问题 问答题

如图18所示,质量为M ="2" kg的小车A静止在光滑水平面上,A的右端停放有一个质量为m ="0.4" kg带正电荷q ="0.8" C的小物体B.整个空间存在着垂直纸面向里磁感应强度B =0.5T的匀强磁场,现从小车的左端,给小车A一个水平向右的瞬时冲量I ="26" N·s,使小车获得一个水平向右的初速度,物体与小车之间有摩擦力作用,设小车足够长,求:

(1)瞬时冲量使小车获得的动能.

(2)物体B的最大速度.

(3)在AB相互作用过程中系统增加的内能.(g =10m/s2

答案

(1)169J(2)vB=" 10m" / s(3)28J

(1)瞬时冲量和碰撞是一样的,由于作用时间极短,可以忽略较小的外力的影响,而且认为,冲量结束后物体B的速度仍为零,冲量是物体动量变化的原因,根据动量定理即可求得小车获得的速度,进而求出小车的动能.

I = Mv0   (1分) v0 = I / M =" 13m" / s   (1分)    Ek = Mv02 / 2 = 169J(1分)

(2)小车A获得水平向右的初速度后,由于AB之间的摩擦,A向右减速运动B向右加速运动,由于洛伦兹力的影响,AB之间摩擦也发生变化,设AB刚分离时B的速度为vB,则: 

BqvB = mg (1分)     即vB = mg / Bq =" 10m" / s (2分)

AB能相对静止。设共同速度为v,由Mv0 = (M + m)v   (2分)

解得v =" 10.8m" / s                                      (1分)

vBv,说明AB在没有达到共同速度前就分离了,  

所以B的最大速度为vB=" 10m" / s.                       (1分)

(3)由于洛伦兹力的影响,AB之间的摩擦力逐渐减少,因此无法用Q = fs求摩擦产生的热量,只能根据机械能的减少等于内能的增加来求解.

由于B物体在达到最大速度时,两个物体已经分离,就要根据动量守恒定律求这时A的速度,设当物体B的速度最大时物体A的速度为vA

AB系统水平方向动量守恒:Mv0 = MvA + mvB    (2分)

vA = (Mv0mvB) / M =" 11m/s                 " (1分)

QE = Mv02 / 2 – MvA2 / 2 – mvB2 / 2 =" 28J      " (2分)

阅读理解

A gentle breeze blew through Jennifer's hair. The golden red sun was setting. She was on the beach, looking up at the fiery (火红的) ball. She was amazed by its color, deep red in the middle, softly fading into yellow. She could hear nothing but the waves and the seagulls flying up above in the sky.    

The atmosphere relaxed her. After all she had been through, this was what she needed. "It's getting late," she thought, "I must go home. My parents will be wondering where I am."

She wondered how her parents would react, when she got home after the three days she was missing. She kept on walking, directing herself where she spent every summer holiday. The road was deserted. She walked slowly and silently. Just in a few hundred meters she would have been safe in her house.

It was really getting dark now. The sun had set a few minutes before and it was getting cold too. She wished she had her favorite sweater on: it kept her really warm. She imagined having it with her. This thought disappeared when she finally saw her front door. It seemed different. Nobody had taken care of the outside garden for a few days. She was shocked: her father was usually so strict about keeping everything clean and tidy, and now... It all seemed deserted. She couldn't understand what was going on.    

She entered the house. First, she went into the kitchen where she saw a note written by her father. It said: "Dear Ellen, there is some coffee ready. I went looking." Ellen was her mother but-where was she? On the right side of the hallway was her parents' room. She went in. Then she saw her. Her mother, lying on the bed, was sleeping. Her face looked so tired, as if she hadn't slept for days. She was really pale. Jennifer would have wanted to wake her up but she looked too tired. So Jennifer just fell asleep beside her. When Jennifer woke up, something was different-she wasn't in her mother's room and she wasn't wearing the old clothes she ran away in. She was in her cozy bed in her pajamas.     

It felt so good being back home. Suddenly she heard a voice, "Are you feeling better now, dear? You know you got us very, very scared."

小题1:Three days later Jennifer came back home     .

A.at sunrise

B.at sunset

C.at night

D.at midday小题2: What does the underlined phrase "This thought" most probably mean?

A.The idea of going back home.

B.Her anxiety about her parents.

C.The feeling of being warm in her favorite sweater.

D.The feeling of getting back home safely.小题3: Her father didn't take care of the garden because     .

A.he was busy looking for her

B.he had to look after his wife

C.he was not strict with his job

D.he no longer enjoyed working in the garden小题4:

单项选择题