问题 计算题

如图所示,光滑圆管形轨道AB部分平直,BC部分是处于竖直平面内半径为R的半圆,圆管截面半径r<<R.有一质量为m、半径比r略小的光滑小球以水平初速度v0射入圆管,问:

(1)若要使小球能从C端出来,初速度v0,多大?

(2)在小球从C端出来的瞬间,对管壁压力有哪几种典型情况?初速v0各应满足什么条件?

答案

(1) (2)①当N=0时,②对管壁有向上的压力,③对管壁有向下的压力,

题目分析:(1)当球恰好能从C端出来时,速度为零,根据机械能守恒定律求解初速度v0

(2)以小球为研究对象,小球经过C点时速度不同,管壁对球的作用力大小和方向不同,分析讨论:当管壁对球无作用力时,在C点由重力提供小球的向心力,由牛顿第二定律求出在C点的速度,由机械能守恒定律求出初速v0.当初速度大于和小于临界速度时,由向心力知识分析管壁对球的作用力大小和方向.

(1)当球恰好能从C端出来时,速度vC=0.根据机械能守恒定律得:,解得,所以要使小球能从C端出来,初速度

(2)在小球从C端出来的瞬间,对管壁压力有三种典型情况:

(3)①当管壁对球无作用力时,即N=0时,,解得,根据机械能守恒定律得,解得

②当管壁对球的作用力方向向下时,球对管壁的压力方向向上,此时

③当管壁对球的作用力方向向上时,球对管壁的压力方向向下,此时

点评:本题难度中等,对于小球在管子里的运动情形与轻杆模型类似,关键抓住临界情况:小球恰好到最高点和在最高点恰好不受管壁作用力两种情况

判断题
单项选择题

The collapse of Enron, the largest bankruptcy in American history, has rung out a banner year for American business failures. In Europe, the fallout from the Swissair and Sabena insolvencies continues. In the current global slump, more companies are likely to go under. Now is a perfect time to reconsider how to handle such failures: let them sink, or give them a chance to swim

In America, bankruptcy has come to mean a second chance for bust businesses. The famous "Chapter 11" law aims to give a company time to get back on its feet, by shielding it from debt payments and prodding banks to negotiate with their debtor. It even allows an insolvent company to receive fresh finance after it goes bust. On the other side of the Atlantic, when companies stumble, almost as much effort is spent in fingering the guilty as in trying to salvage a viable business. British and French laws, for example, can make a failing company’s directors face criminal penalties and personal liability. Moreover, bankers have the power, at the first sign of trouble, to push a company into the arms of the receivers. Some modest changes are afoot, however. Britain is considering moves that would bring its rules closer to America’s. New laws in Germany should also make it easier to revive sick companies, although trade unions still have their say.

But even with the arrival of the euro and moves towards a single financial market, going bust in Europe is a strictly local affair. Long before America had a single currency, the American constitution provided uniform bankruptcy laws, observes Elizabeth Warren of the Harvard Law School. Europe’s patchwork of national laws, according to Bill Brandt of " Development Specialists", a consultancy, inhibits lending and makes it difficult to fix ailing firms.

Transatlantic insolvencies are even harder, as a Belgian-based software company, Lernout and Hauspie, discovered this year. Its American reorganization plan was thwarted by a Belgian judge, who ordered a sale of the firm’s assets. As the European Union inches toward greater harmonization, should it try to mimic America

Critics of Chapter 11 think not. They argue that America’s bankruptcy system is wasteful, lets failed managers go unpunished, and gives some companies an unfair advantage. In Chapter 11, admittedly, lawyers and advisers gobble up fees, but a recent study argues that the fees are no larger than those for most mergers and acquisitions. One common complaint, that managers enjoy the high life while creditors go begging, fails to stand up to the data from America’s previous wave of bankruptcies in the early 1990s. Stuart Gilson of the Harvard Business School found that more than two-thirds of top managers were ousted within two years of a bankruptcy filing. More troubling is that some American firms seem to enjoy second and third trips to bankruptcy court, cheekily termed Chapters 22 and 33. Some see this as evidence that, ton often, they use Chapter 11 to keep running. But there is more to the story.

From the third paragraph we know for sure that()

A. the arrival of the euro smoothes the way to recovery for the bust businesses

B. in America the adoption of a single currency made uniform bankruptcy laws possible

C. there’s no uniform bankruptcy laws in European countries

D. in European countries bankruptcy laws are not enacted effectively