The television coverage of the World Series showed several remarkable slow-motion views of the deflection of the bat as it hit the ball. Major league wood baseball bats are made of ash. A typical major league bat has a length of 0.95m and a tapering circular cross section. The ball typically hits the bat 150mm from the free end (see figure below). Occasionally, the bat breaks as it hits the ball.For this problem, you can assume that the bat is a cylinder of constant radius and that the batter holds the end of the bat rigidly, so that it is loaded as a cantilever beam.
Derive an equation for the bending deflection δ of the bat at B, where the ball hits the bat, in terms of the applied load, P, the span, lAB, the Young's modulus of ash, E and the moment of inertia of the cross section, I.