问题 多选题

如图所示,半径为R的竖直光滑圆轨道内侧底部静止着一个光滑小球,现给小球一个冲击使其在瞬间得到一个水平初速度v0,若v0大小不同,则小球能够上升到的最大高度(距离底部)也不同.下列说法中正确的是(  )

A.如果v0=

gR
,则小球能够上升的最大高度为
R
2

B.如果v0=

2gR
,则小球能够上升的最大高度为
R
2

C.如果v0=

3gR
,则小球能够上升的最大高度为
3R
2

D.如果v0=

5gR,则小球能够上升的最大高度为2R

答案

A、如果v0=

gR
,根据机械能守恒定律得:
1
2
mv02=mgh
,解得:h=
R
2
,当小球运动到
R
2
高度时速度可以为零,则小球能够上升的最大高度为
R
2
,故A正确,B错误;

C、如果v0=

3gR
,根据机械能守恒定律得:
1
2
mv02=mgh
,解得:h=
3R
2
,当根据竖直平面内的圆周运动知识可知小球在上升到
3R
2
处之前就做斜抛运动了,故C错误;

D、如果v0=

5gR
,根据机械能守恒定律得:
1
2
mv02=mg?2R+
1
2
mv2
,解得v=
gR
,根据竖直方向圆周运动向心力公式可知,最高点的速度最小为
gR

满足条件,所以可以到达最高点,即小球能够上升的最大高度为2R,故D正确.

故选AD

完形填空

下面文章中有5处需要添加小标题,请从以下选项( A, B, C, D, E,和F)中选出符合各段意思的小标题。选项中有一项是多余选项。

A.Balanced Study

B.Regular Planning

C.Build the Right Attitude

D.Self-Study and ResearchE. Debates and Conversations

F. Organized and Comprehensive Notes

Study Tips and Techniques

If you often find yourself struggling with your studies, here are some useful study tips and techniques that can help you out …

61._____________

It is a common misconception that self-study can begin only after a particular topic or chapter is taught in class. You should start preparing for the class in advance. After attending the classes, it is of great importance that you have time to review the notes that you have taken during the class as well as try and read more about the subject on your own. Be it reference books, or e-books, try and hunt for more information about your subject so that you have a comprehensive view of the topics. Often while reading and self-studying, it happens that you come across doubts or questions that did not occur to you in the classroom. Try and answer these questions yourself with the help of books or the Internet, however in case you fail to answer, write down these questions so that you remember to clarify the questions in your next class.

62._____________

Yes, one of the important habits that one must acquire to enhance the studying process is involve themselves in group discussions about the subjects that you are studying. Group discussions can be a great way to broaden your viewpoint over important issues since group discussions give every group member a chance to voice their understanding , which might not necessarily be alike. Group discussions are thus a healthy and a rather informal way of exchanging information and discussing issues. Many teachers encourage the group discussion technique in their classroom as well.

63.______________

No matter how much people disapprove of the process and the timetables, it is a known fact that having a clear and detailed project makes it easier for a person to reach the goal. According to your convenience, map out your daily/weekly/monthly study. It is always better to have a weekly or a daily arrangement, so that abrupt changes in class schedules or any other changes can be taken into consideration accordingly.

64._____________

Yes, there exist some species of students who burn the midnight oil. The studying process should be such that it leaves enough room for a student to join in entertainment activities and relaxation. Always chalk out a schedule that will not influence your sleep, your health, your sport/ entertainment activities and other routine tasks. Also studying a single subject at a stretch ( like an entire week or so ), can get boring, for this reason plan a schedule that helps your switch from one subject to another in enough time.

65.____________

Normally students get too caught up with the grades, the percentage and the entire marking system. Always remember that if you study with the aim of acquiring knowledge, the grades will  be brighter. However if you just aim for the high grades, there is a chance you might get the grades, but you will miss out on acquiring comprehensive knowledge on a particular subject. Always study with the right point of view, and you will never have to worry about your grades. Knowledge is way beyond the grades.

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