问题 问答题

如图所示,竖直面内光滑弧形轨道与半径R=0.50m的光滑圆形轨道在最低端C处平滑连接.A、B两滑块(可视为质点)用轻细绳拴接在一起,中间夹住一个被压缩的微小轻质弹簧.两滑块从弧形轨道上距轨道底端高h=0.80m处由静止滑下,刚滑入圆形轨道最低点C时拴接两滑块的绳断开,弹簧迅速将两滑块弹开,最终B保持静止,A恰能通过圆形轨道最高点.已知滑块A的质量mA=0.16kg,滑块B的质量mB=0.04kg,取g=10m/s2,不计空气阻力.求:

(1)A、B一起运动到圆形轨道最低点时速度的大小;

(2)滑块A被弹簧弹开时的速度大小;

(3)弹簧在将两滑块弹开的过程中释放的弹性势能.

答案

(1)设滑块A和B运动到圆形轨道最低点速度为v0,对滑块A和B下滑到圆形轨道最低点的过程,根据动能定理,有
(mA+mB)gh=

1
2
(mA+mB)v02

解得:v0=4.0m/s 
(2)设滑块A恰能通过圆形轨道最高点时的速度大小为v,根据牛顿第二定律有
mAg=mA

v2
R

设滑块A在圆形轨道最低点被弹出时的速度为vA,对于滑块A从圆形轨道最低点运动到最高点的过程,根据机械能守恒定律,有
1
2
mAvA2=mAg2R+
1
2
mAv2

代入数据联立解得:vA=5.0 m/s
(3)对于弹簧将两滑块弹开的过程,A、B两滑块所组成的系统水平方向动量守恒,设滑块B被弹出时的速度为vB,根据动量守恒定律,有
(mA+mB)v0=mAvA+mBvB 
解得:vB=0
设弹簧将两滑块弹开的过程中释放的弹性势能为Ep,对于弹开两滑块的过程,根据机械能守恒定律,有 

1
2
(mA+mB)v02+Ep=
1
2
mAvA2

解得:Ep=0.40J

答:(1)A、B一起运动到圆形轨道最低点时速度的大小为4.0m/s;

(2)滑块A被弹簧弹开时的速度大小为5.0 m/s;

(3)弹簧在将两滑块弹开的过程中释放的弹性势能为0.40J.

单项选择题 A1型题
阅读理解

The story goes that two friends were walking through the desert. During some point of the journey they had an argument, and one friend slapped the other one in the face. The one who got slapped was hurt, but without saying anything, wrote in the sand: "Today my best friend slapped me in the face."  They kept on walking until they found an oasis(绿洲), where they decided to take a bath. The one who had been slapped got stuck in the mire and started drowning, but the friend saved him.  After he recovered from the near drowning, he wrote on a stone: "Today my best friend saved my life."  The friend who had slapped and saved his best friend asked him, "After I hurt you, you wrote in the sand and now you write on a stone. Why?"

The other friend replied: "When someone hurts us we should write it down in the sand where winds of forgiveness can erase it away. But when someone does something good for us, we must engrave it in the stone where no wind can ever erase it."

You have to learn to write your hurts in the sand and to carve your benefits in the stone.

64.One friend slapped the other because ____.

A.he was angry that his friend took him to the desert by mistake.

B.He was angry that his friend did not agree with him about something.

C.He was angry that his friend kept wasting time writing and carving.

D.He had to save his friend from drowning, and this almost took his own life.

65.The underlined sentence means we should _____.

A.not let others know we are angry with them by letting wind erase what we write down.

B.gradually forgive others for bad things they have done to us as time goes by.

C.make sure what we write in the desert does not remain long .

D.not try to find stones to record things on in a desert.

66.What is the right understanding of the last sentence of the passage?

A.We should write and carve to record different kinds of feelings.

B.We should record different kinds of things in different ways.

C.We should remember only good things others have done to us and let go bad things.

D.We should remember things that others do to us, including both good things and bad things.

67.Which of the following can be the proper title of the passage?

A.True Friendship                     B.Sand and Stone 

C.Hurts and Benefits                  D.Forgiveness and Gratitude