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Type a summary of your results on this page. Do not include
the name of your school, advisor, or team members on this page.
The simple harmonic model of baseball collision system
For office use only
T1
________________
T2
________________
T3
________________
T4
________________
Team Control Number
7475
Problem Chosen
A
For office use only
F1
The material difference is also viewed as an influence factor. Some people had done research on the performance of wood, metal and other materials.
In our model, we try to make the outgoing speed of the baseball maximum .This is our definition of the sweet spot. In the process of solving the problem and reach our goal, we will consider the difference of the parameters of different materials. In the finally, we can find which position is the sweet spot.
________________
F2Biblioteka Baidu
________________
F3
________________
F4
________________
2010 Mathematical Contest in Modeling (MCM) Summary Sheet
(Attach a copy of this page to each copy of your solution paper.)
There is a tremendous amount of physics and engineering that goes into the design of a baseball or softball bat and an amazing amount of physics involved in the bat-ball collision, and in the performance and behavior of the bat itself.Sweet spot plays an important role in baseball for it can give the ball maximum of energy. Many studies showed that the bat vibrate violently when meets with the baseball, and cost a lot of energy. Through the careful studying, we abstract the collision system into a simple harmonic motion system which is constituted by 4 parts of objects and elastic force between them. Byanalyzingthe Simple harmonic system, we build differential equations model for the collision, and gain the ball leave speed at all locations of the hitting point. Then, we can get the location of sweet point by finding themaximumreturn speed of the ball. For problem 2 and 3, we change some coefficient of the model used in problem1 according to the situation, and concluded that corking a bat will slow the speed of ball, while using a bat made of aluminum will increase the ball speed.
Keywords:simple harmonic motion system , differential equations model , collision system
The simple harmonic model of baseball collision system
Abstract
There is a tremendous amount of physics and engineering that goes into the design of a baseball or softball bat and an amazing amount of physics involved in the bat-ball collision, and in the performance and behavior of the bat itself.Sweet spot plays an important role in baseball for it can give the ball maximum of energy. Many studies showed that the bat vibrate violently when meets with the baseball, and cost a lot of energy. Through the careful studying, we abstract the collision system into a simple harmonic motion system which is constituted by 4 parts of objects and elastic force between them. Byanalyzingthe Simple harmonic system, we build differential equations model for the collision, and gain the ball leave speed at all locations of the hitting point. Then, we can get the location of sweet point by finding themaximumreturn speed of the ball. For problem 2 and 3, we change some coefficient of the model used in problem1 according to the situation, and concluded that corking a bat will slow the speed of ball, while using a bat made of aluminum will increase the ball speed.
Keywords:simple harmonic motion system , differential equations model , collision system
IIntroduction
There are many definitions for what constitutes the "Sweet Spot" on a baseball bat. From a player's viewpoint, the sweet spot is the place on the bat barrel where the contact between bat and ball results in the best hit - the ball leaves the bat with the greatest speed and the player's hands feel very little vibration from the impact.But the scientific definition is unclear, because different locations can have differing effects. One possible sweet spot is the center of percussion, which is the location where the ball may impact the bat without causing a reaction force on the hand. An impact at any other location can cause the handle to feel like it is jumping in the hand. Another possible sweet spot is a location called a vibrational node. The impact of the ball causes the bat to vibrate in waves that have dead spots, or nodes. A third location of interest is the bat's center of mass, which is located by balancing the bat horizontally. The sweet spot is usually located not at the center of mass, but somewhere between it and the end of the bat. There are some other definitions too.
IIAssumptions of Our Model
Some players believe that “corking” a bat enhances the “sweet spot” effect. There are some arguments about that .Such asa corked bat has (slightly) less mass.,less mass (lower inertia) means faster swing speed and less mass means a less effective collision. These are just some people’s views, other people may have different opinions. Whethercorking is helpful in the baseball game has not been strongly confirmed yet. Experiments seem to have inconsistent results.
the name of your school, advisor, or team members on this page.
The simple harmonic model of baseball collision system
For office use only
T1
________________
T2
________________
T3
________________
T4
________________
Team Control Number
7475
Problem Chosen
A
For office use only
F1
The material difference is also viewed as an influence factor. Some people had done research on the performance of wood, metal and other materials.
In our model, we try to make the outgoing speed of the baseball maximum .This is our definition of the sweet spot. In the process of solving the problem and reach our goal, we will consider the difference of the parameters of different materials. In the finally, we can find which position is the sweet spot.
________________
F2Biblioteka Baidu
________________
F3
________________
F4
________________
2010 Mathematical Contest in Modeling (MCM) Summary Sheet
(Attach a copy of this page to each copy of your solution paper.)
There is a tremendous amount of physics and engineering that goes into the design of a baseball or softball bat and an amazing amount of physics involved in the bat-ball collision, and in the performance and behavior of the bat itself.Sweet spot plays an important role in baseball for it can give the ball maximum of energy. Many studies showed that the bat vibrate violently when meets with the baseball, and cost a lot of energy. Through the careful studying, we abstract the collision system into a simple harmonic motion system which is constituted by 4 parts of objects and elastic force between them. Byanalyzingthe Simple harmonic system, we build differential equations model for the collision, and gain the ball leave speed at all locations of the hitting point. Then, we can get the location of sweet point by finding themaximumreturn speed of the ball. For problem 2 and 3, we change some coefficient of the model used in problem1 according to the situation, and concluded that corking a bat will slow the speed of ball, while using a bat made of aluminum will increase the ball speed.
Keywords:simple harmonic motion system , differential equations model , collision system
The simple harmonic model of baseball collision system
Abstract
There is a tremendous amount of physics and engineering that goes into the design of a baseball or softball bat and an amazing amount of physics involved in the bat-ball collision, and in the performance and behavior of the bat itself.Sweet spot plays an important role in baseball for it can give the ball maximum of energy. Many studies showed that the bat vibrate violently when meets with the baseball, and cost a lot of energy. Through the careful studying, we abstract the collision system into a simple harmonic motion system which is constituted by 4 parts of objects and elastic force between them. Byanalyzingthe Simple harmonic system, we build differential equations model for the collision, and gain the ball leave speed at all locations of the hitting point. Then, we can get the location of sweet point by finding themaximumreturn speed of the ball. For problem 2 and 3, we change some coefficient of the model used in problem1 according to the situation, and concluded that corking a bat will slow the speed of ball, while using a bat made of aluminum will increase the ball speed.
Keywords:simple harmonic motion system , differential equations model , collision system
IIntroduction
There are many definitions for what constitutes the "Sweet Spot" on a baseball bat. From a player's viewpoint, the sweet spot is the place on the bat barrel where the contact between bat and ball results in the best hit - the ball leaves the bat with the greatest speed and the player's hands feel very little vibration from the impact.But the scientific definition is unclear, because different locations can have differing effects. One possible sweet spot is the center of percussion, which is the location where the ball may impact the bat without causing a reaction force on the hand. An impact at any other location can cause the handle to feel like it is jumping in the hand. Another possible sweet spot is a location called a vibrational node. The impact of the ball causes the bat to vibrate in waves that have dead spots, or nodes. A third location of interest is the bat's center of mass, which is located by balancing the bat horizontally. The sweet spot is usually located not at the center of mass, but somewhere between it and the end of the bat. There are some other definitions too.
IIAssumptions of Our Model
Some players believe that “corking” a bat enhances the “sweet spot” effect. There are some arguments about that .Such asa corked bat has (slightly) less mass.,less mass (lower inertia) means faster swing speed and less mass means a less effective collision. These are just some people’s views, other people may have different opinions. Whethercorking is helpful in the baseball game has not been strongly confirmed yet. Experiments seem to have inconsistent results.