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.

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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.

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