问题 计算题

如下图所示,让摆球从图中的C位置由静止开始摆下,摆到最低点D处,摆线刚好被拉断,小球在粗糙的水平面上由D点向左做匀减速运动,到达A孔进入半径R=0.3m的竖直放置的光滑圆弧轨道,当摆球进入圆轨道立即关闭A孔。已知摆线长L=2m,,小球质量为m=0.5kg,D点与小孔A的水平距离s=2m,g取10m/s2。试求:

(1)求摆线能承受的最大拉力为多大?

(2)要使摆球能进入圆轨道并且不脱离轨道,求粗糙水平面摩擦因数μ的范围。

答案

(1)10N(2)0.35≤μ≤0.5或者μ≤0.125

(1)当摆球由C到D运动机械能守恒: (2分)

由牛顿第二定律可得: (1分)

可得:Fm="2mg=10N" (1分)

(2)小球不脱圆轨道分两种情况:①要保证小球能达到A孔,设小球到达A孔的速度

恰好为零,由动能定理可得: (2分)

可得:μ1="0.5" (1分)

若进入A孔的速度较小,那么将会在圆心以下做等幅摆动,不脱离轨道。其临界情况为到达圆心等高处速度为零,由机械能守恒可得:(2分)

由动能定理可得:(2分)

可求得:μ2=0.35(1分)

②若小球能过圆轨道的最高点则不会脱离轨道,在圆周的最高点,

由牛顿第二定律可得: (2分)

由动能定理可得: (2分)

解得:μ3="0.125" (1分)

综上所以摩擦因数μ的范围为:0.35≤μ≤0.5或者μ≤0.125 (1分)

本题考查的是圆周运动与动能定理及机械能守恒定律综合应用的问题,首先根据机械能守恒定律和牛顿第二定律计算出最大拉力;根据动能定理和机械能守恒定律计算出摩擦系数;

阅读理解

阅读理解。

     Thinking is something you choose to do as a fish chooses to live in water. To be human is to think. But

thinking may come naturally without your knowing how you do it. Thinking about drinking is the key to

critical (判断性的) thinking. When you think critically, you take control of your thinking processes (过程).

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     The word "critical" here has a special meaning. It does not mean taking one view against another view, as

when someone criticizes another person for doing something wrong. The nature of critical thinking is thinking

beyond the easily seen-beyond the pictures on TV, the untrue reports in the newspapers, and the faulty

reasoning.

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facts, you are a critical thinker.

     Activities of the mind and higher-order reasoning are processes of deep and careful consideration. They

take time, and do not go hand in hand with the fast speed in today's world: fast foods, instant coffee, and

self-developing film. If you are among the people who believe that speed is a measure of intelligence (智力),

you may learn something new from a story about Albert Einstein. The first time Banesh Hoffman, a scientist,

was to discuss his work with Albert Einstein. Hoffman was too nervous to speak. But Einstein immediately

put Hoffman at ease by saying, "Please go slowly. I don't understand things quickly."

1. Critical thinking is important to us because if we do not think critically, _______.

A. it will be hard for us to think naturally and fast

B. we might be controlled by other people's ideas

C. we will follow the ideas of others naturally

D. we might be footed by other people's ideas

2. If you are a critical thinker, you will _______.

A. think deeply about different ideas

B. trust the reports in the newspapers

C. take one view against another view

D. criticize other people for their mistakes

3. In the last paragraph, "something new" suggests that ________.

A. the smarter you are, the faster you do things

B. the faster you do things, the smarter you become

C. speed can improve intelligence

D. intelligence is not decided by speed

4. What would be the best title for the passage?

A. Thinking and Critical Thinking.

B. Understanding Critical Thinking.

C. Thinking Is Natural and Human.

D. Thinking Fast Means Intelligence.

单项选择题