Posted by: Mike Myers (mike.myers@bell.ca) on Thu Oct 21 20:50:39 2004

>>> Of course, this is the case.
>
> I was merely identifying a contradiction in Jack's previous statements. In his Oct 4 response to Bruce he indicates "bat-head acceleration is exponential rather than linear in nature" with the analogous "acceleration of a dragster is also exponential rather than linear in nature". This suggests rate of velocity change is of power >2 (and possibly increasing):
>
> If c=constant, and vi=0, then vf is:
>
> If a=c, vf=ct
> a=ct, vf=ct*t = ct^2
> a=ct^(>1), vf=ct^(>1)*t = ct^(>2)
>
> He today indicates bat forces applied are constant. If so, bat-head acceleration IS constant, since bat mass does not change (F=ma). <<<
>
> Hi Mike
>
> Tom’s example with gravity should have proved to you that with a constant applied force, the increase in bat velocity is exponential. (F=ma ) also applies to gravity. As the force of gravity remains constant, the velocity of the falling mass increases exponentially.
>
> Jack Mankin
>
No Jack. If force (and thus acceleration) is constant, velocity change is linear, not exponential - position changes exponentially.

Gravity is a force (F = GMm/r^2) which exhibits near constant acceleration locally (i.e. on earth surface), and thus linear velocity change. Position of a falling mass increases exponentially.

I was clarifying for Tom the fact that you indicated, at one time, exponential bat-head acceleration, and at another time, constant force applied to bat. These suggestions are contradictory. Tom seemed to indicate he saw no contradiction and provided his gravity example. (Note 32,64,96 is linear.) His example addressed changing velocity with constant force, which I never questioned.

The contradiction was changing acceleration and constant force.

Regards,
Mike.