### Game, Set and Match

Jon Groszek
Thore Aalvik
Justin Pennisi
Danya Berr

For our project, we analyzed the velocity, acceleration, and force of a tennis ball coming off of a racket for two different types of shots; the serve and the forehand. We also looked at the impulse and work Jon is putting on the ball for both types of shots.  We then also looked at the racket head speed of Jon's racket as he hit the serve.

Materials
• Tennis Ball (57 g)
• Tennis Racket (300 g)
• High Speed camera
• Video Camera
• Laptop
• Tennis player
• Tracker
• Scale Bar

Procedure

The first step our group did was record Jon hitting a regular serve with the high speed camera at 250 frames per second. Then we recorded Jon hitting a forehand groundstroke with the high speed camera at 250 frames per second.  From there, we uploaded the videos onto tracker to calculate the velocity, acceleration, and force of the tennis ball as it leaves the tennis racket.  We also calculated the acceleration and velocity of Jon's arm as it is moving through the stroke. From this program we created graphs that depict all the data from these two types of tennis shots.  We also modeled a serve in Interactive Physics which is attached to the bottom of the page. Now let's take a look at those graphs.

Graphs    The video in the program is of Jon serving at 250 frames per second.  Our group uploaded the video of the serve to Tracker and analyzed it.  Where the red is near the origin is when Jon's ball toss is starting. From this point, where it is not red, the ball goes out of vision from the camera. Where it gets red again is when Jon's ball toss is coming down. Then when the graph sharply turns upward Jon strikes the ball. Now from the chart at the bottom right, we can see that the Velocity of the ball is 26.154 m/s as soon as the ball leaves the strings of the racket. We can also see that the Acceleration of the ball as the ball leaves the strings is 447.747 m/s squared. We then calculated the force of the ball as it left the racket by using the formula F=ma. F=(0.057kg)(447.747m/s squared) = 25.522 Newtons.  We also calculated the momentum (which isn't shown in the screen shot) which is P=mv. P=(0.057kg)(26.154 m/s). P=1.49 kg m/s. Work equals force times distance. W=Fd. W=(25.522Newtons)(.16meters) = 4.08 joules. Next we found Impulse. Impulse equals force times time. To find the time we took .004 (since the video is 250 frames per second) and multiplied it by 3 since the ball was on the racket for 3 clicks and we got .12 seconds. So then Impulse =(25.522 Newtons)(.012 seconds) = 0.31(Newtons)(Seconds).

Now what we did here is we measured the racket head speed of Jon's racket as he was hitting the serve. And of course, we used tracker to do so.

Jon's racket head speed is highest right before he is about to hit the ball; it is 97.656 m/s. WOW THAT'S AMAZING. That equals an astounding 218 mph!!!! You can also see from the chart that before he hits the ball his racket head speed is gradually increasing until he hits the ball. Then after he hits the ball, his racket head speed fluctuates a little bit then it gradually decreases.

Now, take a look at some
INTENSE HIGH SPEED VIDEO

Now we are going to analyze the velocity, acceleration, force and momentum of a forehand groundstroke.

The video in the program is of Jon hitting a forehand groundstroke at 500 frames per second.  We uploaded the video of the forehand to Tracker and analyzed it.  Where the graph is steady, the ball is falling at a constant rate. Then where the graph sharply shoots upward is when Jon strikes the ball with his racket. Now from the chart at the bottom right, we can see that the Velocity of the ball is 59.936 m/s as soon as the ball leaves the strings of the racket. We can also see that the Acceleration of the ball as the ball leaves the strings is 9,498 m/s squared. We then calculated the force of the ball as it left the racket by using the formula F=ma. F=(0.057kg)(9,498 m/s squared) = 541.386 Newtons.  We also calculated the momentum which is P=mv. P=(0.057kg)(59.936 m/s). P=3.42 kg m/s.   Then we calculated work which is force times distance; W=Fd. We found the distance by simply using the scale bar on tracker and adjusting is accordingly so that it equaled the distance the ball was on the racket. W= (541.386 Newtons)(.15 meters) = 81 joules. Next we calculated impulse. Impulse = Force times time. To find the time we multiplied .002 (since this video is 500 frames per second) by 3 (since the ball was on the racket for 3 clicks) and got .006 seconds. So then Impulse=(541.386 Newtons)(.006 seconds) = 3.25(Newtons)(Seconds).

Now let's take a look at the racket head speed of Jon's racket as he is hitting the forehand. We used tracker to do this too.

Jon's racket head speed is highest right before he makes contact with the ball. Right before he hits the ball his racket head speed 67.724 m/s. Then as you can see from the graph, it starts to decrease then right after he hits the ball it starts to increase a little and then it decreases again.

Now for some more intense HIGH SPEED VIDEO!!

#### Slow Motion forehand

Interactive physics

Here is our representation of the serve in interactive physics.
To open this file, you need to have installed the program interactive physics.

Conclusion

Our group really enjoyed working on this project and we learned a lot. One of the cool things about this project was seeing a tennis serve and forehand in slow motion. It was probably a once in a lifetime experience because it's not everyday you run into someone with a high speed camera!! We learned how to use a new program which we have never used before;Tracker. Tracker was very useful in finding velocity, acceleration, and momentum. We also figured out how to find Work and Impulse!!

One of the things we learned which was very interesting was that Jon's racket head speed on his serve and forehand was greatest the moment before he hit the ball; it was 97 m/s for the serve and 67 m/s for the forehand!! Then this turns into a ball speed of 60 m/s for the forehand and 26 m/s for the serve. This makes sense since groundstrokes are easier to generate power than serves are. Therefore, a greater racket head speed is needed to generate power on the serve, as opposed to the groundstroke where you don't need as much racket head speed to generate power. We hypothesized that this happens because of the position of the body and racket on both shots. The racket on the serve is in a more awkward position and therefore it is harder to generate power even though your racket head speed may be greater than a groundstroke's racket head speed.

ċ
interactivephyiscstennis.IP
(25k)
Steve Dickie,
May 15, 2009, 6:44 AM