### Dodge balls in the Face

Dodge ball experiment:
Anthony Agius
Angelo Berlasi
Eric Pachota

We want to explore the physics of throwing and getting hit by dodgeballs

1st Test: Speed of Dodge ball
2nd Test: Speed of arm during throw
3rd Test: Force of dodge ball on face
4th Test: Acceleration of arm: (forearm, wrist, hand)
5th Test: Acceleration of dodgeball on face
6th Test: Momentum of ball
7th Test: Work of Eric's arm
8th Test (main event): Dodge ball to the face!
chyea...

Procedure:

Materials:
• Dodge Balls (Gator Ball)
• High Speed Camera
• Accelerometer
• Weight Scale
• Force Plate
• Video Camera
• Human Face

PROCEDURE
First we are going to test the force of Eric's throw on a force plate.

Next we are going to get a sample of high speed video of Eric's throwing.

After that we are going to get a high speed video of Eric throwing a dodge ball at Anthony's face.

Once we are done, we are going to analyze our video data in video analysis and tracker.

Using the data that we found in tracker, we can make the information into a graph.

After graphing and analyzing our data, we can recreate our experiment in interactive physics.

Report

Have you ever got hit with a dodge ball? I am not talking about a real dodge ball that you see in professional tournaments or like the ones in the movie “Dodgeball”. I am talking about a gator ball, probably the ones that you used in gym class. They weigh about 0.095 kg, which is about 0.21 pounds. They don’t even weigh 1 pound but they still can pack a punch. When thrown at speeds up to 70 mph, these balls can really hurt, especially when you are taking one in the face. Before we get to the “dodge balls in the face,” let’s take a look at the physics of the throw.

Eric’s Throw at the Wall

HIGH SPEED VIDEO RECORDED AT 500fps

While using the high speed camera, we were able to analyze our data on Eric’s throw at the wall a lot easier. Using tracker we used plot points to figure out some critical data. Here is a list of the data we discovered.

Acceleration of wrist= 215 m/s2

Acceleration of forearm = 106 m/s2

Acceleration of hand = 357 m/s2

Acceleration of ball = 95 m/s2

Velocity of ball (after released) = 32 m/s2

Momentum of Ball = 3.04 (kg)(m/s)

Work of Eric’s arm= 1707.5 joules

One thing we did have trouble on was finding the work of Eric’s arm.

This is the steps we used to find the work.

W=Fd, but since we did not know the force, we substituted to insert what we do know.

So now the formula changed to W=(ma)d

We figured out that the mass of Eric’s arm was approximately 5.4 kg and the acceleration of his arm was about 106 m/s2. So F=572.4 Newtons

To measure the Distance, we decided to take the circle approach. Making the path that he took with his arm into a half circle, then we could just solve for the perimeter of the circle and then divide it by 2.

We figured the diameter of the circle route was approximately 1.9m. So the radius of the circle would be 0.95m. Using the formula Perimeter=2πr, we substituted r into the formula and solved. So we came to figure out that the perimeter of the circle that the path Eric’s arm took was 5.97m. When you divide that number by 2, you get the distance of his arm. We got 2.99m. So now that we got the force and the distance, we can solve for Work.

W=Fd

W=(ma)(2πr/2)

W=(5.4*106)((2*3.14*0.95)/2)

W=1707.5 joules

We were also able to graph all the data in tracker. We graphed velocity for each of Eric’s forearm, wrist, hand, and the ball. The graph shows the gradual increasing of velocity of each body part before the ball was released.

As you can see in the graph, all of the velocity increases rapidly from 0.314 seconds to about 0.330 seconds. This is when the most acceleration is occurring in Eric’s arm. All of this is occurring in only about 0.016 seconds. May be your asking yourself, how is it possible that Eric’s hand can accelerate to 357m/s2? Well all of this speeding up is only occurring in that small frame of time. Also when we tried using the 25g accelerometers, we maxed those out very easily. So the acceleration is going to be more than 25*9.8m/s2. Another interesting point that we found in our data was the trend of our points in our graph all coincided with each other. They all peak at the same point and you can see where the ball is released.  We thought that it was also significant to show that Eric’s forearm was not accelerating as fast as his hand was. This is because the radius of the path his forearm is going to be different than the radius of the path his hand takes. Whichever has the larger radius is going to have a larger distance, and larger distance means more acceleration, that is only if the time does not change.

Now the moment you’ve all been waiting for, Dodge Balls in the Face!!!! Yes, he took a couple for the team, but it was all worth it after. Actually we extracted some very impressive data with these videos. We have two high speed videos of Anthony getting hit in the face. The first video was taken inside our school, in the one and only physics room. We have both the normal and high speed videos. Hint, we suggest you watch the normal speed video before you watch the high speed video.

HIGH SPEED VIDEO RECORDED AT 250fps

This is the data that we found on these videos, mostly from tracker.

Hit in the Face inside

Velocity before hitting Anthony in face = 22.1 m/s

Acceleration of ball in flight = -70m/s2

Acceleration of ball hitting Anthony in face= -2024m/s2

Velocity of ball after hitting Anthony in face = 6.7m/s

Momentum of ball = 2.0995 (kg)(m/s)

Force on face = 192.28 Newtons

From tracker we calculated that the speed of the ball that hit Anthony in the face was approximately 22.1m/s which is about 50mph. It’s crazy to think that Eric can throw the ball that hard and then it’s even crazier that Anthony takes it in the face. The force on Anthony’s face that we calculate was somewhere around 192 Newtons. This is not the maximum that Eric can throw. While testing before on a force plate, Eric’s throw hit to about 248 Newtons of force.

FORCE PLATE

Because the ball weighs about 0.095kg, we can calculate the acceleration of Eric’s throw at the force plate. F=ma, and we know two of the three variable.

F=ma

248=0.095(a)

248/0.095=a

a=2610.53m/s2

So the acceleration of the ball from Eric’s throw that was on the force plate was about 2610.53m/s2. We’re just glad this wasn’t the force that was acting upon Anthony’s face, cause that would have been a stinger.

This last normal and high speed video that we have, was taken outside. Like the previous videos, watch the normal speed video before you watch the high speed one. Watch carefully this time at the high speed video because this one was taken at 500 frames per second instead of 250.

HIGH SPEED VIDEO RECORDED AT 500fps

Here is the data that we collected from these set of videos:

Velocity before hitting Anthony’s face = 26.5 m/s

Acceleration of ball in flight = -12m/s2

Acceleration of ball hitting Anthony’s face = -2110m/s2

Velocity of ball after hitting Anthony’s  face = 8.6 m/s

Momentum of ball = 2.5175 (kg)(m/s)

Force on Face = 200.45 Newtons

This time, the velocity of the ball increased by 4.4m/s and you can see the difference in what happened. That is a difference of about 9.84mph. So this time the ball was traveling somewhere around 60mph. While analyzing this video, we decided to take the math a little further and figure out the speed of the wave traveling through my face and neck. What we concluded was that the speed of the wave on Anthony’s neck = 2.526m/s. That is about a 6mph wave traveling through his face. The reason that we cannot see the wave on the normal speed video is because ball is only touching his face for 5/500 of a second which is = 1/100 or 0.01 seconds. The reason that we cannot see the wave on his face is because the wave only lasts for 12/500 of a second, which equals 0.024 seconds. Because these things do not even last 1 second, we need to slow time down to see them more clearly.

Interactive Physics

The last thing we did after analyzing our videos was that we recreated the throwing of the dodge ball at a face. But because it was too hard to make a realistic body in interactive physics, we just tested the ball and the head. We assumed that an average head of a person weights about 5 kg or 12lbs, and the dodge ball that we used weighed about 0.095 kg. We also set the velocity of the dodge ball to 32m/s, which was one of the speeds that Eric threw before. We performed the test in interactive physics and we received these results:

Before Contact

 Dodge Ball Anthony's Head Velocity 32m/s 0 Acceleration 65.31m/s2 0 Momentum 3.040(kg)(m/s) 0 Angular Momentum 0 0 Torque 0 0 Total Force 0.932 N 49.033N Kinetic Energy 48.640J 0

During Contact

 Dodge Ball Anthony's Head Velocity 15.244m/s 0.892m/s Acceleration 0 0 Momentum 1.448(kg)(m/s) 4.461(kg)(m/s) Angular Momentum 0.056 0.156 Torque 0 0 Total Force 0.932 N 49.033N Kinetic Energy 11.168 1.992

After Contact

 Dodge Ball Anthony's Head Velocity 15m/s 0.606m/s Acceleration 0 2.942m/s2 Momentum 1.469(kg)(m/s) 3.030(kg)(m/s) Angular Momentum 0.056 -1.847 Torque 0 -20.594N-m Total Force 0.932 N 14.711N Kinetic Energy 11.489J 1.266J
Interactive physics showed the model of just the ball and Anthony's head. Because there was no neck or shoulders on the model in interactive physics, the results were a little bit different than the ones we got from the high speed video. Another factor we have to take in account of is the fact that my face can absorb some the collision. So the impact is different between the two
CONCLUSION

We learned many things during this physics of sports project. Not only did we learn to use a new program called tracker, but we now know all of the investigations of throwing and getting hit in the face with a dodge ball. The greatest part of this project was using the high speed film to analyze our data. We would love to do another project like this that could record at 1000 frames per second instead of 500.