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Re: correct answer



It looks to me as if the problem rather than the answer is wrong. We
and especially our students are clearly invited to visual the final
motion as a stretched-out firehose moving parallel to its length. That
is not correct in general, and the actual motion is quite complicated.
There is a torque on the coil at the beginning of the motion. Depending
on exactly how the person pulling the firehose handles the resulting
motion, there may or perhaps must be some kind of complicated rotation
of the firehose at the end of the motion. This rotation could destroy
both the work-energy answer and your explicit calculation of the work
done. The answer to the question must depend on the details of the
force and the details of the uncoiling. The latter will depend on the
tensile properties of the firehose.

Since firehoses don't float very well on airtables, I doubt that you can
find even an experimental answer. [GRIN]

Mark Shapiro wrote:

In preparing for class today I was reviewing some problems in
Halliday, Resnick and Walker (5th ed) - Chapter 7. I believe the
answer
to problem 15E on page 150 is incorrect.

The problem states that a 12 m long firehose is uncoiled by
pulling the nozzle end horizontally along a frictionless surface at
the
steady speed of 2.3 m/s. The mass/length of the hose is 0.25kg/m.
How
much work has been done on the hose by the applied force when the
entire
hose is moving?

The solution manual applies the "Work-Energy" theorem and
calculates 0.5mv^2 for the entire hose in motion to get the answer 7.9
J.
However, I believe that this is an incorrect application of the W-E
theorem because the mass being moved by the applied force is not
constant.
i.e. from Newton's second law F = d(mv)/dt = (dm/dt)v in this case, so
the
total work done is the integral of Fdx, which with a little
manipulation I
calculate to be rho*v^2*L where rho is the mass per unit length of the
hose and L is the total length of the hose. This gives an answer
twice as
big.

Since I'm not a "morning person", have I blundered?

Mark

Dr. Mark H. Shapiro
Physics Department
California State University, Fullerton
P.O. Box 6866
Fullerton, California 92834-6866

Phone: ++ (714) 278-3884 PCS: ++ (714) 350-3575
Fax: ++ (714) 278-5810
e-mail: mshapiro@fullerton.edu

--
Maurice Barnhill, mvb@udel.edu
http://www.physics.udel.edu/~barnhill/
Physics Dept., University of Delaware, Newark, DE 19716