Re: [Algorithms] rather curious

[<ro...@do...>]

Steven Clynes  wrote:

>Ron Levine wrote:
>> 
>> >....
>> >So you can see that a body of any mass will hit the earth at the same time.
>> >The difference due to the original gravitation law is that a more massive body
>> > will hit the earth with more FORCE and make a bigger dent.
>> >
>> 
>> Here, I think your use of "FORCE" is not appropriate.  The two bodies
>> fall under the same acceleration, so fall for the same time duration
>> and hit the earth with the same speed, but the more massive body has
>> more kinetic energy and more momentum, so makes a bigger dent.
>
>But I thought (possibly naively), that by definition Force = Mass *
>Accelleration, hence more mass, more force (for a fixed accelleration,
>ie gravity).
>
>Or are you saying the cause of the dent is momentum, not force?
>

The cause of the dent is dissipation of energy.  The body had non-zero
momentum before the collision and (assuming no bounce but entirely
dissipative energy loss) zero momentum after the collision.  The
change in momentum, in the classical picture, is the integral of
F dt, where t is time, integrated over the time of the collision
(usually short).  Force x time is called _impulse_.  In a collision
the time is very short, and the force varies sharply over this short
time period, and we usually do not know the force as a function of
time in this short interval, nor even the length of the interval, so
we can only deal with the impulse, which we know exactly as the change
in momentum.

Note that this "force" under discussion at this point is NOT
gravitational force, but rather the contact force between the body and
the earth--actually it is in the class of electromagnetic interaction,
not gravitational.