问题 问答题

如图所示是某游乐场过山车的娱乐装置原理图,弧形轨道末端与一个半径为R的光滑圆轨道平滑连接,两辆质量均为m的相同小车(大小可忽略),中间夹住一轻弹簧后连接在一起,两车从光滑弧形轨道上的某一高度由静止滑下,当两车刚滑入圆环最低点时连接两车的挂钩突然断开,弹簧将两车弹开,其中后车刚好停下,前车沿圆环轨道运动恰能越过圆弧轨道最高点,求:

(1)前车被弹出时的速度;

(2)前车被弹出的过程中弹簧释放的弹性势能;

(3)两车从静止下滑到最低点的高度h.

答案

(1)设前车在最高点速度为v2,依题意有mg=m

v22
R
(1)

设前车在最低位置与后车分离后速度为v1,根据机械能守恒得

1
2
m
v22
+mg•2R=
1
2
m
v21
(2)

由(1)(2)得:v1=

5Rg

(2)设两车分离前速度为v0

由动量守恒定律2mv0=mv1

v0=

v1
2
=
5Rg
2

设分离前弹簧弹性势能Ep,根据系统机械能守恒得

Ep=

1
2
m
v21
-
1
2
•2m
v20
=
5
4
mRg

(3)两车从h高处运动到最低处机械能守恒

2mgh=

1
2
•2m
v20

h=

5
8
R

答:(1)前车被弹出时的速度是

5gR

(2)前车被弹出的过程中弹簧释放的弹性势能是

5mgR
4

(3)两车从静止下滑到最低点的高度是

5R
8

单项选择题
阅读理解

D

  Just outside the northern Italian town of Bra, there rises a church tower with a clock that is a half hour slow. Though not far from the industrial city of Turin,Bra smells of roses,and leisure(悠闲)is the law. It is both the home of an international movement that promotes slow food and one of Italian cities that have joined the slow cities. In Bra, the population is 27,866. The town fathers have declared that all small food shops be closed every Thursday and Sunday. They forbid cars in the town square. All fruits and vegetables served in local schools must be organic(有机的). And as the movement goes well,the slow concept gradually spreads across Europe.

  The argument for a Slow Europe is not only that it is good,but also that it can work. The Slow City Movement, which started in 1999,has improved local economies(经济)by promoting local goods and tourism. Young Italians are moving from larger cities to Bra,where unemployment is only 5 percent,about half the nationwide rate. Slow food and wine festivals draw thousands of tourists every year. Shops are doing well,many with sales rising at a rate of 15% per year.“This is our answer to the world,”says Paolo Saturnini,the founder of Slow Cities.

  France is in favor of slow economics. Most outsiders have long been doubtful of the French model:short hours and long vacations. Yet the French are more productive than those in the United States and Britain,and have been for years.

  The mystery of French productivity has risen an Europe-wide debate about the advantages of working more slowly.

63.The church clock that is a half hour slow serves as a symbol of __________.

A.industrial development           B.slow movement

C.global economy             D.city growth

64.The low unemployment in Bra proves that__________.

A.the population is not large

B.tourism brings great job chance

C.the Slow City Movement is successful

D.the slow concept works well only in its birthplace

65.It can be inferred from the passage that__________.

A.British workers work longer hours than the French

B.French workers work longer hours than the Italians

C.Italian workers are less productive than the Americans

D.American workers are more productive than the British

66.The increased French productivity tends to__________.

A.favor a fast life style

B.throw doubt on slow economics

C.encourage a slow economic growth

D.confirm advantages of slow economics