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Re: impulse/momentum



Precede this problem with the problem of an elastic collision between a
moving mass m and a stationary mass M, in the limit as M/m => infinity. Eg;
a ping pong ball bounced off a stationary wall (the earth). Impose
conservation of momentum and conservation of kinetic energy. In the above
limit, the return speed of the ball is its initial speed v; the KE gained by
the earth (.5 MU^2)is zero; and the momentum exchanged (MU) is 2mv - gained
by the earth in the forward direction amd gained by the ping pong ball in
the backward direction.


Bob Sciamanda
Physics, Edinboro Univ of PA (Em)
http://www.velocity.net/~trebor/
trebor@velocity.net
----- Original Message -----
From: "Justin Parke" <FIZIX29@AOL.COM>
To: <PHYS-L@lists.nau.edu>
Sent: Thursday, December 11, 2003 2:08 PM
Subject: impulse/momentum


I have another question which is related to one I asked a couple of weeks
ago re: variable mass.

This one is from Halliday Resnick and Walker, problem 10.17, which I
quote: "A stream of water impinges on a stationary 'dished' turbine blade.
The speed of the water is v, both before and after it strikes the curved
surface of the blade, and the mass of water striking the blade per unit time
is constant at the value u. Find the force exerted by the water on the
blade." Included with the problem is a diagram which shows water striking a
blade and "reflecting" in the direction from which it came.

My students typically come up with F = u v, but the answer is F = 2 u v.
It is easy to understand why, as the change in velocity of the water is 2 v,
but I have trouble deriving the result from first principles and the
solution provided by the textbook company is even worse: F = dp/dt =
d(mv)/dt=2v dm/dt = 2 u v.

I have a strong aversion to mystifying physics by saying, "we multiply by
2 since delta v = 2v." Can someone help me with a better proof?

Thanks as always

Justin Parke
Oakland Mills High School
Columbia, MD