【正文】 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。 e. distance between the undetermined COP and the pivot L (the distance between Block 2 and Block 4 in Fig. 43, that is the turning radius) . Fig. 43 Table 41 Block 1 knob Block 2 pivot Block 3 the centerofmass（ CM） Block 4 the center of percussion (COP) Block 5 the end of the bat ? Calculation method of COP[1][4]: distance between the undetermined COP and the pivot: 224?gTL? (g is the gravity acceleration） （ 43） moment of inertia: 220 4?MgLTI ? (L is the turning radius,M is the mass) （ 44） Team 8038 Page 10 of 20 ? Results: The reaction force on the pivot is less than 10% of the batandball collision force. When the ball falls on any point in the “sweet spot” region, the area where the collision force reduction is less than 10% is ),( LL cm, which is called “Sweet Zone 1”. 2) Determining the vibrational node The contact between bat and ball, we consider it a process of wave the bat excited by a baseball of rapid flight, all of these modes, (as well as some additional higher frequency modes) are excited and the bat vibrates .We depend on the frequency modes ,list the following two modes: The fundamental bending mode has two nodes, or positions of zero displacement). One is about 61/2 inches from the barrel end close to the sweet spot of the bat. The other at about 24 inches from the barrel end (6 inches from the handle) at approximately the location of a righthanded hitter39。 3) Both the bat and the ball discussed are under mon conditions. Symbols Table 31 Symbols Instructions k a kinematic factor 0I the rotational inertia of the object about its pivot point M the mass of the physical pendulum d the location of the centerofmass relative to the pivot point L the distance between the undetermined COP and the pivot g the gravitational field strength batI the momentofinertia of the bat as measured about the pivot point on the handle T the swing period of the bat on its axis round the pivot S the length of the bat z the distance from the pivot point where the ball hits the bat f vibration frequency ballm the mass of the ball and Solution Modeling and Solution to Problem I Model Preparation 1) Analysis of the pushing force or pressure exerted on hands[1] Team 8038 Page 7 of