问题 计算题

如图所示,长为R的不可伸长轻绳上端固定在O点,下端连接一小球,小球与地面间的距离可以忽略(但小球不受地面支持力)且处于静止状态。在最低点给小球一沿水平方向的初速度,此时绳子恰好没断,小球在竖直平面内做圆周运动。假设小球到达最高点时由于绳子碰到正下方P处的钉子恰好断开,最后小球落在距初始位置水平距离为4R的地面上,重力加速度为g.试求:

(1)绳突然断开时小球的速度v;

(2)竖直方向上O与P的距离L。

答案

解:(1)由

(2)在最高点  

在最低点  

代入解得

阅读理解

Peter and his seven-year-old sister ,Kate , were at the same school. Not long after his tenth birthday Peter was entrusted to take her to school.

It was only two stops down the road , but the way his parents kept going on about it , you might have thought Peter was taking Kate to the North Pole . He was given instructions the night before. When he woke up , he had to listen to them over and over again. He was to keep hold of Kate’s hand at all times , sit close to the front nearest the window , and tell the bus driver the name of his stop.

Peter repeated all this back to his mother and set out for the bus stop with his sister. They held hands all the way. Actually he didn’t mind this but simply hoped that none of his friends would see him holding a girl’s hand. The bus came. They got on and sat close to the front. It was ridiculous sitting there holding hands and there were some boys from school there, so they let go of each other.

Peter was feeling proud of himself. He could take care of his sister anywhere. If they were alone tighter on a mountain pass and came face to face with a pack of hungry wolves, he could know exactly what to do. Taking care and not to make sudden movement, he would move away with Kate until they had their backs to a large rock. That way the wolves would not be able to surround them.

Then he takes from his pocket two important things—his hunting knife and a box of matches. He takes the knife from its sheath(鞘) and sets it down on the grass, ready in case the wolves attack. They’re coming close now. They’re so hungry and are watering and growling (咆哮). Kate is crying, but he cannot comfort her. He knows he has to concentrate on his plan. Right at their feet are some dry leaves and twigs. Quickly and skillfully, Peter gathers them into a small pile. The wolves are edging closer. He has to get this right. There’s only one match left in the box. He bends down, cups his hand and lights the match. There’s strong rush of wind. The flame flickers, but Peter holds it close to the pile and then first one leaf, then another, then the end of a twig catch fire, and soon the little pile is burning. He piles on more leaves and twigs and larger sticks. The wolves are backing off. Wild animals are terrified of fire. The flames are leaping higher and the wind is carrying the smoke right into their jaws. Now Peter takes holds of the hunting knife and …

Ridiculous! A daydream like this could make him miss his stop if he wasn’t careful. The bus had come to a halt. The kids from his school were already getting off. Peter leaped to his feet and just managed to jump to the pavement as the bus was starting off again. It was more than fifty yards down the road when he realized he had forgotten something. Was it his backpack ? No. It was his sister. He had saved her from the wolves and left her sitting there. For a moment, he couldn’t move. He stood watching the bus pull away up the road. “Come back,” he murmured, “Come back.”

小题1:Which of the following is true according to the passage?

A.Kate didn’t know their destination at all.

B.Peter and Kate missed their stop in the end.

C.Peter is thought to take Kate to the North Pole.

D.Mother asked Peter to hold Kate’s hand all the way.小题2:Before getting on the bus, ________.

A.Peter and Kate let go of each other

B.Peter was told instructions twice

C.Peter recited the instructions to his mother

D.Peter managed to avoid meeting his friends小题3:Which of the following shows the right order of Peter fighting against the wolves?

a. gather dry leaves and twigs into a small pile

b. take out his hunting knife and matches

c. light the leaves and twigs

d. move carefully with back to a rock

e. attack wolves with knife

f. strike a match

g. pile more leaves and sticks

A.d-b-f-c-a-e-g

B.d-b-a-f-c-g-e

C.B-f-a-g-c-e-d

D.A-g-b-c-f-e-d小题4:What can we infer from the passage?

A.Peter felt anxious and helpless when the bus left.

B.Peter succeeded in fighting against wolves.

C.Kate would be absent from school that day.

D.Peter brought hunting knife and matches with him.

单项选择题