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Re: Asymmetrical Newton's Cradle



I've played with a double ball system with the ratio of masses 3:1.
they alternate with one moving only slightly the other reversing
direction on collision.

I suggest analyzing, using the usual conservation law(s).


There has been some discussion shewing the usual analysis is incorrect;
where, I've forgotten.

http://www.lhup.edu/~dsimanek/scenario/cradle.htm
<http://www.lhup.edu/%7Edsimanek/scenario/cradle.htm>


The above does discuss "Newton's asymmetric balls".

bc, whose first try succeeded.



Matt Harding wrote:

We spent some time in my high school class today examining the behavi=
or
of the Newton's Cradle (the good ol' clicky-clacky ball thing). Afte=
r
some thought, my practicum student (pre-service teacher) posed the
following question: =20
Suppose the fist ball in the cradle had a mass 1.5x while the other
balls in the cradle each had a mass of 1x. What would happen if you
pulled back on that slightly more massive ball and released it?

Cheers,
Matt


"An expert is a man who has made all the mistakes which can be made i=
n a
very narrow field."
=20
- Niels Bohr


-----Original Message-----
=46rom: Bob LaMontagne [mailto:rlamont@POSTOFFICE.PROVIDENCE.EDU]=
=20
Sent: Thursday, November 06, 2003 2:08 PM
To: PHYS-L@lists.nau.edu
Subject: Re: Newton's second law

If you are shoveling perpendicular to the motion of the flatcar, you =
are
applying a force perpendicular to the track. That is balanced by a fo=
rce
=66rom the track that keeps the overall motion straight ahead. The v =
in
this case is the sideways speed of the sand, not the speed of the
flatcar down the track - which remains constant because there is no
force in this direction.

Bob at PC

Justin Parke wrote:


I wrote:


Newton' second law:

F =3D dp/dt=3D mdv/dt + vdm/dt

In the third term, what is v?


Justin Parke
Oakland Mills High School
Columbia, MD


Dan replied


F =3D dp/dt =3D d(mv)/dt =3D m dv/dt + v dm/dt

This is the chain rule applied to momentum p =3D mv.
v is velocity throughout

regards,

Dan M


Consider a flatcar on a train track rolling at speed v without


dissipative forces and loaded with sand. As the car rolls sand is
shoveled off to the side at a rate of c, thrown perpendicular to the
direction of motion. Will the speed of the car change as a result of
the decrease in mass?


I suspect the answer is no because the force exerted on the sand, a=


nd
hence the force exerted *by* the sand on the car has no component alo=
ng
the direction of motion.


F =3D mdv/dt + vdm/dt =3D m (0) + v (-c)? This suggests that an o=


utside
force is necessary to maintain a constant speed. What is wrong with =
my
reasoning?


Justin Parke
Oakland Mills High School
Columbia, MD