美赛论文模板.pdf

Team Control Number For office use only For office use only T1 0000 F1 T2 F2 T3 F3 Problem Chosen T4 F4 A 2014 Mathematical Contest in Modeling (MCM) Summary Sheet (Attach a copy of this page to each copy of your solution paper.) Abstract We determine the sweet spot on a baseball bat. We capture the essential physics of the ball-bat impact by taking the ball to be a lossy spring and the bat to be an Euler-Bernoulli beam. To impart some intuition about the model, we begin by presenting a rigid-body model. Next, we use our full model to reconcile various correct and incorrect claims about the sweet spot found in the literature. Finally, we discuss the sweet spot and the perfor- mances of corked and aluminum bats, with a particular emphasis on hoop modes. A The LT XTemplate for MCM Version 5.0 E AA {{ LLTT XStudioXStudio }} EE November 3, 2014 2 Team # 0000 Page 3 of ?? 1 Introduction Although a hitter might expect a model of the bat-baseball collision to yield insight into how the bat breaks, how the bat imparts spin on the ball, how best to swing the bat, and so on, we model only the sweet spot. ˘ ˇ There are at least two notions of