【正文】 d. swing period of the bat on its axis round the pivot T (take an adult male as an example: the distance between the pivot and the knob of the bat is (the distance between Block 1 and Block 2 in Fig. 43)。 second, define the regions that these optional sweet spots may appear as the “sweet zones”, and the length of each sweet zone as distance。 Step 3: Calculating the distance The Euclidean distance of the positive ideal position is: ? ?? ?? )( ** xxd The Euclidean distance of the negative ideal position is: ? ?? ?? )( ** xxd Step 4: Seeking the integrated optimal region The integrated evaluation index of the evaluation object is: ????? dd db… …………………………（ 45） 2) Optimization positioning Considering bat material physical attributes of normal wood, when the period is sT ? and the vibration frequency is 520?f HZ, the ideal “sweet zone” extent can be drawn as ? ?cmcm 0 4 , . As this consequence showed, the “sweet spot” cannot be at the end the bat. This conclusion can also be verified by the model for problem II. Verifying the “sweet spot” is not at the end of the bat 1) Analyzed from the hitting effect According to Formula 411 and Table 42, the maximum battedballspeed of Team 8038 Page 13 of 20 the “sweet spot” can be calculated as smBBS sweet /? , and the maximum battedballspeed of the bat end can be calculated as smBBS end /? . It is obvious that the “sweet spot” is not at the end of the bat. 2) Analyzed from the energy According to the definition of “sweet spot” and the method of locating the “sweet spot”, energy loss should be minimized in order to transfer the maximum energy to the ball. When considering the “sweet spot” region from angle of torque, the position for maximum torque is no doubt at the end of the bat. But this position is also the maximum rebounded point according to the theory of force interaction. Rebound wastes the energy which originally could send the ball further. To sum up the above points: it can be proved that the “sweet spot” is not at the end of the bat by studying the quantitative relationship of the hitting effect and the inference of the energy transformation. Modeling and Solution to Problem II Model Preparation 1) Introduction to corked bat[5][6]: Fig 47 As shown in Fig 47, Corking a bat the traditional way is a relatively easy thing to do. You just drill a hole in the end of the bat, about 1inch in diameter, and about 10inches deep. You fill the hole with cork, super balls, or styrofoam if you leave the hole empty the bat sounds quite different, enough to give you away. Then you glue a wooden plug, like a 1inch dowel, in to the end. Finally you sand the end to cover the evidence. Some sources suggest smearing a bit of glue on the end of the bat and sprinkling sawdust over it so help camouflage the work you have done. 2) Situation studied： Situation of the best hitting effect: vertical collision occurs between the bat and the ball, and the energy loss of the collision is less than 10% and more than 90% of the momentum transfers from the bat to the ball (the hitting point is the “sweet spot”). Team 8038 Page 14 of 20 3) Analysis of COR After the collision the ball rebounded backwards and the bat rotated about its pivot. The ratio of ball speeds (outgoing / ining) is termed the collision efficiency, Ae . A kinematic factor k , which is essentially the effective mass of the bat, is defined as batballI zmk 2? ………………………………………………………… （ 46） where natI is the momentofinertia of the bat as measured about the pivot point on the handle, and z is the distance from the pivot point where the ball hits the bat. Once the kinematic factor k has been determined and the collision efficiency Ae has been measured, the BBCOR is calculated from kkeBBC OR A ??? )1( ………………………………………… （ 47） 4) Physical parameters vary with the material: The hitting effect of the “sweet spot” varies with the different bat material. It is related with the mass of the ball M , the centerofmass (CM ), the location of the centerofmass d , the location of COP L , the coefficient of restitution BBCOR and the momentofinertia of the bat batI . Controlling variable method analysis M is the mass of the object； d is the location of the centerofmass relative to the pivot point； g is the gravitational field strength； batI is the momentofinertia of the bat as measured about the pivot point on the handle。 then, develop a model to predict different behavior for wood or metal bats to find out the reason why Major League Baseball prohibits metal bats?[1][4] The mass (M) and the center of mass (CM) of the bat are different because of the material out of which the bat is constructed. The changes of the location of COP and moment of inertia ( batI ) could be inferred.[2][3] Above physical attributes influence not only the swing speed of the player (the less the moment of inertia batI is, the faster the swing speed is) but also the sweet spot effect of the ball which can be reflected by the maximum batted ball speed (BBS). The BBS of different material can be got by analyzing the material parameters that affect the moment of inertia. Then, it can be proved that the hitting effects of different bat material are different. Team 8038 Page 6 of 20 Assumptions and Symbols Model Assumptions 1) The collision discussed in this paper refers to the vertical collision on the “sweet spot”。 5) Less mass means a less effective collision； 6) The moment of inertia bees smaller.