问题 问答题

如图甲所示,两根相距为L的金属轨道固定于水平面上,导轨电阻不计,一根质量为m、长为L、电阻为R的金属棒两端放于导轨上,导轨与金属棒间的动摩擦因数为µ,棒与导轨的接触电阻不计.导轨左端连有阻值为2R的电阻,在电阻两端接有电压传感器并与计算机相连.有n段竖直向下的宽度为a间距为b的匀强磁场(a>b),磁感强度为B、金属棒初始位于OO′处,与第一段磁场相距2a.

(1)若金属棒有向右的初速度v0,为使金属棒保持v0一直向右穿过各磁场,需对金属棒施加一个水平向右的拉力,求金属棒进入磁场前拉力F1的大小和进入磁场后拉力F2的大小;

(2)在(1)的情况下,求金属棒从OO′开始运动到刚离开第n段磁场过程中,拉力所做的功;

(3)若金属棒初速为零,现对棒施以水平向右的恒定拉力F,使棒穿过各段磁场,发现计算机显示出的电压随时间以固定的周期做周期性变化,在给定的坐标图乙中定性地画出计算机显示的图象(从金属棒进入第一段磁场开始计时).

(4)在(3)的情况下,求整个过程导轨左端电阻上产生的热量,以及金属棒从第n段磁场穿出时的速度.

答案

(1)金属棒进入磁场前,F1=f=μN=μmg

金属棒在磁场中运动时,F2=f+F=f+BIL

I=

E
2R+R
=
BLv0
3R

联立得  F2=μmg+

B2L2v0
3R

(2)在非磁场区域外力F1所做的功为  W1=F1[2a+(n-1)b]=μmg[2a+(n-1)b]

在磁场区域外力F2所做的功为  W2=F2×na=(μmg+

B2L2v0
3R
)na

在此过程拉力所做的总功  W=W1+W2=μmg[(n+2)a+(n-1)b]+

nB2L2avo
3R

(3)要使棒进入各磁场的速度都相同,金属棒在无磁场区域做加速运动,在磁场区域做减速运动,则穿过各段磁场时,感应电动势减小,路端电压减小,而且速度减小时,安培力减小,加速度减小,则路端电压减小变化慢,电压图象的斜率减小,可作出电压图象如图.

(4)进入各磁场时的速度均相同,等于从OO´运动2a位移时的速度,根据动能定理得

   (F-μmg)×2a=

1
2
mv2

每经过一段磁场产生的电能相同,设为E,根据动能定理,有

     Fa-μmga-E=

1
2
mv2-
1
2
mv2

所以

E=Fa-μmga-
1
2
mv2+
1
2
mv′2
=Fa-μmga-(F-μmg)(2a-b)+(F-μmg)×2a
=(F-μmg)(a+b)

Q=

nE
3R
×2R=
2
3
n(F-μmg)(a+b),

解得 v=

(F-μmg)(4a-2b)
m

答:(1)金属棒进入磁场前拉力F1的大小为μmg,进入磁场后拉力F2的大小为μmg+

B2L2v0
3R

(2)金属棒从OO′开始运动到刚离开第n段磁场过程中,拉力所做的功为μmg[(n+2)a+(n-1)b]+

nB2L2av0
3R

(3)电压图象如图;

(4)整个过程导轨左端电阻上产生的热量为

2
3
n(F-μmg)(a+b),金属棒从第n段磁场穿出时的速度为
(F-μmg)(4a-2b)
m

阅读理解

阅读理解

     If you go to a fast food restaurant, you will probably see a lot of teenagers. Today, many teenagers

are overweight, and some of this is because of their bad eating habits . Most teenagers love food with

a lot of fat, oil, salt, and sugar. People often call this kind of food "junk food".

      But bad eating habits go beyond fast food. We find many teenagers eat unhealthily. Some don't have

breakfast before they go to school. During the day, some don't have a proper meal for lunch. In a recent

survey at one school, scientists found that over two-thirds of the students didn't follow a healthy diet. They didn't like vegetables, and many of  them didn't like to eat fruits. They would rather eat food with a lot of

salt, sugar, or fat.

     Parents today also worry about their children's diet. Some doctors give the following advice:

     Teenagers shouldn't eat too much junk food.

     Teenagers shouldn't eat food with too much salt. Salt can cause high blood pressure in the future.

     Teenagers should eat food with less fat, oil, and sugar.

     Teenagers need to eat some fruits and vegetables every day. Fruits and vegetables are rich in vitamins

and have little fat.

     Teenagers need to drink more milk. Milk will help their bones grow.

     Teenagers need to eat breakfast every day. This is good for their body and mind.

1. "Junk food" contains a lot of ____________.

A. milk an sugar                            

B. fruits and sugar

C. vegetables and salt                        

D. fat, oil, salt and sugar

2. In a recent survey at one school, scientists found many students liked _________.

A. vegetables    

B. unhealthy food    

C. fruits      

D. healthy food

3. In this passage, doctors think that teenagers should eat more _____________.

A. food with no vitamins    

B. fat and sugar  

C. vegetables and fruits    

D. salt and oil

4. The passage talks mainly about ______________.

A. bad habits      

B. junk food    

C. unhealthy food    

D. advice on healthy eating

填空题