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So, basically Reed warns Ben that if he throws a baseball to hard, it could cause a titanium bat to buckle:
http://i.imgur.com/9VGD3nm.jpg
Now I found a page with various stats on titanium, since we're talking about buckling I think we're supposed to use the elastic modulus (correct me if I'm wrong). This is 113.8 Gpa.
The diameter of a baseball bat is 2.75 in (0.06985 m). The diameter of a baseball is given various values here, averaging them we get 0.075625 m. To find the surface area that would be affected, we can take this value as the height of a cylinder and the previous one as the diameter. Surface area of the sides of a cylinder = 2 * pi * r * h. Since we're only measuring the half that gets hit by the ball, it's just pi * r * h, or 82.97584334 cm^2. This equals 0.00829758433 m^2, so multiplying that by the elastic modulus gives us 944,265,096.8 N. Multiplying this by the distance (width of the bat), we get 65,956,917.01 joules. Various values for the mass of a baseball are given here. The average is 144.923 g.
65,956,917.01 = 0.5 * 0.144923 * v^2 65,956,917.01 = 0.0724615 * v^2 910,223,945.1 = v^2 v = 30,170.08361 m/s. So Ben can throw a baseball at Mach 88.65991834
http://i.imgur.com/9VGD3nm.jpg
Now I found a page with various stats on titanium, since we're talking about buckling I think we're supposed to use the elastic modulus (correct me if I'm wrong). This is 113.8 Gpa.
The diameter of a baseball bat is 2.75 in (0.06985 m). The diameter of a baseball is given various values here, averaging them we get 0.075625 m. To find the surface area that would be affected, we can take this value as the height of a cylinder and the previous one as the diameter. Surface area of the sides of a cylinder = 2 * pi * r * h. Since we're only measuring the half that gets hit by the ball, it's just pi * r * h, or 82.97584334 cm^2. This equals 0.00829758433 m^2, so multiplying that by the elastic modulus gives us 944,265,096.8 N. Multiplying this by the distance (width of the bat), we get 65,956,917.01 joules. Various values for the mass of a baseball are given here. The average is 144.923 g.
65,956,917.01 = 0.5 * 0.144923 * v^2 65,956,917.01 = 0.0724615 * v^2 910,223,945.1 = v^2 v = 30,170.08361 m/s. So Ben can throw a baseball at Mach 88.65991834
