问题 计算题

如图所示,“×”型光滑金属导轨abcd固定在绝缘水平面上,ab和cd足够长,∠aOc =60°,虚线MN与∠bOd的平分线垂直,O点到MN的距离为L。MN左侧是磁感应强度大小为B、方向竖直向下的匀强磁场。一轻弹簧右端固定,其轴线与∠bOd的平分线重合,自然伸长时左端恰在O点。一质量为m的导体棒ef平行于MN置于导轨上,导体棒与导轨接触良好。某时刻使导体棒从MN的右侧处由静止开始释放,导体棒在压缩弹簧的作用下向左运动,当导体棒运动到O点时弹簧与导体棒分离,导体棒由MN运动到O点的过程中做匀速直线运动,导体棒始终与MN平行。已知导体棒与弹簧彼此绝缘,导体棒和导轨单位长度的电阻均为r0,弹簧被压缩后所获得的弹性势能可用公式Ep=kx2计算,k为弹簧的劲度系数,x为弹簧的形变量。

(1)求导体棒在磁场中做匀速直线运动过程中的感应电流的大小,并判定大小变化特点;

(2)求弹簧的劲度系数k和导体棒在磁场中做匀速直线运动时速度v0的大小;

(3)求导体棒最终静止时的位置距O点的距离。

答案

解:(1)设导体棒在磁场中做匀速直线运动时的速度为v0,某时刻导体棒在回路中的长度为l,则此时感应电动势

此时回路的电阻

回路中的感应电流

因为B、v0均为不变量,所以感应电流I为不变量 

(2)释放导体棒后,在未进入磁场的过程中,导体棒和弹簧组成的系统机械能守恒,则有  

导体棒在磁场中做匀速直线运动的过程中,设某时刻导体棒距O的距离为x,根据牛顿第二定律有  

解得   

(3)导体棒过O点后与弹簧脱离,在停止运动前做减速运动。设某时刻导体棒距O点的距离为x,导体棒在回路中的长度为l,加速度为a,速度为v,回路中的电流为I,根据牛顿第二定律有

又因为

所以

取一段很短的时间△t,导体棒在回路中的长度为l、加速度为a和速度为v,l、a和v可以为不变。设在这段时间内导体棒速度的变化量大小为△v,回路所围面积的变化量为△S。将上式左右两边同乘以△t,可得

则导体棒从O点开始运动到静止的过程可表示为

所以

设导体棒最终静止的位置距O点的距离为x0,则:

 

阅读理解

阅读理解。

      Scientists are trying to make the deserts into good land again. They want to bring water to the deserts, so

people can live and grow food. They are learning a lot about the deserts. But more and more of the earth is

becoming desert all the time. Scientists may not be able to change the desert in time.

      Why is more and more land becoming desert? Scientists think that people make deserts. People are doing

bad things to the earth.

      Some places on the earth don't get much rain. But they still don't become deserts. This is because some

green plants are growing there. Small green plants and grass are very important to dry places. Plants don't let the

hot sun make the earth even drier. Plants don't let the wind blow the dirt away. When a little bit of rain falls, the

plants hold the water. Without plants, the land can become a desert much more easily.

1. Deserts _________. [ ]

A. get very little rain

B. never have any plants or animals in them

C. can all be turned into good land in the future

D. both A and C

2. Small green plants are very important to day places because ________. [ ]

A. they don't let the sun make the earth even drier

B. they don't let the wind blow the earth away

C. they hold the water

D. A, B and C

3. Land is becoming desert little by little because ________. [ ]

A. plants can't grow there

B. there's not enough rain

C. people are doing bad things to the earth.

D. scientists know little about desert

4. Which is the main idea of the first paragraph? [ ]

A. Scientists know how to change land into good land.

B. Land is becoming desert faster than scientists can change it back into good land.

C. If scientists can bring water to the desert, people can live there.

D. More and more places are becoming deserts all the time.

5. After reading this, we learn that ________. [ ]

A. plant can keep dry land from becoming desert.

B. it is good to get rid of (清除) the grass in the desert

C. all places without much rain will become deserts

D. it is better to grow crops on dry land than to grow grass

问答题 简答题