问题 问答题

如图所示,一对平行光滑轨道放置在水平面上,两轨道相距L=1m,两轨道之间用电阻R=2Ω连接,有一质量为m=0.5kg的导体杆静止地放在轨道上与两轨道垂直,杆及轨道的电阻皆可忽略不计,整个装置处于磁感应强度B=2T的匀强磁场中,磁场方向垂直轨道平面向上.现用水平拉力沿轨道方向拉导体杆,使导体杆从静止开始做匀加速运动.经过位移s=0.5m后,撤去拉力,导体杆又滑行了相同的位移s后停下.

求:(1)全过程中通过电阻R的电荷量;

(2)匀加速运动的加速度;

(3)画出拉力随时间变化的F-t图象.

答案

(1)设全过程中平均感应电动势为E,平均感应电流为I,时间△t,

则通过电阻R的电荷量:

q=I△t,I=

E
R
E=
△φ
△t
=
2BLs
△t

q=

2BLs
R
=1C

(2)拉力撤去时,导体杆的速度为v,拉力撤去后杆运动时间为△t2,平均感应电流为I2

根据牛顿第二定律有:

BI2L2=m

v
t2

BI2L△t2=mv

I2t2=q′=

q
2
=
BLs
R

B2L2s
R
=mv,

v=

B2L2s
mR
=
22×12×0.5
0.5×2
m/s=2m/s2

所以a=

v2
2s
=4m/s2

(3)F=ma+BIL=ma+

B2L2at
R

拉力作用时间t=

v
a
=0.5s,此时Fmax=6N;

t=0时,F=ma=2N

画出拉力随时间变化的F-t图象

答:全过程中通过电阻R的电荷量为1C,匀加速运动的加速度为4m/s2

填空题

When I was growing up, I was embarrassed to be seen with my father. He (1) severely crippled and very short, and when we would walk together, his hand on my arm (2) balance, people would stare. I would inwardly be afraid (3) squirm at the unwanted attention. If he ever noticed or was bothered, he never let (4) .
It was difficult to coordinate (5) steps - his halting, mine impatient - and because of that, we didn’t say much as we went along. But as we started out, he always said, "You (6) the pace. I will try to adjust to you. "
Our usual walk was to or (7) the subway, which was how he got to (8) . He went to work sick, and (9) nasty weather. He almost never missed a day, and would (10) it to the office even if (11) could not: a matter of pride!
He never talked about himself as an object of pity, (12) did he show any envy of the more fortunate or able. What he looked for in others was a "good heart", and if he found one, the owner was good enough for him.
Now that I am older, I believe that is a proper standard (13) which to judge people, even though I still don’t know precisely (14) a "good heart" is. But I know the times I don’t have one myself.
He has (15) gone many years now, but I think (16) him often. I wonder if he sensed my reluctance to be seen with him during our (17) . If he did, I am (18) I never told him how sorry I was, how unworthy I was, how I regretted it. I think of him when I complain about trifles, when I am (19) of another’s good fortune, when I don’t have a "good heart".
At such times I put my hand on his arm to regain my (20) , and say, "You set the pace, I will try to adjust to you.\

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