By Derek F. Lawden
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Extra resources for A Course in Applied Mathematics, Vols 1 & 2
It was a gift question, one the professor had put on the exam to get everybody off to a good start; to answer it all you had to do was remember a formula that had been derived in lecture and in the course text and that we had used on at least a couple of homework assignments. All the exam required was plugging numbers into the formula. The professor had kindly provided all the numbers, too. Unfortunately, I couldn’t remember the formula, and so no gift points for me. Later, back in the dorm, I was talking with a friend in the class, who was most grateful for that gift question; he wasn’t doing well in the course, and the “free’’ points were nice.
Since the ﬂoor end is moving at the constant speed v0 , this condition is satisﬁed. For a nice tutorial discussion of this issue, see Fredy R. Zypman, “Moments to Remember: The Conditions for Equating Torque and Rate of THREE EXAMPLES OF THE MUTUAL EMBRACE _ _ _ _ 17 Change of Angular Momentum’’ (American Journal of Physics, January 1990, pp. 41–43). One reviewer has observed that, since the ﬂoor is frictionless, to maintain a constant speed for the ﬂoor end of the pole, one would actually have to push to the left rather than pull to the right.
This is easy to demonstrate. 5), we have x t du = 0 0 1 du = − (1 − 2u) 2 √ 1 − 2u t 0 , 6 _ _ _ _ DISCUSSION 1 or x = 1− √ 1 − 2t. 6) That is, as t → 1/2, we have x → 1, which means that our mass achieves inﬁnite speed in just 1/2 second after moving just one meter! After t = 1/2 second and x = 1 meter, our solution offers no answers to either how fast the mass is moving or where it is. 3 This is, of course, absolutely absurd. The problem with both of these examples is that we have assumed unphysical forces that have no bound, as well as used physics that is not relativistically correct as the speed of the mass approaches the speed of light.