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问题 问答题

质量为m=0.5kg、可视为质点的小滑块，从光滑斜面上高h0=0.6m的A点由静止开始自由滑下．已知斜面AB与水平面BC在B处通过一小圆弧光滑连接．长为x0=0.5m的水平面BC与滑块之间的动摩擦因数μ=0.3，C点右侧有3级台阶（台阶编号如图所示），D点右侧是足够长的水平面．每级台阶的高度均为h=0.2m，宽均为L=0.4m．（设滑块从C点滑出后与地面或台阶碰撞后不再弹起）．

（1）求滑块经过B点时的速度vB；

（2）求滑块从B点运动到C点所经历的时间t；

（3）（辨析题）某同学是这样求滑块离开C点后，落点P与C点在水平方向距离x的：

滑块离开C点后做平抛运动，下落高度H=4h=0.8m，在求出滑块经过C点速度的基础上，根据平抛运动知识即可求出水平位移x．

你认为该同学解法是否正确？如果正确，请解出结果．如果不正确，请说明理由，并用正确的方法求出结果．

答案

（1）物体在斜面AB上下滑，机械能守恒：mgh0=

1
2
mvB2+0

vB=

2gh0
=
2×10×0.6
=2
3
m/s．

（2）根据动能定理得：mgh0-μmgx0=

1
2
mvC2-0

vC=

2g(h0-μx0)
=
2×10×(0.6-0.3×0.5)
=3m/s．

根据牛顿第二定律得：μmg=ma

则a=μg=0.3×10m/s2=3m/s2．

t1=

vC-vB
-a
=
3-2
3
-3
s=0.155s．

（3）不正确，因为滑块可能落到某一个台阶上．正确解法：

假定无台阶，滑块直接落在地上，t′=

2H
g
=
2×0.8
10
s=0.4s

水平位移x′=vct′=1.2m，恰好等于3L（也就是恰好落在图中的D点），因此滑块会撞在台阶上．

当滑块下落高度为2h时，t″=

2×2h
g
=
2×2×0.2
10
s=0.283s

水平位移x″=vct″=3×0.283m=0.85m，大于2L，所以也不会撞到①、②台阶上，而只能落在第③级台阶上．

则有：3h=

1
2
gt22，t2=
2×3h
g

xpc=vct2=3×

2×3×0.2
10
=
3
3
5
≈1.04m．

答：（1）滑块经过B点时的速度为2

3
m/s．

（2）滑块从B点运动到C点所经历的时间t为0.155s．

（3）不正确，最终水平位移为1.04m．

阅读理解

Research shows that humans switch from selfish to unselfish behaviour when they are watched. Do you?

A picture of a set of eyes on a computer screen can cause a change in the way people act. Even images of eyes on a charity donation, collection box encourage people to be unselfish, because people put more money in a collection box that has a picture of eyes on it than they do when a flower symbol is on the box.

Manfred Milinski from the Max-Planck Institute for Evolutionary Biology in Germany and Bettina Rockenbach of the University of Berlin, the authors of a new study, found that people act better when they are being watched because they feel they will be rewarded for good behaviour. Their report also referred to other research showing that this response of behaving well when watched is somehow coded into humans and people respond this way unconsciously, or without realizing it.

It is not just humans that act unselfishly when they are being watched. A fish called the grooming fish cleans other fish. When other fish are around, it is gentler. When no other fish are around, however, the grooming fish bites chunks from the fish it is supposed to be cleaning.

The researchers suggest that the best way to get people to behave in the correct way is to make them feel watched. This could be the reason for the success of a famous American army poster. On it was a picture of an elderly man staring fiercely and pointing, it appeared, to the person who was looking at the poster. Under the picture was the caption 'I Want You' It encouraged hundreds of thousands of young American men to join the army during the Second World War to fight the Germans and Japanese.

小题1:According to the report, why does a person behave better when he feels he is being watched?

A．He does not want to be shamed by others.

B．He needs to show he is a good person.

C．He desires others to like him more.

D．He feels he will receive some social reward.小题2:What is the text mainly about?

A．It describes changed behaviour when observed.

B．It details ways to control people's behaviour.

C．It tells how to make people work harder.

D．It discusses different advertising methods.小题3:Where would the study described in the text most likely be found?

A．In a newspaper.

B．In a scientific journal.

C．In an advertising magazine.

D．In a science textbook.
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问答题 简答题

2011年5月，甲市烟草专卖局内管人员小张通过内管信息系统查询到如下信息：（1）A品牌卷烟4月份共销售183万支，该品牌3月份销量为112万支。（2）B品牌当月销量97万支，其中4月11日销量18万支。（3）零售户张某4月份共订购卷烟448条，四次访销记录分别为98条、102条、80条、168条。（4）营销中心本月3次对零售户李某的结算账户做了变更处理。（5）零售户韩某4月份订购卷烟528条，3月份订购数量为147条。（6）C品牌卷烟4月份销量105万支，其中日销量前三位的日期为：4月8日、14日、23日，日销量分别为17.3万支、13.5万支、12万支。小张对上述信息进行筛选后发现，A品牌卷烟生产商因货源供应不足，3月份合同中约定40万支卷烟未发货，于4月3日补发了该批卷烟；乙市烟草专卖局于4月份查处了3起甲市C品牌卷烟外流到乙市的案件。另外，小张还了解到，零售户陈某向专卖部门反映，4月份，烟草公司送货后的次日，有人3次到其店中收购本地平销的Y品牌卷烟。

以上信息中应确定为有效预警的有几条？
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