问题 计算题

如图所示,A、B两个小物体(可看成质点)的质量分别为2m、m,它们栓接在跨过定滑轮的细绳两端,细绳不可伸长,且能承受足够大的拉力。B物体悬吊着静止时,A也静止在地面上,A、B与定滑轮轮轴之间的竖直距离分别为2l、l。现将B物体竖直向上提高距离l,再将其从静止释放。每次细绳被拉直时A、B速度的大小立即变成相等,且速度方向相反,细绳被拉直的时间极短。物体与地面接触时,速度立即变为0,直到再次被细绳拉起。细绳始终在滑轮上,且不计一切摩擦,重力加速度为g。求:

(1)细绳第一次被拉直瞬间绳对A冲量的大小;

(2)A第一次上升过程距离地面的最大高度;

(3)A运动的总路程。

答案

解:(1)B做自由落体,下降高度为I时的速度为

      根据

      此时细绳被拉直,A、B速度的大小立即变成

      设绳子对A、B的冲量大小为I,根据动量定理得

      对B:

      对A:

      解得细绳第一次被拉直瞬间绳对A冲量的大小 

(2)由(1)可得A第一次离开地面时速度的大小

      从A离开地面到A再次回到地面的过程中,A、B组成的系统机械能守恒,假设A第一次上升过程距离地面的最大高度为,则

     

      解得

(3)从A离开地面到A再次回到地面的过程中,A、B组成的系统机械能守恒,所以,A再次回到地面时速度的大小依然为,即B再次回到距离地面高度为时速度的大小也为。此后B做竖直上抛运动,落回距离地面高度为时速度的大小还是

      根据(1)求解可得A第二次离开地面时速度的大小

      同理可求A第二次离开地面上升的最大高度为

      ……

      A第次离开地面时速度的大小

      同理可求第次离开地面上升的最大高度为

      由于A的质量大于B的质量,A最终会静止在地面上

      所以A运动的总路程

阅读理解

阅读理解。

    

     Many earthquakes (地震) happen without warning, so it is important to know what to do wherever you

are during an earthquake. Here are some top tips on how to stay safe in an earthquake. 

    ◆ Keep a cool head. Worry may make bad decisions. Think about what you should do. The first several

seconds are important. 

    ◆ If you are indoors during an earthquake, hide under a heavy desk and protect your head. Stay away from

windows and anything that could fall on you.

    ◆ If you are in a crowded hall away from the door, don't rush to the exit. You will find too many people

trying to get out at the same time. Instead, hide under a desk or a table. Do not get into a lift during an

earthquake!

    ◆Stay in a safe area until you are sure it's OK to leave. Some aftershocks (余震) may follow an earthquake.

These are as dangerous as the earthquake. 

    ◆If you are at home and you smell gas, open a window and leave the building quickly.

    ◆ If you are outdoors, find a clear place away from buildings, trees, street lights and power lines.

    ◆If you are buried in debris (埋在废墟), you may make noises by knocking at the rocks. Shouting will use

up your energy. You could be without help for up to 72 hours. Try to find some water and food. These are

important for you.

1. The underlined words "top tips" mean _________.

A. useful advice

B. boring news

C. interesting stories

2. If you are in a crowded hall away from the door when an earthquake happens,

    you mustn't try to get out because _________.

A. it's more dangerous outside

B. you may lose the way

C. people may hurt each other when rushing out at the same time

3. Which one is right during an earthquake?

A. If you smell gas, stay at home and wait for help.

B. Hiding under a heavy desk if you are indoors.

C. Using the lift to go downstairs.

4. You should _________ if yo u are buried in debris.

A. find a clear place

B. keep shouting for help

C. catch people's attention by knocking at the rocks

5. From the passage we know that _________.

 A. keeping a cool head is very important during an earthquake

B. we can hide under the tree during an earthquake

C. we needn't care about aftershocks

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