Link to Mailbag item: http://www.straightdope.com/mailbag/mbat.html
In the question about which is better: a heavy bat or a light one, SDSTAFF Ken
appeals to F=ma. I strenuously object:
- F= ma is not applicable here
- Ken applied it incorrectly
- acceleration magically becomes synonomous with velocity (ack! choke!
Yes, application of a bat to a ball will cause a force on that ball,
but a lot of that force goes into deforming the ball. (Imagine the
differences in batting a rock, a baseball, a tennis ball, and a
water balloon. In that last case, the deformation is spectacular.)
The baseball will spring back into shape and this whole complex
process is what makes the ball switch directions. This complex
process cannot be described with the simple F=ma equation.
Ken also seems to think that the force on the ball is equal
to the mass of the bat times the acceleration of the bat.
Yeesh! This is why we teach freshman to draw plastic bags
around their objects. The force on the ball is equal to
the mass of the ball times the acceleration of the ball.
In Ken’s interpretation, if the bat has zero acceleration (I think
this is called bunting), then it applies zero force to the ball,
And last, acceleration is NOT the same as velocity. Acceleration
is the change of velocity with respect to time (dv/dt).
The physics that Ken should have appealed to is the impulse
(the change in momentum) where the momentum of the bat (its
mass times velocity) can be transfered to the ball.
(think billiards). What’s weird is that all the rest of
Ken’s remarks are correct, namely a heavy bat has plenty of
momentum but a light bat swung faster has plenty of momentum
too. Ken’s quips about Popeye and robots are far superior
to anything I could inject.
[Note: This message has been edited by CKDextHavn]