dwelltime

zeio wrote: tt4me wrote: AgentHEX wrote: The energy is from the relative speed of the collision, ie present in the system from before any dwelling happens. I agree that no or little energy is added to the system during the dwell time but I think zeio was just referring to the ball and the ball does get a big boost in energy. Sigh, Newtons's second law of motion is all you need to dispel this nonsense.  When a net force acting on an object causes it to accelerate in the direction of motion, work is said to be done.  The transfer of mechanical energy requires mechanical work.  During a swing, the paddle experiences an acceleration in the direction of motion of the player, and work is done on the paddle, which is said to have gained kinetic energy.  The paddle then transfers most of that energy to the ball during collision.  While that happens, the ball experiences an acceleration in the direction of motion of the paddle.  Since there is work done, there is also a transfer of kinetic energy.  There you have it.

Not even nearly most of that energy.  It transfers just a small fraction of it.  Otherwise, the racket would nearly stop during the collision.

zeio, what part is non sense? You aren't clear and neither is AgentHex. You and AgentHex are talking past each other because you are talking about what happens to the ball and AgentHex is talking about what is happening to the system which includes the ball and paddle and everything else that is moving. 

Edited by tt4me - 09/20/2013 at 2:23pm

zeio wrote: wturber wrote: zeio wrote: tt4me wrote: AgentHEX wrote: The energy is from the relative speed of the collision, ie present in the system from before any dwelling happens. I agree that no or little energy is added to the system during the dwell time but I think zeio was just referring to the ball and the ball does get a big boost in energy. Sigh, Newtons's second law of motion is all you need to dispel this nonsense.  When a net force acting on an object causes it to accelerate in the direction of motion, work is said to be done.  The transfer of mechanical energy requires mechanical work.  During a swing, the paddle experiences an acceleration in the direction of motion of the player, and work is done on the paddle, which is said to have gained kinetic energy.  The paddle then transfers most of that energy to the ball during collision.  While that happens, the ball experiences an acceleration in the direction of motion of the paddle.  Since there is work done, there is also a transfer of kinetic energy.  There you have it. Not even nearly most of that energy.  It transfers just a small fraction of it.  Otherwise, the racket would nearly stop during the collision. Note the phrase "during collision".  There is a reason for that.  Real collisions are not instantaneous even though they are often treated that way where the force is infinite and duration is zero.  The paddle and ball do not separate at an instant.  They remain in contact and travel at the same velocity for a certain amount of time during the swing, albeit extremely brief, not unlike what happens during a perfectly inelastic collision, before separating.  It is during this phase of collision that most of the kinetic energy of the paddle is transferred to the ball.

This has nothing to do with the near instantaneous nature of the collision.  If most of the kinetic energy of the paddle was transferred to the ball, the paddle would slow down rather dramatically and the ball would travel a LOT faster than it does (or perhaps shatter or deform dramatically)  But those things don't happen.  Only a small fraction of the kinetic energy of the paddle is ever transferred. Most of the energy is retained in the racket as evidenced by the fact that it doesn't slow down much.



Edited by wturber - 09/20/2013 at 7:06pm

mercuur wrote: AgentHEX wrote: COR is just a number to balance the equation. It has no actual physical manifestation. Cor is a rationumber, A rationumber reperesents a ratio and this is a true phyical manvfestation. One reason for that is that Vin --> V out has time : -->. The topic for this thread.

I'm not sure what you're trying to correct. A ratio is a unitless number, in this case the aftereffect of a specific collision. What physical manifestation of the blade or whatever is it supposed to be of?

AgentHEX wrote: tt4me wrote: AgentHEX wrote: The energy is from the relative speed of the collision, ie present in the system from before any dwelling happens. I agree that no or little energy is added to the system during the dwell time but I think zeio was just referring to the ball and the ball does get a big boost in energy. I think it should be clear by now what zeio means, and there's no need for us to dwell on the issue any more than the ball on the bat.

tt4me wrote: At what other time would energy be transferred to the ball?

Magic.

zeio wrote: Yes, it does have to do.

Jay is right and you are wrong on this.  Show us the math!

Check out the section for "Kinetic energy of colliding bodies" of thissite.

That is a very good site.  Do you understand it? 

They have a diagram showing the collision of two identical blocks moving on a smooth floor.......

Do the math and show us.  I repeat, Jay is right.
Since you will not I can and will.  It is easy.
The paddle would have to slow down by 1/sqrt(2) or to 0.707 of its initial speed to lose half of its energy and we all know that the paddle doesn't slow down that much during the contact time so how do you justify your statement?  Not all the energy the paddle loses is converted to ball kinetic energy.

tt4me wrote: zeio wrote: Yes, it does have to do. Jay is right and you are wrong on this.  Show us the math! Check out the section for "Kinetic energy of colliding bodies" of thissite. That is a very good site.  Do you understand it?    They have a diagram showing the collision of two identical blocks moving on a smooth floor....... Do the math and show us.  I repeat, Jay is right. Since you will not I can and will.  It is easy. The paddle would have to slow down by 1/sqrt(2) or to 0.707 of its initial speed to lose half of its energy and we all know that the paddle doesn't slow down that much during the contact time so how do you justify your statement?  Not all the energy the paddle loses is converted to ball kinetic energy.

Suppose the setup is the one in my signature:

Paddle mass m1 = 185g, Ball mass m2 = 2.7g
Before collision, Paddle initial velocity = 20m/s, Ball initial velocity = -10m/s
After collision, Paddle final velocity = 19.8m/s, Solve for Ball final velocity = ?
Solve for initial and final kinetic energy = ?, ?
Compare the ratio of KEi and KEf = ?

Initial momentum = Final momentum
m1v1i + m2v2i = m1v1f + m2v2f
185g*20m/s + 2.7g*-10m/s = 185g*19.8m/s + 2.7g*v2f
3.7kg m/s - .027kg m/s = 3.663kg m/s + 2.7g*v2f
v2f = 3.7037

Initial kinetic energy
1/2m1v1i^2 + 1/2m2v2i^2
185g/2*20m/s^2 + 2.7g/2*-10m/s^2
37J + .135J = 37.135J

Final kinetic energy
1/2m1v1^2 + 1/2m2v2f^2
185g/2*19.8m/s^2 + 2.7g/2*1m/s^2
36.2637J + .01851J = 36.2822J

KEf/KEi
36.2822J/37.135J = .977

97.7% of the kinetic energy of the paddle has been transferred to the ball during the collision.  See now?


Edited by zeio - 09/21/2013 at 1:22am

Now I gotta catch the women's world cup.

AgentHEX wrote: zeio wrote: Final kinetic energy of system / Initial kinetic energy of system => 97.7% of the kinetic energy of the paddle has been transferred to the ball during the collision. LOLWUT

Can't you see that zeio is trying to weasel word out of his embarrassing predicament?
It is true that given his assumptions that the ball and paddle system retain 97.7% of its initial kinetic energy but it is not true that that 97.7% of the energy of the paddle has been transferred to the ball.

I stand corrected. Not all the latter group learned how to turn the crank.

WHAT???  How can you be corrected by something that is wrong?
I am still waiting for someone that can 'turn the crank'.

This is turning the crank.

The first part of the document derives the speed after impact using two equations to solve two unknowns that are the final velocities of the paddle and ball.   The two equations are the conservation of momentum and the definition of the coefficient of restitution.  I assumed a coefficient of restitution of 0.5 which is typical.  Notice that the paddle slows down a little more than in zeio's example but the ball does go faster than the paddle as it should.

mercuur, it is hard to tell what you are trying to say.  You are misusing terms.

tt4me wrote: mercuur, it is hard to tell what you are trying to say.  You are misusing terms. Different people use different symbols for the coefficient of restitution. Putting the paddle in a vise that is fixed simplifies the calculation but it isn't necessary if you do all the calculations relative to the paddle.   For instance, in the example above the paddle velocity can be subtracted from the ball velocity to get a paddle relative velocity.   In the example above the relative velocity of the ball before impact is -10-20=-30.   The relative velocity of the ball after impact is 34.35269-19.35269=15.   Notice the relative velocity is the opposite and half and opposite of the incoming velocity as one would expect when the coefficient of restitution is 0.5. Now lets relate this to the dwell time.  In this example it should be obvious that since the incoming velocity relative to the blade is twice that of the outgoing velocity, the time to stop the ball relative to the paddle is about 1/2 the time to accelerate the ball again.  If the COR was 0.3333 the time to accelerate would be 3 times longer than the stop time so a lower COR does increase dwell time as people have stated above.   The extreme case occurs when the COR is 0 so the impact is inelastic, like hitting a ball of putty, so the dwell time is infinite.

It,s  pretending to take C=0,5 or any other particular value and then pretend you (or I or others) know by that C=0,5 for value.
That,s what I understand. I.m not even starting then to go into equations and calculations.

Then from a random chosen value and a random rel V before explain rel v out from that while it needs this value first for knowing C as ratio to begin with.

Or pretend to know V before ánd - after by giving two example values and then calculate a value for their ratio as C and use that for the bounce.

Picking one or two random numbers outside the bounce and use this as information for the bounce and/or pick an example ratio for the bounce and use this as information for the bounce. 
V4 and V3 doesn,t allow this type of easy skipping as for schoolwork.

V after/ - before seems to allow this and repeat the bounce over and over again.

V before is a V after during any bounce and V after is a future V for the period before any bounce.
When this is confusing then better so as mistaking randomchoice numbers for information or knowledge (I think your fooling yourself with this).

On itself I wouldn,t have a problem with this but then do it from a first fixed dwelltime.
Choose any fixed T for dwell and work from there. 
This choice can also be symbol T ( Tdwell =T then) but problem for that can be that it can take any value later on and then it,s all vague (until it has an outcome as some rabbit from some hat prooving there was a rabbit in the hat).
So better pick a fixed value in millisec.
Then you may pick two values for rel V before and after..

This example then has a delta Vrel =zero, neg or pos and a period T to combine it with for an overall decelleration (or accelleration) over the period of dwell between before and after.

Under these circumstances your welcome to try explain again. A deceleration and an accellertion inside the period for dwell must then correspond to this overall outcome and effect to both sides (accelleration also relative).





Edited by mercuur - 09/21/2013 at 4:03pm

zeio wrote: The ball final velocity depends on a large extent of the paddle final velocity.

NO!!!  There are two unknowns.   The final paddle and ball velocities.  The initial ball and paddle velocity plus the coefficient of restitution determine the velocities of the ball and paddle  after impact.   See my example.   I can simply change the coefficient of restitution from 0 to 1 to match the results you got below.

The more the paddle slows down, the more the ball speeds up.  Consider the following: Paddle mass m1 = 185g, Ball mass m2 = 2.7g Before collision, Paddle initial velocity = 20m/s, Ball initial velocity = -10m/s After collision, Paddle final velocity = 19.5m/s, Solve for Ball final velocity = ?

This is better.  So did you just pick lower v1f until v2f>v1f?

Initial momentum = Final momentum m1v1i + m2v2i = m1v1f + m2v2f 185g*20m/s + 2.7g*-10m/s = 185g*19.5m/s + 2.7g*v2f 3.7kg m/s - .027kg m/s = 3.6075kg m/s + 2.7g*v2f v2f = 24.2593m/s For perfectly elastic collision, v2f would become 49.1369m/s, where v1f = 19.1369m/s. Happy now?

I will be when you answer my question about what determines the speed of the paddle after impact.  I looks like you just picked speeds, using my hint, until you found a result that makes sense.

Now consider the phase of that collision where the paddle and ball move along at the same velocity vf: Initial momentum = Final momentum m1v1i + m2v2i = m1vf + m2vf 185g*20m/s + 2.7g*-10m/s = (185g + 2.7g)vf (3.7kg m/s - .027kg m/s)/(187.7g) = vf vf = 19.5685m/s Initial kinetic energy = same as before = 37.135. Final kinetic energy (1/2m1 + 1/2m2)vf^2 (185g/2 + 2.7g/2)19.5685m/s^2 35.9374J During that time, most of the paddle's energy is transferred to the ball through "bonding".  However, the paddle doesn't stop because its momentum is conserved.

Your numbers are right but what you are saying about transferring energy is wrong because the paddle retains over 90% of it energy.   Therefore the paddle can't be transferring most of its energy.  This is the point Jay was making.

tt4me wrote: zeio wrote: The ball final velocity depends on a large extent of the paddle final velocity. NO!!!  There are two unknowns.   The final paddle and ball velocities.  The initial ball and paddle velocity plus the coefficient of restitution determine the velocities of the ball and paddle  after impact.   See my example.   I can simply change the coefficient of restitution from 0 to 1 to match the results you got below.   The more the paddle slows down, the more the ball speeds up.  Consider the following: Paddle mass m1 = 185g, Ball mass m2 = 2.7g Before collision, Paddle initial velocity = 20m/s, Ball initial velocity = -10m/s After collision, Paddle final velocity = 19.5m/s, Solve for Ball final velocity = ? This is better.  So did you just pick lower v1f until v2f>v1f? Initial momentum = Final momentum m1v1i + m2v2i = m1v1f + m2v2f 185g*20m/s + 2.7g*-10m/s = 185g*19.5m/s + 2.7g*v2f 3.7kg m/s - .027kg m/s = 3.6075kg m/s + 2.7g*v2f v2f = 24.2593m/s For perfectly elastic collision, v2f would become 49.1369m/s, where v1f = 19.1369m/s. Happy now? I will be when you answer my question about what determines the speed of the paddle after impact.  I looks like you just picked speeds, using my hint, until you found a result that makes sense. Now consider the phase of that collision where the paddle and ball move along at the same velocity vf: Initial momentum = Final momentum m1v1i + m2v2i = m1vf + m2vf 185g*20m/s + 2.7g*-10m/s = (185g + 2.7g)vf (3.7kg m/s - .027kg m/s)/(187.7g) = vf vf = 19.5685m/s Initial kinetic energy = same as before = 37.135. Final kinetic energy (1/2m1 + 1/2m2)vf^2 (185g/2 + 2.7g/2)19.5685m/s^2 35.9374J During that time, most of the paddle's energy is transferred to the ball through "bonding".  However, the paddle doesn't stop because its momentum is conserved. Your numbers are right but what you are saying about transferring energy is wrong because the paddle retains over 90% of it energy.   Therefore the paddle can't be transferring most of its energy.  This is the point Jay was making.

The lower and upper limit of the slowdown is 19.1m/s and 19.5m/s.  I chose 19.8 randomly just to see how much velocity would affect the ratio of kinetic energy.  Then I knew you would pick on it and went to change it.  That's where the KE ratio .967 came from.  But I forgot to change the rest of the value before updating the post.  And then it was time for the world cup.  I said to hell with it and reverted the ratio.

Your hint?  I chose 19.5m/s because that's the value where both paddle and ball move together with the same kinetic energy during the collision, which is what I've always been saying.  What you and Jay refer to is after the collision where the two separate with their own share of that energy.

Intrinsic time it was and possible intrinsic math unit for time I was thinking.

I stumbled on this a few years ago but couldn,t google it until I remembered the word intrinsic to use for finding it back.
http://www.vip.ocsnet.net/~ancient/Constants-Version%20Postprint.pdf..

For some Zeio support .

A workingline or line  of motion is not a euclid space. It has no coordinates or point zero for coordinate.
Needs to use a space for the system (can be one dimensional on the workingline but free to move to the workingline). Not tying it solidly to the tabe, floor or a workingline without coordinates.

In that case the paddle would move from the neg sector to the positive part or vice versa passing through this point.
This would count for an all sudden turn of direction for the paddle while the ball stays in the same sector.
That heavily intereferes then with "relV before/rel V after" as much higher or lower (dependant wether the bat starts in pos or neg secor.)



Edited by mercuur - 09/22/2013 at 9:14am