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I A ball struck by a cue in billiards with English goes straight at first...

  1. Dec 20, 2016 #1
    Hi, let me ask probably dumb questions to physics experts... Why does the cue ball goes almost straight when its right (or left) side is struck by a cue (right English)? This is quite different from when a ball hits another ball, in which case the ball goes almost perpendicular from the contact surface. Here, I want to focus on the ball direction immediately after the impact and ignore the curve after the ball starts to roll.

    I heard that it is because the ball and cue can be thought as unity so the force only propagates to the cue direction. But if so, would it be possible that the cue makes the ball spin? My guess is that the friction between the ball and cue tip makes the ball not only spin but also go to the right direction and counteracts the force perpendicular from the contact surface (left), resulting that the ball goes to the cue direction? I heard that the friction coefficient is pretty high ~0.6. Any comments will be appreciated!
     

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  3. Dec 20, 2016 #2

    fresh_42

    Staff: Mentor

    The ball first slips over the cloth, with or without rotation and independent of where it was hit. Once it hits another ball friction takes over and the linear movement becomes a rotation, such that the ball rolls from there on. During the collision, the linear movement comes to a hold for a moment which forces the existing angular momentum into a rotation.
     
  4. Dec 20, 2016 #3
    Thank you for the comment! I didn't know that a ball always slips after I hit the ball. Would it be also the case when I strike the ball right above the center very softly? And I still wonder why the ball doesn't go to the left when I strike its right side with a cue stick...
     
  5. Dec 20, 2016 #4
    It surely goes to left a little bit, but it goes relatively straight (the direction of the cue stick).
     
  6. Dec 20, 2016 #5

    fresh_42

    Staff: Mentor

    If you play the ball properly, it receives a single force in the direction of the cue. For a change in direction you would need another force, either from a different direction or in addition to the cue's force. It happens if your cue slips off or along the ball which usually is a foul.
     
  7. Dec 20, 2016 #6
    But, if a cue ball collides with the right side of an object ball, the object ball goes to the left, right? What is the difference between the ball-ball collision and ball-cue collision? I am sorry, but I am really weak at physics... I guess this is a very basic question.
     
  8. Dec 20, 2016 #7
    To make it clear, I posted a drawing. Why does a ball go to different direction between ball-ball and cue-ball collision?
     

    Attached Files:

  9. Dec 20, 2016 #8
    The answer is indeed friction. The acceleration is not parallel to the normal of the contact point, so there must be a tangential component to the force. That requires friction or adhesion. The cue tip is soft compared to the balls and the contact lasts much longer than a ball to ball collision. The cue tip deforms, effectively sticks to the ball, and forces it along in the same direction the cue tip is traveling. It is something like throwing the ball rather than a hard elastic collision. During the contact with the cue the cue ball does indeed slide across the felt. This is easy to see if you look for it.

    The need for high friction, or even adhesion is the purpose of chalk. A miscue is the result of the cue slipping along the surface of the ball. This happens when the friction is low due to lack of chalk, the contact is poor due to a poorly shaped, worn, or hard tip, or the friction required exceeds the friction available because the ball was struck too far off center and the tangential component is too large. Even with sticking the ball will deflect some. I've seen claims that say the stickier the chalk the less the cue ball deflects off axis. However that doesn't make sense to me. Either the cue tip slips or it doesn't. Once you've avoided slipping more stickiness is not any better.

    The critical difference with the collision of two balls is that they are very hard and elastic and the contact lasts a very short time. There is a little bit of friction and some nonneglible throw in ball to ball collisions. However they are much closer to an ideal elastic collision and the direction is usually very close to the normal. On the other hand, accounting for the throw particularly at thin angles is part of what separates a good player from the rest of us.
     
  10. Dec 20, 2016 #9

    fresh_42

    Staff: Mentor

    Cue.jpg

    On the right side the red line shows the part of the force that applies to the object ball. The rest of the momentum is carried away by the white ball whereas the cue doesn't take any momentum to a different direction.
     
  11. Dec 21, 2016 #10
    The cue has a constraint and experiences external forces. Momentum conservation is not relevant. If you took the cue ball in hand and rammed it straight ahead through the object ball without deflecting I believe you would find that the object ball still goes off at an angle. (Somebody with a pool table please try). I don't think this is why the cue is different.
     
  12. Dec 21, 2016 #11
    Thank you for your answers! I am still trying to understand the insights into momentum conservation (if so, is cue ball direction different when hit by rolling ball and ball-in-hand?). But friction explanation makes a lot of sense to me.

    You know cue makers sell "low-deflection" cues with low density (mass) at the cue tip. Striking with a low-deflection cue with right English, a cue ball goes even more straight with less deflection to left direction. Is this probably due to increase in contact time between the cue and ball (because the cue is softer) and more friction*time to the right direction (and maybe less coefficient of restitution reduces the cue ball deflection to left)?

    My thought is that if it is friction that makes the cue ball go straight, it would be theoretically possible to make the cue ball to the same direction as English if friction force can be increased (one could strike the right side of a ball and the ball goes to the right).
     
    Last edited: Dec 21, 2016
  13. Dec 21, 2016 #12
    I am pretty sure that the ball goes off though I haven't tried it.
     
  14. Dec 21, 2016 #13
    If the ball completely completely stuck to the cue (like fused with it or something) it would travel straight with the cue. I think straight with the cue is the limit. I don't think you can make the ball turn towards the English during the collision. Of course if you can get the ball spinning correctly you can make it curve that way after the collision.
     
  15. Dec 22, 2016 #14

    sophiecentaur

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    Gold Member

    That comment worries me. Momentum (linear and angular) still has to be conserved. The cue / arm / rest of the world have a momentum change due to the collision. The resulting velocity change of the cue is 'near' zero because the effective mass is so high.
    This would happen for a collision in space, with no contact with the ground. Whatever happens, due to friction etc., is a separate issue - total Momentum will still be conserved during the spinning interaction. The initial motion (Impulse) will be to the left but any friction effect of the ball spinning will be in addition to this and happens after the contact with the cue.
    PS What is "turning to the English"?
     
  16. Dec 22, 2016 #15
    I think you are right... Is this because the friction force is product of friction coefficient (<1.0) and the force perpendicular to the impact surface?

    I was wondering whether the softness of the cue tip could reduce the initial velocity of the ball to left by reducing restitution coefficient or spring constant so that the friction force dominates and ball goes to right... I also noted that the cue could be bent to right during the impact (right English). I am not sure whether this bend significantly affects the ball direction though (I guess the bend increases both friction force to right and bouncing force to left)

    It refers to what I said: when a ball was hit on the right side (right English), the ball goes to the right, which may be impossible.
     
    Last edited: Dec 22, 2016
  17. Dec 22, 2016 #16

    sophiecentaur

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    Right hand side then?
    If it is struck on the right hand side then it (the centre of mass of the ball) cannot move to the right initially. It has to move towards the left. That is what momentum conservation tells us and there will be a force on the cue tip, to the right. The tip may bend or be rigid and the details of what happen to the ball will depend on the stiffness of the cue etc. and also the friction of the tip on the ball and the ball on the table. There is no simple answer but friction will make the ball rotate anticlockwise (looking down on it) and, depending on whether the contact is above or below the mid point, the ball will also have top spin or bottom spin. So the path of the ball can follow a right hand or left hand curve, depending.
    The whole business of striking the ball with the cue will have many variables involved and what the player 'thinks' is happening may well not be what is actually happening. That doesn't matter to the player, who learns, from experience and from 'discussions' what to do. The Physics may be very loosely connected with the player's subjective feeling about what's gong on. This doesn't matter; a good player is a good player and doesn't have to be a good Physicist.
     
  18. Dec 22, 2016 #17
    When I said the ball couldn't go the other way I hadn't thought about the idea that the cue may deflect. However, under the assumption the the player is trying to move the stick in a straight line and any deflection is a reaction to hitting the ball, I would think that would move the ball off more in the expected way by Newton's law of action and reaction.

    Now if the player jerks the tip the outside direction during the collision that is a different story.
     
  19. Dec 22, 2016 #18

    sophiecentaur

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    You are neglecting the question of top spin and bottom spin. All good players are well aware of the effects of these on the path of the ball.
     
  20. Dec 22, 2016 #19
    So, the bend would make the ball goes even more left (more cue ball deflection). I don't know its math, but I believe you. I will do a little research and find how I can calculate them. Thank you for your suggestions!

    Right, but I wanted to know basic Physics as well! So, do you think that the friction only affects the curve and does not affect initial direction? Curve is of course an important factor in the game. But I will think about curves in other time, and here I want to focus on the initial direction/velocity of the cue ball.
     
    Last edited: Dec 22, 2016
  21. Dec 22, 2016 #20
    This is a good point. Some people do this hoping to reduce cue ball deflection.
     
    Last edited: Dec 22, 2016
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