F=MA by Steve
Hi All
Steve Taylor wrote a very important post regarding bat velocity and its’ relationship to energy imparted to the baseball.  Steve I hope you will not mind that I brought it to the top of the page so all may gain from it. Many coaches have used F=MA incorrectly  Thanks Steve
Jack Mankin,
******
If the force you apply to the ball, as you're saying, is F= MA, and the batspeed is constant, this means acceleration is zero, therefore the force is zero! With no acceleration, F becomes zero, because anything multiplied by zero, is still ZERO!
Now, we KNOW the force on the ball is not zero. And the bat velocity can be constant and still impart a large force to the ball, can it not? This is why I said you were mixing apples and oranges.
So what would the zero force term mean in this example? It means there is no force acting on the BAT, to accelerate IT (you already reached top speed.) But there is kinetic energy in the bat's momentum this is what is transferred to the ball at impact. Both objects' speeds (momenta) change at impact, but the total momentum is conserved.
If the bat could move faster after contact than before contact (which is impossible), you've struck the ball with less than maximum batspeed. You have to look at it as a moment in time (for all practical purposes, the changes in the speeds of bat and ball are instantaneous.) The bat instantaneously loses momentum and the ball instantaneously gains some.
In an impact problem, what is relevant is momentum (product of inertia (or mass) and velocity.) Look at it this way:
Since F=ma, then, stated another way (with respect to time)
Ft = mv, where Ft =
force x time [impulse] and mv = mass x velocity
[momentum]
So the force you apply to the ball is proportional to the product of the bat's mass and its velocity, over time. You're trying to make it proportional to an INCREASE in velocity (acceleration.) This violates the fundamental conservation laws (you can't get more out than you put in.) In your theory the bat would have more momentum after the collision than before it (can a bullet go through a wall and come out going faster than it went in?)
If this is still unclear, I'll be happy to refer you to some other sources to clarify matters. But I think I've spent enough time on it for now. Thanks for the lively discussion.
Regards,
SteveT
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