Dear Straight Dope:
Can you hit a baseball farther with a light or a heavy bat? To be more specific, suppose that you build a machine to swing, with a fixed torque T, uniform (outside) diameter, axially symmetric cylinders of length L, diameter D and weight distribution w(l), where l is the axis variable and the cylinders are made of some standard alloy used to make baseball bats. Then what angle of swing, diameter, and weight distribution would make standard baseballs struck the by this cylinder travel furthest, as function of T? Is that specific enough?
Harlan, via e-mail
SDStaff Ken replies:
Plenty specific, Harlan. In fact, more specific than it has to be. The law of physics governing baseball bats, and a lot of other things, is:
F = ma
Where F= force resulting, m=mass and a=acceleration.
We can affect the amount of force generated by either changing the mass (weight) of the bat, or the acceleration of the bat (bat speed).
If you lighten the bat, the amount of mass applied is less, but since we don’t have machines playing baseball (except Cal Ripken, Jr.), the amount of acceleration is greater, i.e., it weighs less, so you can swing it faster. Conversely, if the bat weighs more (increase in mass), the amount of force would go up, if it weren’t harder to swing a heavier bat, thus reducing the acceleration. To increase both the mass and acceleration would result in more power, but you’d need forearms like Popeye to keep this up day after day. This explains Mark McGwire’s biceps.
So to answer your question, a baseball can be hit farthest with a heavy bat, assuming the game were played strictly by laboratory robots. In the real world, though, whether a light bat or a heavy bat is best depends on the skills and strength of the batter.
BTW, all of us here at the Straight Dope Science Advisory Board loved that stuff about angle of swing and diameter D and a function of T, etc. You can come sit with us next time we go to the ballgame. But you should know we make the newbies buy the beer.
SDStaff Ken, Straight Dope Science Advisory Board
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