The General Description of the Tennis Strokes. For math oriented players only!

Discussion in 'Tennis Tips/Instruction' started by toly, Aug 14, 2012.

  1. sureshs

    sureshs Bionic Poster

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    There is nothing wrong, but there is nothing useful either. If you remember all the collision problems you have solved, do you ever recall any mention of acceleration? No, it was always, u1, v1, u2, v2 etc. Why? Because no force was acting on those objects. When a racket head hits a ball, it is accelerating just prior to impact. So, conservation of momentum cannot be applied.
     
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  2. bhupaes

    bhupaes Professional

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    Going directly to your post #32...

    This is a different problem, isn't it? The original problem assumed an elastic collision to simplify the calculation, which would be true if the energy lost in the collision is small (as I think it is). But in any case, even with totally inelastic collision, the relative speed between the two masses after the collision is zero in both of the cases you have mentioned. Not sure what I am missing...
     
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  3. bhupaes

    bhupaes Professional

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    I understand, and you are right in the large picture. But we are applying the rules differentially, as when solving a problem in numerical analysis, by dividing time into very small segments.
     
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  4. sureshs

    sureshs Bionic Poster

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    I am asking why the difference in speeds if analyzed with one at rest, then with the other at rest. If m is moving to the right with v towards M, isn't it the same as M moving to the left with v towards m? Then why is there a difference in the speed of the combined mass after the collision? (direction will of course be different).
     
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  5. sureshs

    sureshs Bionic Poster

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    Then you are saying the velocity is constant almost at collision, even if the racket was accelerating before? Then toly's point would be that the person applies no force, and of course he doesn't, because we just made the acceleration 0. That would be true for anything! If we say we will go by a boxer's hand's final speed only, we can claim that the boxer did not do anything at the instant of impact!

    What use is that?
     
    #55
  6. bhupaes

    bhupaes Professional

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    In a given coordinate system or frame of reference, of course there is a difference between a small mass and a big mass moving with a given velocity. I don't think anybody is disputing that. As I recall, this argument started because someone wanted to measure the angle of reflection of a ball when it hits a racquet, and that is a relative entity which only depends on the relative movement between the racquet face and the ball.
     
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  7. bhupaes

    bhupaes Professional

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    The racquet could be accelerating all the way to impact. But the actual impact lasts only a few milliseconds. As toly pointed out, how much energy could the force have contributed in that time? IMO, negligible for the purposes of this calculation. If someone can prove this to be wrong, I will accept it - I don't have any means other than the above logic to prove my assertion.
     
    #57
  8. toly

    toly Hall of Fame

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    I analyzed Federer inside out hard FH on the APAS System http://www.youtube.com/watch?v=pPLmCqGIotM

    There are data about his arm speed and acceleration around the wrist during forward swing.

    [​IMG]

    The picture demonstrates that Federer is able to increase acceleration/force of the arm from frame #1 to #9. The magnitude of the force declined after frame #9. Around impact, frame #24, acceleration decreased more than 70%.

    So, he is not able to accelerate the arm significantly near impact. But, this is very hard FH and without doubt he is trying to produce maximum acceleration/force.

    Question: What is wrong with Federer?
    The answer will be tomorrow.
     
    #58
  9. toly

    toly Hall of Fame

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    IMO you are right. Thanks for clarification!!!:)
     
    #59
  10. toly

    toly Hall of Fame

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    1. In first case momentum before collision was mv. After collision momentum is

    (M+m)(mv/(m+M))=mv. So, mv=mv and everything is fine with law of conservation of momentum.

    2. In second case momentum before collision was Mv. After collision momentum is

    (M+m)(Mv/(m+M))=Mv. Again everything is fine and Mv=Mv. :)
     
    Last edited: Dec 5, 2012
    #60
  11. sureshs

    sureshs Bionic Poster

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    The force has already driven the acceleration of the racket, that is why it has reached that velocity! Moreover, the force that acts during collision is huge and when multiplied by the small time is called the impulse. The force is called the impulsive force. See the example of the magnitude of the force below. toly is saying that the force is negligible!!!!

    http://www.acs.psu.edu/drussell/bats/impulse.htm

    The impact between bat and ball is an extremely violent one, in which the bat imparts a huge force on the ball thereby causing it to change directions and gain speed. Consider a baseball weighing 5.125oz (mass = 0.145kg) which approaches the bat at a speed of 90mph (40.2m/s). After the collision with the bat, with a contact time of 0.7milliseconds (0.0007s)[1,2] the bat has a speed of 110mph (49.1m/s) in the opposite direction. Using Newton's second law we can estimate the average force acting on the ball during the hit:



    Plugging in the numbers we find the average force to be Favg=18,436 N, which is equivalent to 4124 lbs of force.
     
    #61
  12. sureshs

    sureshs Bionic Poster

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    Circular argument since I derived the speed using the conservation of momentum and you used that expression.

    I am asking why the system behavior is different in the two cases. I know I am wrong, but I want to know why.
     
    #62
  13. sureshs

    sureshs Bionic Poster

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    Acceleration will obviously decrease as he is swinging up into the ball, compared to swinging down with gravity. So what? Whatever force he is exerting needs to counteract gravity, so he cannot keep on increasing the force. What counts is the momentum already built up leading to collision.
     
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  14. BreakPoint

    BreakPoint Bionic Poster

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    Without nerds, you wouldn't be able to post on a message board on this thing called "the Internet".
     
    #64
  15. Swissv2

    Swissv2 Hall of Fame

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    Indeed! :)

    Nerds created the "precious" iPhone, i-This, i-That, that most everyone cannot live without.
     
    #65
  16. bhupaes

    bhupaes Professional

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    Suresh, the force we need to worry about is the external one being applied by the player wielding the racquet. That is a component that could skew the otherwise perfect equations of momentum and energy conservation, should it be significant enough.

    Of course, the racquet and ball exert huge forces on each other. The equation for conservation of momentum will apply if that is the only force we need to worry about. The equation for energy conservation will also apply if the collision is perfectly elastic. However, an external force like the player can skew things, but in this case, as pointed out earlier, its contribution in terms of energy during the collision period can be ignored for the purposes of getting an approximate result.
     
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  17. r2473

    r2473 Legend

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    I believe it's called "The Internets"

    I hear there's rumors on the Internets that we're going to have a draft. I don't know how many of these Internets are carrying these rumors, but they're just wrong. I think the problem here may be more of a question of getting rid of the bad Internets and keeping the good Internets. You know, 'cause I think we can all agree... there're just too many Internets

    http://new.hulu.com/watch/1623
     
    Last edited: Aug 24, 2012
    #67
  18. sureshs

    sureshs Bionic Poster

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    The impulsive force is the force of collision and the equation for it is just the 2nd law. It applies whether or not momentum is conserved. The calculation uses the observed speed of the ball before and after to determine the change of momentum, and some other technique to determine the contact time.

    From the racket point of view, the same force would be calculated it its initial and final speeds were recorded. We are interested in the initial speed because that is the independent variable.

    This speed (at contact) is due to the acceleration of the racket till impact. For this acceleration, the force applied is difficult to calculate - it is the integral of m*a as a itself changes. The player then must exert this force plus the component of gravity force which is pulling down on the upward swing.

    As I said before, toly can suspend a ball and a racket and swing the racket back and see if the ball shoots off at 80 mph. That will settle once for all whether gravity is the main force. I suspect strongly it is not. It is better to do this than claim stuff based on some math.
     
    Last edited: Aug 24, 2012
    #68
  19. toly

    toly Hall of Fame

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    There is figure from http://sanderroosendaal.wordpress.com/2010/07/26/muscle-power-vs-contraction-speed/

    [​IMG]
    Figure 1. Muscle force versus muscle contraction speed

    Figure 1 shows the muscle force versus muscle contraction speed. It’s a very important graph because it marks where classical mechanics stops and exercise physiology starts. Note that the graph is idealized, with no absolute values on the axis. Each athlete will have a slightly different graph, which will probably also change as a result of training.

    This fundamental property of muscle has numerous biomechanical consequences, including limiting racquet speed and force around impact.

    So, there's nothing wrong with Federer. It's just a biomechanical law that he must unquestioningly obey!:):shock:
     
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  20. pushing_wins

    pushing_wins Hall of Fame

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    what is the question?
     
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  21. toly

    toly Hall of Fame

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    The question is - after reading this thread can you clearly explain:

    1. How carpenter hit a nail without spin component of the hammer velocity?

    2. What exactly you should do to hit pure flat serve, FH, and so on? :):):)
     
    Last edited: Aug 27, 2012
    #71
  22. pushing_wins

    pushing_wins Hall of Fame

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    inside out swing path. for power, you want draw spin not slice spin.
     
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