问题 问答题

如图所示,一固定绝缘且足够长的斜面倾角为37°,与斜面同一空间足够大的范围内存在水平方向的匀强电场,场强大小与方向均未知。一质量为m=1kg,带电量q=0.5C的带电滑块从斜面顶端由静止出发,经过时间t=2s,发生位移s=15m,已知滑块与斜面间的动摩擦因素μ=0.5。在第2s末,加上方向垂直于纸面向里,磁感应强度大小为B=0.4T的匀强磁场,滑块在斜面上继续滑行L=10m的距离后恰好离开斜面。(重力加速度g=10m/s2

(1)试说明该带电滑块所带电荷的性质及滑块在斜面上的运动情况,要求说明理由;

(2)计算说明匀强电场的场强大小和方向。

(3)滑块在斜面上运动过程中,系统产生的内能。

答案

(1)见解析(2)E=-10N/C,负号表明,水平向右。(3)

(1)依题意,滑块在加上磁场后的运动过程中能离开斜面,说明其所受的洛仑兹力方向垂直于斜面向上,由左手定则判断出该滑块带正电;(3分)

滑块的运动情况:由运动开始到第2s末,滑块受重力、电场力(方向可能水平向左,也可能水平向右)、支持力、摩擦力作用下,做初速度为零的匀变速直线运动;(1分)

从第2s末开始,滑块还受一个垂直于斜面向上的洛仑兹力作用,随着斜面对其支持力的不断减小,摩擦力也随之不断减小,所以滑块做加速度增大的加速运动,继续滑行10m后离开斜面。(1分)

(2)设匀强电场的场强为E,方向水平向左(如图所示)

以滑块为研究对象,其受力分析如图所示

由匀变速直线运动规律有:

      ①

解得加速度     (2分)

建立如图所示直角坐标系,根据滑块的运动状态有:

,即

    ②(1分)

,即

      ③(1分)

                       ④(1分)

联立以上各式代数求解得:E=-10N/C,负号表明,电场强度实际方向与假设方向相反,即水平向右。(2分)

(3)滑块恰好离开斜面的临界条件为:斜面对滑块的支持力恰好为零,即洛仑兹力恰好与重力沿与斜面垂直方向的分力及电场力沿斜面垂直方向的分力矢量和为零。设离开斜面时滑块的速率为,则有:

     ⑥  

解得:  (2分)

小球从开始运动到离开斜面这一过程中,重力做正功,设其为,则

   ⑦    (1分)

电场力做正功,设其为,则

    ⑧    (2分)

洛仑兹力不做功。

摩擦力做负功,所做的功全部转化为系统的内能,设其为Q。由动能定理有:

   ⑨    (2分)

联立以上四式求解得:  (1分)

说明:用其它方法计算,只要正确,同样给分。

完形填空

(任务型阅读)

阅读下面的短文,并根据短文后的要求答题(请注意问题后的字数要求)。

Safety in the highway is not totally out of hands. Here are four ways we can protect ourselves when we travel.

You are safer in a large car. People in small cars are injured more often and more severely than people traveling in large cars. Factories of small cars are strengthening their products’ safety, which helps. But the mix of large cars and small cars on the road is the main reason of the problem.

Being thrown into glass and metal car parts, or being thrown from the car, can really damage to you. That’s why safety belts should be worn. The safety belt’s main purpose is ___________if your car has a sudden crash with another vehicle or object, or if it rolls over. A belt can reduce the chance of fatal injury by 45% and the chance of serious injury by 50%.

Air bags are important. More than half of all new cars sold have air bags. Air bags provide protection in frontal(正面的)crashes—the type of crash that kills the most drivers—when they are also wearing safety belts. Most people are demanding air bags in the cars they buy. But the protection provided by air bags is limited in side or rear crashes; effective as they are, they can’t take the place of safety belts.

Drunk driving crashes are less likely to happen if you don’t drink. Drunk driving is the most serious problem. Many people have realized that drunk driving can lead to death and injury, prison time and other results. There are movements to strengthen penalties(处罚) for drinking and driving.

1. What is the main idea of the passage? (Please answer within 10 words.)

2. Which of the sentences in the passage can be replaced by the following one?

Although they are effective, you should still wear your safety belts while driving.

3. Please fill in the blank with proper words to make the sentence completed.(Please answer within 6 words.)

4. Please translate the underlined sentence into Chinese.

6. What other suggestions can you offer? Why?(Please answer within 30 words.)

多项选择题