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7/27/2019 Physics of Wall Balls
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All right, ladies and gentlemen! We're here to talk about wall balls. Yeah, tall people don't get so excited
because I'm here to show just how much wall balls suck for short people and why we're at a
disadvantage scientifically. And what better way to win an argument than with science?
So to start off let's just describe what is going on when we do this retched movement ala games
standards. Since we all do our wall balls perfectly, what is about to be said, should come as no surprise.
First, we start out at the bottom of our squat, with the ball held at chin level in front of us but still close
to our body. Then we start to accelerate upwards applying a force to the ball and doing work to it,
helping the ball gain speed so that it can reach the 10 foot (or for ladies 9 foot) target. We continue to
accelerate until our knees, hips, and arms are locked out over head at which point the ball is thrown and
out of our control and under the influence of only gravity. Now, we hope that by the time we let it go we
have given it enough speed to reach the desired target.
Great, we have talked about it conceptually, now let's get into the nitty gritty. I talked about giving the
ball enough speed so that when it is out of your reach and under the influence of only gravity it should
be able to reach the target. If you guys/gals go ahead and dust off your physics high school textbook,
you should remember that gravity is a conservative force. Meaning, that if an object were moved
around in any form of closed loop in a gravitational field then no work would be done because it ended
right where it started. Our total mechanical energy ( the potential energy plus the kinetic energy) is
conserved.
Let's talk about what kinetic energy and potential energy are. Kinetic energy is the energy something has
because it's moving. Simple enough. A thrown ball has kinetic energy, we have kinetic energy whenjogging, and even a slow rolling bowling ball has kinetic energy. Potential energy is the energy
something has due to its position. A barbell held overhead has potential energy. If you get from under
the bar it will fall, gain speed and crash with the ground. A stretched band when we are doing mobility
has potential energy. If you were to let it go it would snap back to its original position.
7/27/2019 Physics of Wall Balls
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Phew, deep breath guys. So I will illustrate what is happening via stick figures. In figure 1.,the demo girl
is at full extension and at this instant the ball is no longer being applied a force by her and is only under
being affected by gravity.
Figure 1.
H is the height of her full extension. V is the velocity of the ball the instant it left her hand. So by the
conservation of mechanical energy, the sum of the total mechanical energy at the moment she let's go
of the ball should be equal to the total mechanical energy at the top where it reaches its target.
Mathematically, this is :
Where the first term on the left side is its gravitational potential energy the second you let it go, the
second term on the left side is kinetic energy the second you let it go, and on the right side we only have
gravitational potential energy. m is the mass of the ball, and g is the acceleration of gravity. Multiply
these two together and you get the weight of an object. The 120 on the left side represents the height
of the target, 10 feet, in inches. Now you're probably wondering why the right side of the equation only
has potential energy. Good question. I'll answer it for you. At the top of any objects arc or trajectory is
has no velocity. That's why your coaches tell you to catch the bar while its floating when your squat
cleaning. It has no velocity at that point because its at the top of its arc hence no broken or bruised
collar bones.
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With a bit of high school algebra you'll find that the velocity required to reach the 10 foot target at a
height of full extension H is:
You've probably already noticed that the taller you are the smaller the difference 10 - H is. This means
for taller people a smaller velocity is required to reach a 10 foot target. Already you're probably thinking
to yourself, "Well if they need a smaller velocity they probably don't need to put as much work into it as
us short people do." You sir are correct.
So we worked backwards to figure out the speed we need to just reach the 10 foot target. But how
much work does it require to accelerate our ball to such a speed? Well luckily physics has already
figured that out for us. It's called the work-energy theorem. Basically, what the work-energy theorem
says is that the change in kinetic energy is equal to the work done. Makes intuitive, physical sense right?
We do work to move something and its speed changes. For the mathematically inclined:
Where W stands for work, the first term is the final kinetic energy, and the second term is the kinetic
energy it started with. In our case, since we started at the bottom of a squat our initial kinetic energy is
zero so we only have to deal with the first term. We're doing work on the ball until the very instant we
let go of it, at which point the velocity is identical to the velocity we figured out earlier need to reach the
10 foot target. So plugging that velocity in we get:
When you square a squared root, you end up with whatever is inside of the square root so we end up
with:
Now the 2 on the numerator cancels with the 2 on the denominator and we end up with our final
expression:
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So basically the work done to just reach our 10 foot target depends on the weight of the ball , mg, and
the our height. Based on our experience with wall balls this comes as no surprise and makes sense to us.
Now, you're probably scoffing at this formula as a tall person thinking it doesn't make any difference.
Well, I'm here to provide an example on the difference in work a 2 inch difference makes. Let's say we
have a person of a tall reach of 72 inches (6 feet when they are at full extension) and they are throwinga 20 lb wall ball. The work required for one rep is:
Say this person has an identical twin in every way except having a reach of 2 inches more. We get:
One lb in is equal to 0.027 calories. So let's assume the two twins do Karen (150 wall balls) . The shorter
twin will use up 3890 calories. While the taller one use up 3727 calories. That's a difference of 163
calories for only two inches! What? You don't think that's a big difference? Ok go on the rower and row
163 calories then tell me that.
In conclusion, wall balls suck for short people.
7/27/2019 Physics of Wall Balls
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