问题 计算题

(14分)如图所示,AB两个矩形木块用轻弹簧相接静止在水平地面上,弹簧的劲度系数为k,木块A和木块B的质量均为m

(1)若用力将木块A缓慢地竖直向上提起,木块A向上提起多大高度时,木块B将离开水平地面.

(2)若弹簧的劲度系数k是未知的,将一物体CA的正上方某位置处无初速释放,CA相碰后立即粘在一起(不再分离)向下运动,它们到达最低点后又向上运动.已知C的质量为m时,把它从距A高为H处释放,则最终能使B刚好离开地面.若C的质量为,要使B始终不离开地面,则释放时,CA的高度h不能超过多少?

答案

(1)

(2)

(1)开始时,木块A处于平衡,则kx1=mg(弹簧压缩)

木块B刚好离开地面时,有kx2=mg(弹簧伸长)

故木块A向上提起的高度为

(2)物块C的质量为m时,它自由下落H高度时的速度        ①

CA碰撞后的共同速度为v2,根据动量守恒定律,有

  ②

以后AC继续压缩弹簧,后又向上弹起,最终能使木块B刚好离开地面.此过程中,AC上升的高度为上升的高度为,由于最初弹簧的压缩量x1与最后的伸长量x2相等,所以,弹簧势能相等,根据机械能守恒定律,有

       ③

物块C的质量为时,设在距Ah处自由下落后刚好能使木块B离开地面.

C下落h高度时的速度                       ④

CA碰撞后的共同速度为.则有

解得                      ⑤

AC碰后上升高度时,木块B刚好离开地面,此过程中,由机械能守恒定律有

                         ⑥

由以上各式消去解得

阅读理解

My husband and I were once in Nepal(尼泊尔)to see sunrise over the Himalayas.

One morning we awoke to total darkness at 5 o’clock.As we rushed through a town with cameras in hand,I noticed the calm,gentle way the Nepalese people greeted the morning.One man boiled a huge pot of milk tea,and other villagers gathered around his fire,cupping their hands around small glasses of the steaming sweet mixture.It was fascinating,but not to be left behind,we joined the stream of tourists moving quickly up to the lookout point.

The top was crowded when we arrived,but after 10 minutes of cold waiting,the assembled group gave up.“The cloud cover is too heavy,”one said.Then one by one they rushed down the hill to the next item on their sightseeing list.I was disappointed as well,but suddenly I noticed a small Nepalese boy absently playing with a stick and shooting quick glances at the clouds.He must know something we don’t,I thought.I decided to wait with him.

The boy and I didn’t have to wait long.Moments later,a tiny stream of golden light burned through one thick cloud,then another.Rose-colored fog warmed the backs of the clouds,and suddenly the morning sun stole a glance around the side of the mountain,mile above where I’d expected it to be.

Nothing I’d seen before prepared me for the moment the clouds withdrew with bowed heads,and the magnificent Himalayas were revealed before,around,and above me.I sat in astonishment,not breathing,not daring to look away,certain that God had placed me here at the backdoor of Earth to show me what Heaven really looks like.I certainly got the message.Never again will I rush a sunrise.I now know Nature will supply her fruits to me only when I am truly ready to receive them.

小题1:What does “It” in Paragraph 2 most probably imply?

A.The darkness of the town in the morning.

B.The huge pot of milk tea boiling on the fire.

C.The way the local people welcomed the day.

D.The stream of tourists rushing to the lookout point.小题2:The author decided to wait with the Nepalese boy because _____.

A.she felt kind of having faith in him

B.the restless tourists disappointed her

C.that boy was praying to the sun with a magic stick

D.she had nothing more to see on her sightseeing list小题3:What can be concluded from the passage?

A.Do in Rome as the Romans do.

B.God helps those who help themselves.

C.Time and tide wait for no man.

D.Fortune rewards those having patience.

单项选择题