问题 问答题

如图,一足够长的固定斜面与水平方向成α=37?角,空间有垂直于斜面的无限多个匀强磁场,其磁感应强度的大小均为B=0.5T,相邻磁场区域的磁场方向相反.每个磁场区域的宽度均为L1=0.1m,磁场区的边界均与斜面底边平行.现有一质量为m=0.05kg、电阻为R=0.5Ω的矩形金属框abcd沿此斜面下滑,已知ad=L1=0.1m,ab=L2=0.2m,下滑过程中,金属框的ab边始终与斜面底边平行,金属框与斜面间的动摩擦因数为μ=0.2,金属框下滑距离s=3m时速度达到最大,求:

(1)金属框下滑的最大速度;

(2)当金属框下滑的加速度为a=2m/s2时,金属框的焦耳热功率;

(3)从开始下滑到速度达到最大的过程中金属框中产生的焦耳热量.

答案

(1)金属框做加速度逐渐减小的加速运动,直到最后运动运动为止,当匀速时速度达到最大,此时有:

mgsinα=Ff+2BIL2

mgsinα=μmgcosα+

4B2L22vm
R

解得:vm=2.75m/s

故金属框下滑的最大速度为:vm=2.75m/s.

(2)根据牛顿第二定律有:

mgsinα-μmgcosα-2BIL2=ma

解得:I=0.6A

P=I2R=0.18W

故当金属框下滑的加速度为a=2m/s2时,金属框的焦耳热功率为:P=0.18W.

(3)下落过程,根据功能关系有:

WG+Wf+W=

1
2
mvt2-
1
2
mv02

mgssinα-μmgscosα-Q=

1
2
mvm2

解得:Q=0.47J

故从开始下滑到速度达到最大的过程中金属框中产生的焦耳热量为:Q=0.47J.

阅读理解
阅读理解。
A. Decide to Be Happy
B. Lower Your Expectations
C. Learn to Enjoy the Moment
D. Look for the Good in Everything
E. Let People Deal with Their Own Problems
F. Focus More on What You Can Control Than on What You Can't
     So many times I hear people say that they will be happy once a certain event occurs. They think that
once they move into a new house, start their new job, travel or retire they will be happy. But it doesn't
work that way.
     If you truly want to be happy, here's what to do.
1._____
     You are not just a victim of circumstances or your emotions. Think about it this way. If you are in a
horrible argument with someone, and the person you most respect enters the room, what will happen?
The fighting will likely stop immediately, your mood will change, and so will your behavior. You do have
control, and you are the one who decides how you will face the day!
2._____
     We are never disappointed unless we have expectations. If you base your emotions on the need for
certain things to happen, you will likely be let down most of the time. Instead, work hard, and treat
everything good that happens as a bonus for which you can be thankful.
3._____
     Don't get too wrapped up in issues involving friends or family. We are each responsible for our own
lives, and even when someone makes a bad mistake, it is not up to you to make things better. And
remember that worry doesn't help anyone!
4._____
     You might not be satisfied with your income, but there's no point complaining about it. Improve your
diploma so that you can get a better job in the future. You may have an incurable illness, such as diabetes, but the fact that it's incurable doesn't mean that it cannot be managed.
5._____ 
      You don't have to be a Pollyanna (盲目乐观者) about life, but you can see the bright side of almost
every situation if you just make a point of looking for it. Happiness is not an uncatchable mouse! Once
you have made up your mind that you are going to be happy despite what is going on around you, the
task becomes easier. One of the key things to remember is that happiness doesn't come from outside but
begins on the inside and actually spread outward, and can influence everyone around you in a positive
manner.
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