问题 计算题

(10分)如图甲,MN、PQ两条平行的光滑金属轨道与水平面成θ = 30°角固定,M、P之间接电阻箱R,导轨所在空间存在匀强磁场,磁场方向垂直于轨道平面向上,磁感应强度为B = 0.5T。质量为m的金属杆a b水平放置在轨道上,其接入电路的电阻值为r。现从静止释放杆a b,测得最大速度为vm。改变电阻箱的阻值R,得到vm与R的关系如图乙所示。已知轨距为L = 2m,重力加速度g取l0m/s2,轨道足够长且电阻不计。

(1)当R = 0时,求杆a b匀速下滑过程中产生感生电动势E的大小及杆中的电流方向;

(2)求金属杆的质量m和阻值r;

(3)当R = 4Ω时,求回路瞬时电功率每增加1W的过程中合外力对杆做的功W。

答案

(1)   电流方向从b→a    (2) m=0.2kg,r=2Ω   (3) W=0.6J 

题目分析:(1)由图可知,当R=0时,杆最终以v=2m/s匀速运动,产生电动势

 由右手定则判断可知杆中电流方向从b→a

(2)设杆运动的最大速度为v,杆切割磁感线产生的感应电动势 

由闭合电路的欧姆定律得:,杆达到最大速度时满足 

联立解得:

由图象可知:斜率为,纵截距为v0=2m/s,

得到:

解得:m=0.2kg,r=2Ω    

(3)由题意:

得 

瞬时电功率增大量

由动能定理得: 

比较上两式得 

代入解得 W=0.6J  

阅读理解

阅读理解。

     Jerry Baldwin was 30 years old. He was the manager of a pizza restaurant. He lived in an apartment

about one mile north of the restaurant. He walked to and from work. When it was raining, he took the

bus.

     Jerry loved gangster (匪徒) movies. When a new one came out, he would go to the theater and

watch the new movie three or four times. Then, when it went to video, Jerry would buy the video at

Barney's Video Store. Jerry had a home collection of over 1,000 gangster videos. Old ones, new ones,

color, black and white, English, Spanish, and Japanese-he loved them all. He could tell you the name of

the movie, the director( 导演), the stars, etc.

     Jerry finally decided that he would like to own a gun, just like the gangsters. So he saved his money

for some years. Then he went to a gun store and bought a used gun for $300. While there, he also

bought many bullets (子弹) .

     The following Saturday morning, he went to the gun club to practice with his new gun. He was in the

club for only 10 minutes when he dropped his gun by accident. The gun went off (走火), and the bullet

went into Jerry's right leg.

     Jerry now walks with a stick, just like some gangsters.

1. Jerry Baldwin often went to work _____.

A. by car

B. on foot

C. by bike

D. by bus

2. Jerry knew a lot about _____.

A. all the gangsters

B. most directors

C. gangster movies

D. all kinds of' movies

3. Jerry decided to buy a gun because _____.

A. he wanted to be a real gangster

B. he wanted to do just like a gangster

C. he became a real gangster

D. he wanted to behave like a gangster

4. Jerry became lame (瘸的) because _____.

A. he was shot by accident

B. he fell and hurt himself

C. he shot himself with the gun

D. he was shot by his friend

5. Which statement is true according to the passage?

A. Jerry's dream to be a gangster came true at last.

B. Jerry had a strong interest in collecting gangster videos.

C. To be just like a real gangster, Jerry shot himself with a gun.

D. Jerry practiced shooting day and night and became good at it.

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