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.
δ =
Estimate the deflection δ of the bat at B, where it hits the ball, just before it breaks, as a function of the Young's modulus, E, and the bending strength, σb, of the ash wood, and of the span of the bat between A and B, lAB, and the bat radius, r. You can assume that the bat breaks when the maximum normal stress reaches the bending strength of ash.
Express your answer in terms of σmax,lAB,E, and r.
|δ| =
Calculate the value for the deflection δ of the bat at B, given that ash has a Young's modulus, E=10GPa and a bending strength, σb=100MPa, and that lAB=0.8m and the (assumed constant) radius of the bat is 22mm.
|δ| (in mm):
sigma_max*l_AB^2/(3*E*r) answer for second one
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I am having problems with the first part. Because I found the deflection as:
delta=((P*(l_AB)^2)*((3*(l))-l_AB))/(6*E*I)
But l is not permitted, so I replaced l=0.95[m]. but I obtained a wrong answer.
My deduction is correct?
What is my error?
Please, some help.
Some help please.
I really don't know what is my error
try - sign
-(P*l_AB^3)/(3*E*I)
second part: express above formula in terms of maxm bending stress.
sigma*l^2*r/(3E) pls check
second part is wrong :(
try sigmal^2/(6*E*r) (with correct sign)
pl confirm, all?