【正文】 Team 8038 Page 4 of 20 of the Problem Explain the “sweet spot” on a baseball bat. Every hitter knows that there is a spot on the fat part of a baseball bat where maximum power is transferred to the ball when hit. Why isn’t this spot at the end of the bat? A simple explanation based on torque might seem to identify the end of the bat as the sweet spot, but this is known to be empirically incorrect. Develop a model that helps explain this empirical finding. Some players believe that “corking” a bat (hollowing out a cylinder in the head of the bat and filling it with cork or rubber, then replacing a wood cap) enhances the “sweet spot” effect. Augment your model to confirm or deny this effect. Does this explain why Major League Baseball prohibits “corking”? Does the material out of which the bat is constructed matter? That is, does this model predict different behavior for wood (usually ash) or metal (usually aluminum) bats? Is this why Major League Baseball prohibits metal bats? of the Problem Analysis of Problem I First explain the “sweet spot” on a baseball bat, and then develop a model that helps explain why this spot isn’t at the end of the bat.[1] There are a multitude of definitions of the sweet spot: 1) the location which produces least vibrational sensation (sting) in the batter39。s hands 2) the location which produces maximum batted ball speed 3) the location where maximum energy is transferred to the ball 4) the location where coefficient of restitution is maximum 5) the center of percussion For most bats all of these sweet spots are at different locations on the bat, so one is often forced to define the sweet spot as a region. If explained based on torque, this “sweet spot” might be at the end of the bat, which is known to be empirically incorrect. This paper is going to explain this empirical paradox by exploring the location of the sweet spot from a reasonable angle. Based on necessary analysis, it can be known that the sweet zone, which is decided by the centerofpercussion (COP) and the vibrational node, produces the hitting effect abiding by the law of energy conversion. The two different sweet spots respectively decided by the COP and the viberational node reflect different energy conversions, which forms a twofactor influence. This situation can be discussed from the angle of “spacedistance” concept, and the “Technique for Order Preference by Similarity to Ideal Solution (TOPSIS)” could be used.[2] The process is as follows: first, let the sweet spots decided by the COP and the viberational node be “optional Team 8038 Page 5 of 20 sweet spots”。 then, the sweet spot could be located by sequencing the sweet zones of the two kinds on the bat. Finally, pare the maximum hitting effect of this sweet spot with that of the end of the bat. Analysis of Problem II Problem II is to explain whether “corking” a bat enhances the “sweet spot” effect and why Major League Baseball prohibits “corking”.[4] In order to find out what changes will occur after corking the bat, the changes of the bat’s parameters should be analyzed first: 1) The mass of the corked bat reduces slightly than before。 3) The mass center of the bat moves towards the handle。 5) Less mass means a less effective collision； 6) The moment of inertia bees smaller.[5][6] By analyzing the changes of the above parameters of a corked bat, whether the hitting effect of the sweet spot has been changed could be identified and then the reason for prohibiting “corking” might be clear. Analysis of Problem III First, explain whether the bat material imposes impacts on the hitting effect。 2) The process discussed refers to the whole continuous momentary process starting from the moment the bat contacts the ball until the moment the ball departs from the bat。 b. length of the bat S (the distance between Block 1 and Block 5 in Fig 43)。 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)。s right hand. Fig. 44 Fundamental bending mode 1 (215 Hz) The second bending mode has three nodes, about inches from the barrel end, a second near the middle of the bat, and the third at about the location of a righthanded hitter39。 Step 2: Determining the most ideal position ?*x and the acceptable most unsatisfied position ?*x Assume that the most ideal position is }min{ *1* xx ?? , and the acceptable most unsatisfied position is }max{ *2* xx ?? 。 z is the distance from the pivot point where the ball hits the bat； inlv is the ining ball speed； batv is the bat swing speed just before collision. The following formulas are got by sorting the above variables[1]: gLM gdIT b a t ?? 22 ?? ……………………… ………………… … （ 48）224? gTMdILC O P b a t ??? ………………………………… ……… …… （ 49） Team 8038 Page 15 of 20 ? ? batAinA veveBBS ??? 1………………… ……………………… （ 410） Associating the above three formulas with formula (46) and (47), the formulas amongBBS , the mass M , the centerofmass (CM ), the location of COP, the coefficient of restitution BBCOR and the momentofinertia of the bat batI are: batin vk kB B C O Rvk kB B C O RBBS )11(1 ? ???? ?? ……………………… （ 411） 224?MgdTIbat ?………………………………… ………………………… （ 412） Mmk ball?……………………………………………………………… （ 413） It can be known form formula (411), (412) and (413): 1) When the coefficient of restitution BBCOR and mass M of the material changes, BBS will ch