- #1

jonjacson

- 453

- 38

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?

Thanks for your time!