问题 计算题

(2011·上海高考物理·T33)如图(a),磁铁A、B的同名磁极相对放置,置于水平气垫导轨上。A固定于导轨左端,B的质量m=0.5kg,可在导轨上无摩擦滑动。将B在A附近某一位置由静止释放,由于能量守恒,可通过测量B在不同位置处的速度,得到B的势能随位置x的变化规律,见图(c)中曲线I。若将导轨右端抬高,使其与水平面成一定角度(如图(b)所示),则B的总势能曲线如图(c)中II所示,将B在处由静止释放,求:(解答时必须写出必要的推断说明。取)

(1)B在运动过程中动能最大的位置;

(2)运动过程中B的最大速度和最大位移。

(3)图(c)中直线III为曲线II的渐近线,求导轨的倾角。

(4)若A、B异名磁极相对放置,导轨的倾角不变,在图(c)上画出B的总势能随x的变化曲线.

答案

(在5.9 ~ 6.3cm间均视为正确) 

⑵ 1.31m/s (在1.29~1.33 m/s间均视为正确),18.0cm (在17.9~18.1cm间均视为正确)

⑶59.7°(间均视为正确)

⑷见解析

(1)势能最小处动能最大          

由图线II得

                   

(在5.9 ~ 6.3cm间均视为正确)

(2)由图读得释放处势能,此即B的总能量。出于运动中总能量守恒,因此在势能最小处动能最大,由图像得最小势能为0.47J,则最大动能为

     

(在0.42 ~ 0.44J间均视为正确)

最大速度为

                             

(在1.29~1.33 m/s间均视为正确)

x="20.0" cm处的总能量为0.90J,最大位移由E=0.90J的水平直线与曲线II的左侧交点确定,由图中读出交点位置为x=2.0cm,因此,最大位移

                                           

(在17.9~18.1cm间均视为正确)

(3)渐近线III表示B的重力势能随位置变化关系,即

                                           

由图读出直线斜率

        

间均视为正确)

(4)若异名磁极相对放置,A,B间相互作用势能为负值,总势能如图。      

完形填空
My husband and I are both musicians. I took it  36  granted that one day our daughter Holly would learn to play an instrument.
In 2000 Holly fell  37  and the doctor said she may have been left   38   deaf. “She won’t be able to hear music in any shape or form,” said the doctor. It was a great   39  .
In 2001, her right ear was fitted with a cochlear implant --- electronic equipment that provides a sense of    40   for people who are completely deaf. Seven years later, another was fitted in her    41   ear. The doctors played us a model of what music would sound like to Holly --- I was horrified   42  it was just white noise.
“Holly will hear music,” I   43   saying to myself. I tried to put what had gone wrong right, so we constantly   44  words and sounds to her. She has been having lessons since she was seven . she’s   45  all the time. I’m always surprised by just how much better she does.
When she   46  a national piano competition, the adjudicator   47  Holly for appearing to listen to the sounds she was making --- her whole body, he said to us, was   48  in the process of making music.
I   49  that the model we originally heard of how music sounds with a cochlear implant isn’t   50  holly hears it. The brain is complex and adapts to many   51  ;in some way, Holly has made   52  of it all. She loves life. She doesn’t think about what happened to her and says   53  , “I don’t want to talk about bad things. Let’s talk about good things.”
I was determined that her life would not be   54  by a miserable event, but never imagined that she could   55  what she has. I can only describe this as a miracle.
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小题20:
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