Is this book wrong? Tennis ball rebound speed

• jonjacson
In summary, the conversation discusses the results of a book on tennis physics, specifically the impact of a tennis ball on a stationary racket and a moving racket. The variables considered include ball speed, racquet speed, "rebound power," relative speed between the ball and racket, and rebound speed. The conversation also explores the use of different coordinate systems and the proper use of the coefficient of rebound. There is a disagreement about whether a racquet at 60 mph can generate a ball speed of 84 mph.
jonjacson
I am reading a book abut tennis physics and I have seen a result that I feel is wrong.
We have a tennis ball and a racket, and several cases:
1.- Ball hitting stacionary racquet that is sustained with your hand.
(I agree with the results of the book here, it is just to show how they are reasoning)

I assume that if the racquet wouldn't have any support, the ball would transfer the energy to the racquet that would fly backwards and the ball would rest quiet after the impact. *Doubt 1, Is this correct?These are the variables:

ball speed (straigh line perpendicular to the racquet)= 60 mph
racquet speed=0
"Rebound power"=0.4, and it is defined as the ratio of the exit speed to the incoming speed of the ball for that racquet
Relative speed between ball and racquet=60 mph
Rebound speed= Relative speed x Rebound power= 24 mph
Exit speed of the ball=Rebound speed = 24mph

In this case I think the impact absorbs part of the energy and obviously the exit speed is lower than the ball speed before the contact, it seems correct to me.

2.- Raquet and ball hitting each other with speed.

ball speed (straigh line perpendicular to the racquet)= 20 mph
racquet speed=40 mph
"Rebound power"=0.4, and it is defined as the ratio of the exit speed to the incoming speed of the ball for that racquet
Relative speed between ball and racquet=60 mph
Rebound speed= Relative speed x Rebound power= 24 mph
Exit speed of the ball=Rebound speed + Racquet speed= 40+24=64 mph

In this case there is an impact that absorbs part of the energy of the incoming ball, but they add the racquet speed, I have some doubts:

*Let's imagine that we choose a coordinate system that is in the center of gravity of the tennis ball, and let's repeat the calculation:

ball speed (straigh line perpendicular to the racquet)= 0 mph, it is the origin of our system
racquet speed=40 mph + 20 mph = 60 mph
"Rebound power"=0.4, and it is defined as the ratio of the exit speed to the incoming speed of the ball for that racquet
Relative speed between ball and racquet=60 mph
Rebound speed= Relative speed x Rebound power= 24 mph
Exit speed of the ball=Rebound speed + Racquet speed= 24+60=84 mph, I get a different result to the original which is absurd right? And I don't understand how a racquet moving at 60 mph could give a speed of 84mph to the ball which is higher. Is this possible?

*Let's imagine that we choose a coordinate system that is in the center of gravity of the racquet, and let's repeat the calculation:

ball speed (straigh line perpendicular to the racquet)= 60 mph, now the racquet is quiet and this is the sum of ball and racquet speeds.

racquet speed=0 mph, it is the origin

"Rebound power"=0.4, and it is defined as the ratio of the exit speed to the incoming speed of the ball for that racquet
Relative speed between ball and racquet=60 mph
Rebound speed= Relative speed x Rebound power= 24 mph
Exit speed of the ball=Rebound speed + Racquet speed= 24+0=24mph, Now I get a different result because in the coordinate system of the racquet all the movement is on the ball which is the same as case 1.

What am I doing wrong? Why do I get different results with different coordinate systems?

3.- Ball quiet and racquet hitting the ball.

ball speed (straigh line perpendicular to the racquet)= 0 mph
racquet speed= 60 mph
"Rebound power"=0.4, and it is defined as the ratio of the exit speed to the incoming speed of the ball for that racquet
Relative speed between ball and racquet=60 mph
Rebound speed= Relative speed x Rebound power= 24 mph
Exit speed of the ball=Rebound speed + Racquet speed= 24+60=84 mph

That is the third case of the book. How is that possible? I mean, a racquet at 60mph generating 84mph looks absurd to me. In this case there is not any rebound because the ball was quite, I guess the exit speed is just 60mph like the racquet, or a lower speed because some energy will be lost in the impact, but a HIGHER speed looks weird. Is this possible?

Are these all examples from the same book? Or your solutions to questions from the book?

It may be that you are using this coefficient of rebound improperly.
By definition it is the ratio between the ball's speeds when bouncing from a stationary rocket.
It is not obvious that the same value will apply when you have the ball stationary and the rocket moving.

In order to use this coefficient you can always move to a frame where the rocket is at rest.
But not to one where the ball is at rest.

nasu said:
Are these all examples from the same book? Or your solutions to questions from the book?

It may be that you are using this coefficient of rebound improperly.
By definition it is the ratio between the ball's speeds when bouncing from a stationary rocket.
It is not obvious that the same value will apply when you have the ball stationary and the rocket moving.

In order to use this coefficient you can always move to a frame where the rocket is at rest.
But not to one where the ball is at rest.

Cases 1, 2 and 3 are a copy from the book. The reasoning with the coordinate systems is mine.

Do you think is it possible to get a 84mph speed with a 60mph racquet speed?

So yes, the first 3 seem to be OK.
But for the next one you should use the rebound power of the ball (and not of the racket) which is not the same 0.4.

nasu said:
So yes, the first 3 seem to be OK.
But for the next one you should use the rebound power of the ball (and not of the racket) which is not the same 0.4.

So I understand you agree with the last one?

I mean racquet at 60 mph on serve gets a ball speed of 84 mph.

jonjacson said:
I mean, a racquet at 60mph generating 84mph looks absurd to me.
It's OK, if the racket + arm have more mass than the ball:
https://en.wikipedia.org/wiki/Elastic_collision#One-dimensional_Newtonian

jonjacson said:
I guess the exit speed is just 60mph like the racquet, or a lower speed because some energy will be lost in the impact, but a HIGHER speed looks weird.
You seem to confuse speed and energy.

jonjacson
Thanks, yes I was confusing the speed with the energy.

and don't forget the rotational energy that is transferred into motion when it hits the ground with a lot of "top spin"

jonjacson
zanick said:
and don't forget the rotational energy that is transferred into motion when it hits the ground with a lot of "top spin"

Thanks, the book talks about that at the end.

jonjacson said:
I assume that if the racquet wouldn't have any support, the ball would transfer the energy to the racquet that would fly backwards and the ball would rest quiet after the impact. *Doubt 1, Is this correct?
First, this is not a "doubt" it is a question: https://www.physicsforums.com/showthread.php?t=607274

Second, no it is not right. You are forgetting the inertia of the racket. If you tossed the racket upwards with no rotation and managed to hit it just at the top of its arc when it is motionless and unsupported, the ball would NOT just fall directly to the ground. How it would act would depend on its speed and weight and the weight of the racket.

phinds said:
First, this is not a "doubt" it is a question: https://www.physicsforums.com/showthread.php?t=607274

Second, no it is not right. You are forgetting the inertia of the racket. If you tossed the racket upwards with no rotation and managed to hit it just at the top of its arc when it is motionless and unsupported, the ball would NOT just fall directly to the ground. How it would act would depend on its speed and weight and the weight of the racket.

Fourth, this is an international forum with people from around the world. It is completely logical to expect finding expressions that are not written in perfect English. That makes the forum better since there are more opinions, QUESTIONS, threads etc.

Fourth, How many languages do you know a part from English? Maybe one day in the future you will have questions about something and you won't find an English forum that helps you and instead is in German, Will you be able to ask QUESTIONS there in perfect german? Maybe not, but for sure people there will be kind and will understand your issues.

1. What factors affect the rebound speed of a tennis ball?

The rebound speed of a tennis ball can be affected by a variety of factors, including the composition and condition of the ball, the type of surface it is bouncing off of, and the force with which it is struck. In general, a softer ball will have a slower rebound speed compared to a harder ball, and a rougher surface will result in a faster rebound compared to a smoother surface.

2. How does the rebound speed of a tennis ball change over time?

The rebound speed of a tennis ball can decrease over time due to wear and tear on the ball, which can cause it to become softer and less bouncy. Additionally, the rebound speed can also be affected by changes in temperature and humidity, as these can impact the elasticity of the ball.

3. Can the rebound speed of a tennis ball be measured?

Yes, the rebound speed of a tennis ball can be measured using a device called a ball tester. This tool measures the time it takes for the ball to bounce off a surface and calculates the rebound speed based on that time. Professional tennis organizations also have specific regulations for the rebound speed of tennis balls.

4. How does the rebound speed of a tennis ball affect gameplay?

The rebound speed of a tennis ball can greatly impact gameplay, as it can affect the speed and trajectory of the ball. A faster rebound can make the game more challenging and require players to react quickly, while a slower rebound can result in longer rallies and a more strategic gameplay.

5. Can the rebound speed of a tennis ball be manipulated?

Yes, the rebound speed of a tennis ball can be manipulated by changing the factors that affect it, such as the type of ball, the surface, and the force used to strike it. This is often done by professional players to gain an advantage in a match, but it is important to note that any manipulation must comply with the regulations set by the governing organizations.

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