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