问题 选择题

如图所示,匀强电场场强大小为 E ,方向与水平方向夹角为θ(θ≠45°) ,场中有一质量为 m ,电荷量为 q 的带电小球,用长为 L 的细线悬挂于O点,当小球静止时,细线恰好水平.现用一外力将小球沿圆弧缓慢拉到竖直方向最低点,小球电荷量不变,则在此过程中(     )

A.外力所做的功为mgLcotθ

B.带电小球的电势能增加 qEL ( sinθ+cosθ)

C.带电小球的电势能增加 2mgLcotθ

D.合外力所做的功为0

答案

AB

分析:对小球进行受力分析可知,小球受重力、电场力及绳子的拉力而处于平衡;由共点力的平衡可求得电场力的大小;

由功的计算公式可求得小球运动中电场力所做的功;则由电场力做功与电势能的关系可求得电势能的变化;再由动能定理可求得外力所做的功.

解答:解:小球在水平位置静止,由共点力的平衡可知,Fsinθ=mg,则F=

小球从最初始位置移到最低点时,电场力所做的功W=-EqL(cosθ+sinθ),因电场力做负功,故电势能增加,故B正确,C错误;

由动能定理可知,W+W+WG=0;

W=-(W+W)=EqL(cosθ+sinθ)-mgL=mgLcotθ;故A正确,D错误;

故选AB.

点评:本题考查了动能定理的应用及电场力做功与电势能的关系,在解题中要注意理解重力做功及电场力做功的特点,正确求得两种功的表达式.

单项选择题
阅读理解

The journey two divers made some time ago to the deepest point on the earth makes us realize how much of the world still remains to be studied. The two men went down seven miles to the bottom of the Pacific Ocean inside a small steel ball to find out if there are any ocean currents(水流) or signs of life.

It was necessary to set out early, so that the ball would come to the surface in daylight, and be easily found by the mother ship which would be waiting for it. The divers began preparations early in the morning and soon afterwards, when all was ready, the steel ball disappeared under the surface of the water.

The divers felt as if they were going down steps as they passed through warm and cold layers (层) of water. In time the temperature dropped to the freezing point. They kept in touch with the mother ship by telephone telling how they felt. Then, at a depth of 3,000 feet, the telephone stopped working and they were quite cut off from the outside world. All went well until some four hours later at 30,000 feet, the men were frightened by a loud, cracking noise. Even the smallest hole in the ball would have meant instant death. Luckily, though, it was only one of the outer windows that had broken. Soon afterwards, the ball touched the soft ocean floor raising a big cloud of "dust" made up of small dead sea creatures. Here, powerful lights lit up the dark water and the men were surprised to see fish swimming just above them quite untroubled by the great water pressure. But they did not dare to leave the lights on for long, as the heat from them made the water boil. Quite unexpectedly, the telephone began working again and the faint but clear voices of the divers were heard on the mother ship seven miles away. After a stay of thirty minutes the men began their journey up, arriving three hours later, cold and wet through, but none was worse for their experience.

65. The purpose of the divers' journey to the deepest point on the earth was to find

A. if there are water currents, and life in the great depths

B. if people can stand the severe cold in the great depths

C. if there are steps in the great depths

D. if the telephone works well in the great depths

66. The divers set out early in the morning so that                .

A. they could return to the surface during the day

B. they could see at the bottom of the ocean

C. they could avoid the cold at night

D. they could stay long at the bottom

67. As the divers went down to the ocean floor, the telephone              .

A. kept working all the time

B. stopped working at a depth of 3,000 feet and began working again after they reached the bottom

C. stopped working at a depth of 3,000 feet and began working again at 30,000 feet

D. stopped working at a depth of 3,000 feet and began working again when they returned to the same depth

68. On the ocean floor, the divers found that               .

A. there was no life but some small dead sea creatures

B. fish were swimming as freely as they do near the surface

C. fish were not swimming freely in the dark water

D. fish were not swimming freely under the high water pressure