问题 计算题

(12分)如图所示,水平桌面上有一轻弹簧,左端固定在A点,自然状态时其右端位于B点。水平桌面右侧有一竖直放置的轨道MNP,其形状为半径R=1.0m圆环剪去了左上角120°的圆弧,MN为其竖直直径,P点到桌面的数值距离是h=2.4m。用质量m1=0.4kg的物块将弹簧缓慢压缩到C点,释放后弹簧恢复原长时物块恰停止在B点,用同种材料、质量为m2=0.2kg的物块将弹簧缓慢压缩到C点释放,物块通过B点后做匀变速运动,其位移与时间的关系为x=6t-2t2,物块飞离桌面后恰好由P点沿切线落入圆轨道(不计空气阻力,g取10m/s2)。求:

⑴物块m2过B点时的瞬时速度vB及与桌面间的滑动摩擦因数μ;

⑵若轨道MNP光滑,物块m2经过轨道最低点N时对轨道的压力FN;=×-·

⑶若物块m2刚好能到达轨道最高点M,则释放m2后整个运动过程中其克服摩擦力做的功W。

答案

⑴vB=6m/s,μ=0.4;⑵FN=16.8N;⑶W=8.0J

题目分析:⑴由题意质量为m2的物块将弹簧缓慢压缩到C点释放,物块通过B点后做匀变速运动,其位移与时间的关系为x=6t-2t2可知,物块m2过B点时的瞬时速度为:vB=6m/s,加速度为:a=-4m/s2

物块离开B点后在桌面上受重力m2g、桌面的支持力N和滑动摩擦力f作用,根据牛顿第二定律可知,在水平方向上有:-f=m2a               

在竖直方向上有:N-m2g=0              

根据滑动摩擦定律有:f=μN               ④

由①②③④式联立解得:μ==0.4

⑵物块从D点离开桌面后做平抛运动,设至P点时速度在竖直方向上的分量为vy,则在竖直方向上,根据自由落体运动规律有:h=           ⑤

因物块由P点沿切线落入圆轨道,由几何关系和物块水平方向做匀速运动的规律可知:vy=vDtan60° ⑥

物块由D运动至N的过程中,只有重力做功,根据动能定理有:m2g(h+R-Rcos60°)=

在N点处,物块受重力m2g和圆轨道的支持力FN′作用,根据牛顿第二定律有:FN′-m2g=  ⑧

根据牛顿第三定律可知,物块m2经过轨道最低点N时对轨道的压力FN=FN′             ⑨

由⑤⑥⑦⑧⑨式联立解得:FN+m2g(3-2cos60°)=16.8N

⑶设CB距离为x1,BD距离为x2,在物块m1由C运动至B的过程中,根据功能关系有:Ep=μm1gx1  ⑩

在物块m2由C运动至B的过程中,根据功能关系有:Ep=μm2gx1            ⑪

在物块m2由B运动至D的过程中,根据动能定理有:-μm2gx2          ⑫

由于物块m2恰好通过圆轨道的最高点M,设通过速度为vM,根据牛顿第二定律有:m2g=  ⑬

设物块m2运动至P点时的速度为vP,在m2由P运动至M的过程中,克服摩擦力做功为W3,根据动能定理有:-m2g(R+Rcos60°)-W3          ⑭

根据几何关系可知:vP          ⑮

释放m2后整个运动过程中其克服摩擦力做的功为:W=μm2gx1+μm2gx2+W3             ⑯

由①⑤⑥⑩⑪⑫⑬⑭⑮⑯式联立解得:W=+m2gh()-m2gR(+cos60°)

代入数据解得:W=7.2J+4.8J-4.0J=8.0J

单项选择题 A1/A2型题
单项选择题

The majority of successful senior managers do not closely follow the classical rational model of first clarifying goals, assessing the problem, formulating options, estimating likelihood of success, making a decision, and only then taking action to implement the decision. Rather, in their day-by-day tactical activities, these senior executives rely on what is vaguely termed "intuition" to manage a network of interrelated problems that require them to deal with ambiguity, inconsistency, novelty, and surprise; and to integrate action into the process of thinking.

Generations of writers on management have recognized that some practicing managers rely heavily on intuition. In general, however, such writers display a poor grasp of what intuition is. Some see it as the opposite of rationality; others view it as an excuse of capriciousness.

Isenberg’s recent research on the cognitive processes of senior managers reveals that managers’ intuition is neither of these. Rather, senior managers use intuition in at least five distinct ways. First, they intuitively sense when a problem exists. Second, managers rely on intuition to perform well-learned behavior patterns rapidly. This intuition is not arbitrary or irrational, but is based on years of painstaking practice and personal experience that build skills. A third function of intuition is to synthesize isolated bits of data and practice into an integrated picture, often in an "Aha!" experience. Fourth, some managers use intuition as a check on the results of more rational analysis. Most senior executives are familiar with the formal decision analysis models and tools, and those who use such systematic methods for reaching decisions are occasionally suspicious of solutions suggested by these methods which run counter to their sense of the correct course of action. Finally, managers can use intuition to bypass in-depth analysis and move rapidly to find out a plausible solution. Used in this way, intuition is an almost instantaneous cognitive process in which a manager recognizes familiar patterns.

One of the implications of the intuitive style of executive management is that "thinking" is inseparable from acting. Since managers often "know" what is right before they can analyze and explain it, they frequently act first and explain later. Analysis is invariably tied to action in thinking/acting cycles, in which managers develop thoughts about their companies and organizations not by analyzing a problematic situation and then acting, but by acting and analyzing in close concert.

Given the great uncertainty of many of the management issues that they face, senior managers often initiate a course of action simply to learn more about an issue. They then use the results of the action to develop a more complete understanding of the issue. One implication of thinking/acting cycles is that action is often part of defining the problem, not just of implementing the solution. (454 words)

Notes: capriciousness 多变,反复无常。run counter to 与……背道而驰;违反。bypass 绕过。in close concert一齐,一致。given prep.考虑到,由于。

According to the text, which of the following would most probably be one major difference in behavior between Manager X, who uses intuition to reach decisions, and Manager Y, who uses only formal decision analysis()

A. Manager X checks possible solutions to a problem by systematic analysis; Manager Y does not

B. Manager X takes action in order to arrive at the solution to a problem; Manager Y does not

C. Manager Y draws on years of personal experience in creating a solution to a problem; Manager X does not

D. Manager X depends on day-by-day tactical activities; Manager X does not