问题 计算题

装甲车和战舰采用多层钢板比采用同样质量的单层钢板更能抵御穿甲弹的射击.通过对以下简化模型的计算可以粗略说明其原因.

质量为2m、厚度为2d的钢板静止在水平光滑桌面上。质量为m的子弹以某一速度垂直射向该钢板,刚好能将钢板射穿.现把钢板分成厚度均为d、质量均为m的相同两块,间隔一段距离平行放置,如图所示.若子弹以相同的速度垂直射向第一块钢板,穿出后再射向第二块钢板,求子弹射入第二块钢板的深度.设子弹在钢板中受到的阻力为恒力,且两块钢板不会发生碰撞。不计重力影响。

答案

设子弹初速度为v0,射入厚度为2d的钢板后,

由动量守恒得:mv0 =(2m+m)V(2分)

此过程中动能损失为:ΔE=f·2d=mv×3mV2 (2分)

解得ΔE=mv

分成两块钢板后,设子弹穿过第一块钢板时两者的速度分别为v1和V1:mv1+mV1=mv0(2分)

因为子弹在射穿第一块钢板的动能损失为ΔE损1=f·d=mv(1分),

由能量守恒得:

mvmVmv-ΔE损1(2分)

且考虑到v1必须大于V1

解得:v1v0

设子弹射入第二块钢板并留在其中后两者的共同速度为V2

由动量守恒得:2mV2=mv1(1分)

损失的动能为:ΔE′=mv×2mV (2分) 

联立解得:ΔE′=×mv 

因为ΔE′=f·x(1分),

可解得射入第二钢板的深度x为:(2分)

子弹打木块系统能量损失完全转化为了热量,相互作用力乘以相对位移为产生的热量,以系统为研究对象由能量守恒列式求解

填空题
阅读理解

                         HANS Christian Andersen put Denmark on the map of the world literature with his stories The Emperor's New Clothes, The Little Mermaid (小美人鱼) and The Ugly Duckling.Now Copenhagen, the country's capital, has become the center of the world political map, with 190 world leaders attending the climate talks there, not to mention thousands of reporters.

Just how much do you know about the Scandinavian country?

Denmark is famous for its design culture.At the heart of “Danish Design” is the idea that, as poet and designer Piet Hein puts it: “There is one art, not more, nor less, [and that is] to do all things with artlessness (朴实)”.

Danish design places equal emphasis on practicality and quality.From Lego toys to furniture, Danish products are known for their clean lines, simplicity and functionality.“Remove material where it's not needed.Keep things simple and functional and make them carefully,” explained Hans J.Wegner, the first Danish designer to achieve worldwide fame: “The aim is not to create a work of art, but to produce a good chair.”

“The Danes have done a better job than most in promoting arts in Europe, considering their country's size and population, in the fields of architecture, sculpture and design,” writes Helena Smith, reporter with British newspaper the Guardian.

The simplicity of Danish design may extend to the quality of life there.Some even claim that the Danes have the highest quality of life of any nation in the world.

Kate Vial, a 55-year-old American who has lived and worked in Denmark for more than 30 years, explaining why she chooses to live in Denmark rather than the US, told Germany's biggest news weekly Der Spiegel: “I just chose a simpler lifestyle, one where I could ride my bike all over and where I don't have to make a great living to survive.”

小题1:What’s the writer’s purpose of mentioning Denmark’s literature?

A.To show the readers that Denmark is best known for its stories.

B.To arouse readers’ interest in Denmark.

C.To tell the readers that this passage is related to literature.

D.To show why Denmark can attract so many political leaders.小题2:What is Denmark famous for according to the passage?

A.Design culture

B.Making chairs

C.Writing poems

D.Climate prediction小题3:Which statement is true according to the passage?

A.Danish design pays more attention to arts than its function.

B.Danish products don’t need much material.

C.Danish people like to keep simple life.

D.Compared with other countries in Europe, Denmark does little in promoting arts.小题4:In Piet Hein’s opinion, the characteristic of Danish culture is _____________.

A.Creative

B.Complicated

C.Impractical

D.Simple小题5:What is the best title for the passage?

A.Danes conquer the world with simple designs.

B.Denmark—a new political center.

C.Life in Denmark.

D.Designer’s idea of Denmark.