问题 问答题

如图所示,坐标系xOy在竖直平面内,长为L的水平轨道AB光滑且绝缘,B点坐标为(0,

3
2
L).有一质量为m、电荷量为+q的带电小球(可看成质点)被固定在A点.已知在第一象限内分布着互相垂直的匀强电场和匀强磁场,电场方向竖直向上,场强大小E2=
mg
q
,磁场为水平方向(在图中垂直纸面向外),磁感应强度大小为B;在第二象限内分布着沿x轴正向的水平匀强电场,场强大小E1=
B2qL
6m
.现将带电小球由A点从静止释放,设小球所带的电量不变.试求:

(1)小球运动到B点的速度大小;

(2)小球第一次落地点与O点之间的距离;

(3)小球从开始运动到第一次落地所经历的时间.

答案

(1)小球从A到B的过程中,由动能定理得

1
2
m
v2B
=qE1L

所以小球运动到B的速度vB=

2qE1L
m
=
2qL
m
B2qL
6m
=
3
qBL
3m

(2)小球在第一象限受到的电场力:qE2=mg,所以小球做匀速圆周运动,设半径为R,

m

vB2
R
=BqvB

R=

mvB
qB
=
m
qB
3
BqL
3m
=
3
3
L

设图中C点为小球做圆周运动的圆心,它第一次的落地点为D点,则

.
CD
=R,

.
OC
=
.
OB
-R=
3
2
L-
3
3
L=
3
6
L

所以,落地点到O点的距离为

.
OD
=
R2-
.
OC
2
=
(
3
3
L)
2
-(
3
6
L)
2
=
L
2

(3)小球从A到B所需时间tAB=

vB
a
=
3
BqL
3m
q2B2L
6m
=
2
3
m
qB

小球做匀速圆周运动的周期为T=

2πm
qB

由几何关系知∠BCD=120°,

小球从C到D所用的时间为tBD=

T
3
=
2πm
3qB

所以小球从开始运动到第一次落地所经历的时间为tAD=tAB+tBD=

2
3
m
qB
+
2πm
3qB
=(2
3
+
3
)
m
qB

答:(1)小球运动到B点的速度大小vB=

3
qBL
3m

(2)小球第一次落地点与O点之间的距离

L
2

(3)小球从开始运动到第一次落地所经历的时间tAD=(2

3
+
3
)
m
qB

阅读理解

A. Be brave in your requests

B. You get what you tolerate

C. Don’t feel guilty of your requests

D. Don’t think others are mind readers

E. Don’t make a “no” mean more than it does

F. Be specific about what you want and when you want it

Be Bold: Ask for What You Really Want!

Have you ever been in a situation that is causing you to feel annoyed, frustrated, or unappreciated? We all experience them, but often we don’t have the courage to change them or ask for what we really want. Complaining about your problems never solves them. Only when you get clear about what you want, and are willing to ask for it, will you experience not only a lot less stress in your life, but greater success in your relationship, career and life. Here are five tips to help you on your way.

小题1:________________

We often think our bosses, colleagues and even our friends can understand our thought even without being told. So when they don’t act as we’d like, we feel hurt and upset. For any relationship to develop, both parties have to communicate their needs. Whether it’s how you’d like your colleague to communicate with you about a work project, or how you’d like your boss to assess your work, it’s necessary to convey what you want.

小题2:________________

When asking for what you really want, you will seldom, if ever, be given more than what you have the courage to ask for. So don’t weaken your requests to avoid being turned down. Think about what your ideal outcome would be and then confidently, courageously, ask for it. While you may not always get as much as you asked for, you will get more than you would have otherwise.

小题3:________________

In the workplace, the biggest reason for unmet expectations is a lack of understanding of exactly what is expected. A request that holds water needs to make clear not just what you want, but also the time limit within which you want it. That is, both a clear “what” and “when”. For example, “Could you please get the monthly sales report to me by midday Friday?

小题4:________________

Whether it’s asking your friend to show up on time, or asking your colleague to stop making jokes in your presence, every day, through what you say and do, you teach others how to treat you. Letting others know what you will (and will not)put up with and what you expect from them, is important to your wellbeing and success—at home and work.

小题5:________________

In reality you won’t always get what you ask for. Your boss won’t always give you the pay raise you’d like and your parents may not agree to mind your three kids every second weekend. When people say no, you can take it really personally and decide never to speak to them again—or you can accept it graciously and move on. At least now you know where you stand and can plan accordingly.

Asking for less than you really want—from yourself, from others and from life—doesn’t serve anyone. Remember that fortune favors the bold. So make bigger, better, bolder requests, and ask for what you really want. Who knows…you might just get it!

单项选择题