问题 计算题

“和平号”空间站已于2001年3月23日成功地坠落在南太平洋海域,坠落过程可简化为从一个近圆轨道(可近似看做圆轨道)开始,经过与大气摩擦,空间站的大部分经过升温、熔化、最后汽化而销毁,剩下的残片坠入大海。此过程中,空间站原来的机械能中除一部分用于销毁和一部分被残片带走外,还有一部分能量E'通过其他方式散失(不考虑坠落过程中化学反应的能量)。

(1)试导出用下列各物理量的符号表示散失能量E'的公式;

(2)算出E'的数值(结果保留两位有效数字)。

坠落开始时空间站的质量为M=1.17×105 kg;

轨道离地面的高度为h=146km;

地球半径为R=6.4×106m;

坠落空间范围内重力加速度可看做g=10m/s2

入海残片的质量m=1.2×104kg;

入海残片的温度升高了△T=3 000K;

入海残片的入海速度为声速v=340m/s;

空间站材料每1kg升温1K平均所需能量c=1.0×103J;

每销毁1kg材料平均所需能量μ=1.0×107J。

答案

解:(1)根据题目所给条件,从近圆轨道到地面的空间中重力加速度g=10m/s2。若以地面为零势能面,坠落过程开始时空间站在近圆轨道的势能为Ep=Mgh ①

以v0表示空间站在近圆轨道上的速度,根据引力提供向心力,由牛顿运动定律得

由②式可得空间站在近圆轨道上的动能为

由①、③得在近圆轨道上空间站的机械能

在坠落过程中,用于销毁所需的能量为Q=(M-m)/μ ⑤

用于残片升温所需的能量为Q=cm△T ⑥

残片入海时的动能为E=

以E'表示其他方式散失的能量,则由能量守恒得E=Q+E+Q+E' ⑧

将④⑤⑥⑦式代入⑧式整理得

(2)将题目所给的数据代入⑨式可解得E'=2.9×1012J

单项选择题
阅读理解

A Brown University sleep researcher has some advice for people who run high schools: Don’t start classes so early in the morning. It may not be that the students who nod off at their desks are lazy. And it may not be that their parents have failed to enforce (确保) bedtime. Instead, it may be that biologically these sleepyhead students aren’t used to the early hour.

“Maybe these kids are being asked to rise at the wrong time for their bodies,” says Mary Carskadon, a professor looking at problem of adolescent  (青春期的) sleep at Brown’s School of Medicine.

Carskadon is trying to understand more about the effects of early school time in adolescents. And, at a more basic level. she and her team are trying to learn more about how the biological changes of adolescence affect sleep needs and patterns.

Carskadon says her work suggests that adolescents may need more sleep than they did at childhood, no less, as commonly thought.

Sleep patterns change during adolescence, as any parent of an adolescent can prove. Most adolescents prefer to stay up later at nigh and sleep later in the morning. But it’s not just a matter of choice –their bodies are going through a change of sleep patters.

All of this makes the transfer from middle school to high school—which may start one hour earlier in the morning  ---- all the more difficult , Carskadon says. With their increased need for sleep and their biological clocks set on the “sleep late, rise late” pattern, adolescent are up against difficulties when it conics to trying to be up by 5 or 6 a.m. for a 7:30 a.m. first hell. A short sleep on a desktop may be their body’s way of saying. “I need a timeout.”

小题1:Carskadon suggests that high schools should not start classes so early in the morning because ________.

A.it is really tough for parents to enforce bedtime

B.it is biologically difficult for students to rise early

C.students work so late at night that they can’t get up early

D.students are so lazy that they don’t like to go to school early小题2:The underlined phrase “nod off” most probably means “ _______”.

A.turn around

B.agree with others

C.fall asleep

D.refuse to work小题3:What might be a reason for the hard transfer from middle school to high school?

A.Adolescents depend more on their parents.

B.Adolescents have to choose their sleep patterns.

C.Adolescents sleep better than they did at childhood.

D.Adolescents need more sleep than they used to.小题4:What is the test mainly about?

A.Adolescent heath care.

B.Problems in adolescent learning.

C.Adolescent sleep difficulties.

D.Changes in adolescent sleep needs and patterns.