问题 计算题

(22分)如图所示,在xoy坐标平面的第一象限内有一沿y轴负方向的匀强电场,在第四象限内有一垂直于平面向里的匀强磁场,现有一质量为m、电量为+q的粒子(重力不计)从坐标原点O射入磁场,其入射方向与y的方向成45°角。当粒子运动到电场中坐标为(3L,L)的P点处时速度大小为v0,方向与x轴正方向相同。求:

(1)粒子从O点射入磁场时的速度v;

(2)匀强电场的场强E0和匀强磁场的磁感应强度B0

(3)粒子从O点运动到P点所用的时间.

答案

(1)(2)(3)

题目分析:(1)粒子从O点进入匀强磁场后在洛伦兹力作用下做匀速圆周运动,则其运动轨迹如图所示,经过磁场后进入电场,到达P点               (2分)

假设粒子在O点时的速度大小为v,OQ段为圆周,QP段为抛物线。

根据洛伦兹力与速度垂直不做功 可知粒子在Q点时的速度大小也为v,根据对称性可知方向与x轴正方向成45°角,可得:

Q点速度大小为,方向与X轴成斜向上。

进入电场后,电场力为竖直方向,水平方向匀速直线运动,所以有           (2分)

解得:          (1分)

(2)在粒子从Q运动到P的过程中,由动能定理得:

          (2分)

解得:        (1分)

又在匀强电场由Q到P的过程中,

水平方向匀速直线运动的速度,为位移为           (1分)

竖直方向初速度匀减速到0的位移为             (1分)

可得             (2分)

由几何关系可得粒子在OQ段圆周运动的半径:

根据洛伦兹力提供向心力得

             (2分)

(3)在Q点时,竖直分速度            (1分)

设粒子从Q到P所用时间为,在竖直方向上有:t1==               (1分)

粒子从O点运动到Q运动的圆心角为90度,所用的时间为:     (1分)

则粒子从O点运动到P点所用的时间为:     (1分)

单项选择题

I have just come home after viewing some astonishing works of art that were recently discovered in Church Hole cave in Nottinghamshire. They are not drawings, as one would expect, but etchings, and they depict a huge range of wild animals. The artists who created them lived around 13,000 years ago, and the images are remarkable on a variety of counts. First of all, their sheer number is staggering. There are ninety all together. Moreover, fifty-eight of them are on the ceiling. This is extremely rare in cave art, according to a leading expert, Dr. Wilbur Samson of Central Midlands University. "Wall pictures are the norm," he says. "But more importantly, the Church Hole etchings are an incredible artistic achievement. They can hold their own in comparison with the best found in continental Europe." I am not a student of the subject, so I have to take his word for it. However, you do not have to be an expert to appreciate their beauty.

In fact, it is the wider significance of the etchings that is likely to attract most attention in academic circles, since they radically alter our view of life in Britain during this epoch. It had previously been thought that ice-age hunters in this country were isolated from people in more central areas of Europe, but the Church Hole images prove that ancient Britons were part of a culture that had spread right across the continent. And they were at least as sophisticated culturally as their counterparts on the mainland.

An initial survey of the site last year failed to reveal the presence of the etchings. The reason lies in the expectations of the researchers. They had been looking for the usual type of cave drawing or painting, which shows up best under direct light. Consequently, they used powerful torches, shining them straight onto the rock face. However, the Church Hole images are modifications of the rock itself, and show up best when seen from a certain angle in the natural light of early morning. Having been fortunate to see them at this hour, I can only say that I was deeply and unexpectedly moved. While most cave art often seems to have been created in a shadowy past very remote from us, these somehow, convey the impression that they were made yesterday.

Dr. Samson feels that the lighting factor provides important information about the likely function of these works of art. "I think the artists knew very well that the etchings would hardly be visible except early in the morning. We can therefore deduce that the chamber was used for rituals involving animal worship, and that they were conducted just after dawn as a preliminary to the day’s hunting."

To which I can only add that I felt deeply privileged to have been able to view Church Hole. It is a site of tremendous importance culturally and is part of the heritage, not only of this country, but the world as a whole.

It is obvious that the writer ().

A.can now fully envisage the life of ice-age hunters

B.was profoundly impressed by the images in the cave

C.has now realized the true significance of most cave art

D.thinks the images should receive more publicity

判断题