问题 问答题

(18分)一个质量为的小球被长为L的轻质细绳悬挂,小球可以绕悬点O在竖直平面内摆动,不计空气阻力,则开始小球静止且恰能与地面接触而不发生相互作用,一个质量为的小物块在光滑水平面上滑行并与小球发生正碰,碰后物块静止不动而小球在竖直平面内刚好可以通过最高点做圆周运动,当小球再次与物块发生正碰后,小物块速度变为最初速度的一半,已知重力加速度为,两物体均可视为质点,试求

小题1:小物块最初的速度V0的大小;

小题2:第二次碰撞中系统损失的机械能

答案

小题1:小球恰好通过最高点作圆周运动,此时重力刚好提供向心力,设速度为V,有

         (3分)

V=

设小球第一次碰完后速度为V1,其后在摆至最高点过程中,根据动能定理:

-2·2mgL=·2m V2-·2m V12   (3分)

代入V值可得V1=

第一次碰撞过程中,物块和小球系统动量守恒,有

    mV0=2m V1

代入V1值可得V0=2   (3分)

小题2:小球从第一次碰后到第二次碰前,由于机械能守恒且同在最低点,所以第二次碰前的速度仍为V1

设小球第二次碰完后的速度为V2,根据第二次碰撞物块和小球系统动量守恒

2m V1=2m V2+m˙V0           (2分)

代入V1V0值可得V2= (2分)

故第二次碰撞系统损失的机械能

ΔE=·2m V12-·2m V22-mV02  (3分)

代入所求的的速度值可得

ΔE=mgL             (2分)

阅读理解

阅读理解。

     On a hot summer day in south Florida, a little boy decided to go for a swim in the old swimming

hole behind his house.In a hurry to dive into the cool water, he ran out of the back door, leaving behind

shoes and shirt as he went.

     He flew into the water, not realizing that as he swam toward the middle of the lake, a crocodile was

swimming toward him.His mother in the house was looking out of the window and saw the two. In great

fear, she ran toward the water,shouting to her son as loudly as she could. Hearing her voice, the little boy

became alarmed and made a U-turn to swim to his mother. It was too late. Just as he reached her, the

crocodile reached him.From the shore, the mother caught her Iittle boy be the arms just as the crocodile

snatched his legs. That began an incredible tug-of-war between the two.The crocodile was much stronger

that the mother, but the mother was much too eager to let go. A farmer happened to drive by, heard their

screams, raced from his truck, took aim and shot the cmcodile.

     After several weeks in hospital,the Iittle boy survived. His legs were extremely scarred by the attack of the

animal. And, on his arms, were deep scratches where his mother's fingernails dug into his flesh in her effort

to hang on to the son she loved.

     A newspaper reporter, who interviewed the boy, asked if he would show him his scars (伤疤). The boy

Iifted his legs. And then, with obvious pride,he said to the reporter,"But look at my arms. I have great scars

on my arms, too. I have them because my Mom wouldn't let go."

     Never judge another person's scars, because you don't know how they were made.

1. What is probably the best title for the passage?

A. Scars of love

B. Women hold up half sky

C. A terrible experience

D. Don't judge by appearances

2. Hearing Mother's shouts, the boy _______.

A. remained in the middle in great fear

B. didn't stop swimming forwards

C. swam back towards the bank

D. was ready to fight the crocodile

3. Which of the following statements is true according to the text?

A. A crocodile attacked him when the boy and his mother were bathing.

B. The crocodile bit the ams of the boy when is reached him.

C. It was the farmer who shot the crocodile.

D. There is always an interesting story behind every scar.

4. By saying "But look at my arms. I have great scars on my arms, too." in paragraph 4,

   the boy really wants to show ______.

A. how deep the scars made by the crocodile were

B. What a brave boy he was

C. how many scars and scratches he had

D. how great and beloved his mother was

选择题