2015年美国大学生数学建模优秀论文7011.docVIP

For office use only T1 ________________ T2 ________________ T3 ________________ T4 ________________ Team Control Number7011 ? Problem ChosenA For office use only F1 ________________ F2 ________________ F3 ________________ F4 ________________ Abstract This paper mainly makes a detailed discussion about “the sweet spot” from the physics point of view. Here, we focus on the following three issues by using elastic mechanics, material mechanics, dynamics, and some other theories. Part of energy is absorbed by the bat for the vibration during the moment of impact. Without considering the absorbed energy, we can use the conservation of angular momentum theorem to get the maximum batted-ball speed point at the end of the bat. On the circumstance of the absorbed energy, we show the relationship between the kinetic of the batted ball and the hit point by using MATLAB. Thus, we get “the Sweet Spot” which is the maximum energy transfer point. Furthermore, taking advantage of the impulse from theorem, we can also obtain that “the Sweet Spot” is the minimum sensation point. It shows that “the Sweet Spot” is not at the end of the bat. According to the analysis to the material normal stress at the moment of collision, a “corking” bat has no effect on the sweet spot location. “Corking” a bat will reduce the quality so that the batted-ball would get a higher speed. At the same time, the centre-of-mass backward movement makes the batted-ball speed higher, too. As a result, the batter could gain a longer time to reach the next point. Compared with the material of the aluminum bat and that of the wood bat with the same quality, it can be seen that the COR (Coefficient of Restitution) of the wood bat is bigger than that of aluminum. Since the batted-ball speed and COR are positively correlated, the batted-ball speed when the ball is hit by a aluminum bat is higher than that when the ball is hit by a wood bat. If the batter uses a aluminum bat, the batted ball gets a higher speed,