ok, I only did this as to satisfy my long time curiosity. And as I did this example, I know full well at the back of my head that weight is not entirely the only factor when doing a stunt such as toss to extension. I did specifically specify too that weight only comes into the picture with all else being the same.

Most times, weight is not to be an issue, techniques, skills, locking, power in jumping outweighs it. People say having that little extra weight is because of having more muscles and with these muscles the jump will be higher and locking tighter. I can fully agree with this statement, as I know the importance of having muscle strength. But the difficult part and key to it is to develop more compact, efficient and lean muscles, with a high strength to mass ratio.

P.S: Is your weight a direct proportion of your muscles and strength? Or are they a direct proportion to your fats and liability? Be truthful to yourself and do not lie to yourself about it. Respect yourself and respect the sport; it is time to get in shape if you are not already. I am not an advocate of weight loss, but I am one of staying in good physical shape and strength.