教学研究心得选讲

1. 教学研究心得选讲 精品习题 06.10.2014.

2. 精品习题 1. 课程论文是相当有效的一种训练方式，然而对教师和学生都有相当的难度 2. 当学生身经百战，把大做习题作为重要学习方式，当他们熟练到老师都‘自叹不如’，当他们以此考入了大学，你怎么能够说服他们‘题海战术不好’

3. 精品习题 既起到复习、巩固一些知识点的常规作用 又能够拓宽思路、有利于探究精神的养成 特别强调物理思想

4. x Problem 6.3 A length l of flexible tape is tightly wound. It is then allowed to unwind as it rolls down a steep incline that makes an angle q with the horizontal, the upper end of the tape being tacked down. Show that the tape unwinds completely in a time Problem 12-41 in Resnick R, Halliday D. Physics 3rd ed. John Wiley & Sons, 1977

5. The normal reasoning is that the tape is very thin and winded part can be taken as a rigid disc. (1) (2) (3)

6. The “normal” solution is

8. Class 2005, 6c300 Geometric relation From the geometric relation we have It is same as in the case of rigid disc. But

9. Is it reasonable to drop the second term? If not, Physicallywhat we expect? Surely The acceleration should be smaller due to the smaller circumference. set the thickness of the taped To find crosssection

10. Simply substitute we have It is d – independent! What is its implication? Is it possible anticipate physically?

11. *a student of class 56, Tsinghua The acceleration does become smaller: Mr. Hu Yueke* estimated at x ~ l/2 The exact contribution needs a solution of the differential equation

12. Write it as a differential equation It is a nonlinear equation of x against t.

13. But a simple change of the variable leads to It is linear of v2 against x. Why is it so? Does it mean things get simple in phase space?

14. Measuring a and x in terms of a0, l,we have dimensionless quantities: and That linear equation becomes (All tildes omitted)

15. According to the standard procedure, the equation can be solved and leads to The corresponding acceleration is

16. v1 a1

17. Calculation ofunwind time is more involved. The final result is Where K is the complete elliptic integral of the first kind.

18. Dynamic effect From consideration of geometry, we know the acceleration should be reduced. But ? what is the dynamic effect of The change rate of the angular momentum has to be written as instead of

19. That is Physically we can expect: the smaller the inertia of rotation the larger the acceleration. So dynamic effect is against the geometric effect but we didn’t know the result of competition yet.

20. Leave the tedious math alone we just plot the results in the following figure.

21. v0 a0 a2 v2

22. Curves rise up. We know the dynamic effect prevails over.

23. variable mass Take the disc as a system of “variable mass”. It is indeed an open problem. At contact point the exhaust speed is naught. It seems that no exhaust term should be considered. But we have written the equation of motion of com. Relative to com the exhaust speed is finite. So physically we may expect a recoil. Taking the exhaust term into account we have newer results:

24. v0 a0 a3 v3

26. v3 a3 v2 a2 v0 v1 a0 a1

27. Bravo

28. t1 t2 t3

29. From the relation we have the trajectory of the center of the disc a parabola.

31. 谢 谢 dxlu@nju.edu.cn

32. Work-energy relation?