Re: [Phys-l] conservation versus constancy

["Robert Cohen" <Robert.Cohen@po-box.esu.edu>]

I'm trying to fit this "sling shot" example within the following
perspective.  If we take N2L in its usual form:
   Fnet = m dv/dt
And integrate with respect to position to find the average force (with
respect to position), we get
   Fnet,avg dot Delta x = Delta (1/2 mv^2)
Defining the right-hand-side as the change in the object's kinetic
energy (macro), I find that in a collision the KE "lost" by one object
is "gained" by the other object only if the total displacement of each
object during the collision is the same (since the average net force on
each object is equal and opposite; assuming no other forces contributing
to the net force).

Is this a valid way of looking at things?  If so, during the "sling
shot" is the displacement of each object the same during the
"interaction"?

Also, in this interaction is the relative motion the same before and
after?  I thought that if KE is the same before and after than the
relative motions are the same before and after (i.e., v_1,i - v_2,i =
v2,f - v1,f).  Is this wrong?

----------------------------------------------------------
Robert A. Cohen, Department of Physics, East Stroudsburg University 
570.422.3428   rcohen@po-box.esu.edu    http://www.esu.edu/~bbq 

> The slingshot effect is elastic - i.e., the KE before equals 
> the KE after.
> The mass of the planet is so much more than the mass of the 
> satellite that one sees a visible change in the speed of the 
> satellite but not the planet.
>
> It's just like a bowling ball striking a stationary tennis 
> ball. The bowling continues on with no visible change in 
> speed, whereas the tennis ball moves at twice the speed of 
> the bowling ball (a slingshot in one dimension!)