It doesn''t matter, a final impulse force is given and we have to assume that takes into account any forces the player puts on the ball for any amount of time the player is in contact, for any reason.

We have an initial velocity, an initial (and for all intended purposes, constant) mass, and an impulse (change of momentum). Assuming elastic collision, this is a simple equation:
Impulse force = mΔv = m(v2 - v1)

V2 = (Impulse force / m) + v1

Don''t try to overcomplicate the problem too much. The player changes the momentum of the ball - it doesn''t matter how or why or for how long or with what intent, all we know is that the player does what he does, and the momentum changes.

quote:
-An object with constant velocity and momentum M1V1 collides with an object with constant velocity and momentum M2V2. The objects stick together for some time period (T1, T1'') and then go their separate ways.
- An object with constant acceleration and momentum M1V1 at the time of collision collides with an object with constant velocity and momentum M2V2. The objects stick together for some time period (T2, T2'') and then go their separate ways.

This two situation are not equal.

You should think about things which happen when object collides.

When objects start collides in T1,impact force F12 (object1->object2) and F21 (object2->object1)affect on object.The size of F12 and F21 is FUNCTION OF DEFORMATION,VELOCITY AND ACCELERATION:
F12=F12(d2,v2,a2)
F21=F21(d1,v1,a1)
and F12=F21=0 when objects does not collide.
These forces (should) affect only for short time and result is changed velocity.
In books you can find only this v2(T1'')=e*v1(T1),where e is coefficient of restitution.This equation is not valid for every cases,it is approximation.

When i experimented herewith for a first time i made ''trampoline effect'' and i think it could be good solution for your problem.It is simple,make player''s(swing''s?)force proportional to distance from (first)point of collision.

In short:
Force_on_ball= k*A*distance_from_original_position_of_player_hands + k*B*velocity_of_ball
k should be 0 when ball is before point of interaction,be carefull with signs.
I hope you understand,what i wanted to tell you.

quote:Original post by Zipster
It doesn''t matter, a final impulse force is given and we have to assume that takes into account any forces the player puts on the ball for any amount of time the player is in contact, for any reason.

The impulse force you speak of depends on the conservation of linear momentum and is therefore internal to the system. I contend that an acceleration in the player''s swing is external to the system so that conservation of linear momentum does not hold.

For instance, comparing the player''s muscle to the thrust of a self-propelled block of wood: A block with mass 10 and initial velocity 0 is stuck to a block with mass 30 and initial velocity 0. Total momentum is currently 0. The first block accelerates forward with a force of 10N, pushing the second block along with it. After 8 seconds the two blocks are travelling at 2 m/s. Total momentum is now 80 kg*m/s. 0 != 80.

quote:Original post by chronos
The accelerating sphere in my example is supposed to represent the player''s swing, to account for "follow through" impulse forces on the ball. I don''t intend to take the ball''s acceleration due to gravity into account at the time of collision exactly for the reasons you suggest. So it''s the swing''s acceleration that I''m trying to account for, though perhaps I''m wasting my time?

That probably won''t be significant either. I would say just treat the velocity as constant throughout the collision. Use the start or end velocity, or maybe the average of the two.

Okay. So you all agree I should ignore the acceleration at the time of collision and think of the problem strictly in terms of momentum. After skipping forward on Hecker's paper on collision response I noticed the section where he talks about "Newton's Law of Restitution for Instantaneous Collisions with No Friction". He says to ignore noncollision forces and rely instead on collision impulses. So I'll do that.

Interesting problem, though. Thanks to each of you for your help, and for putting up with my arguments.

(AlexanderCZ: I'm afraid I don't understand your formulae. For instance, what are k, A and B, and what do F12 and F21 look like on the inside? Any references you might recommend?)

[edited by - chronos on November 7, 2002 5:40:05 AM]

A,B are constants which will determine behaviour of collision.
k is 1 during collision, otherwise 0-look at condition of impact forces,they must be zero when collision does not occur.