问题 选择题

欧盟和我国合作的“伽利略”全球定位系统的空间部分由平均分布在三个轨道面上的30颗轨道卫星组成,每个轨道平面上等间距部署10颗卫星,从而实现高精度的导航定位.现假设“伽利略”系统中每颗卫星均绕地心 O做匀速圆周运动,轨道半径为r,一个轨道平面上某时刻10颗卫星所在位置分布如图所示.其中卫星1和卫星3分别位于轨道上的A、B两位置.若卫星均顺时针运行,地球表面处的重力加速度为g,地球半径为R,不计卫星间的相互作用力.则以下判断中正确的是(  )

A.这10颗卫星的加速度大小相等,均为

R2g
r

B.这10颗卫星的运行速度大小为2R

g
r

C.这10颗卫星的运行速度一定大于7.9km/s

D.卫星A由位置运动到位置B所需的时间为

2πr
5R
r
g

答案

A、根据万有引力提供向心力G

Mm
r2
=ma和黄金代换式GM=gR2

可得a=

R2g
r2
.故A错误.

B、根据万有引力提供向心力G

Mm
r2
=m
v2
r
和黄金代换式GM=gR2

可得这10颗卫星的运行速度大小为R

g
r
,故B错误

C、7.9km/s是第一宇宙速度,是发射卫星的最小速度,是卫星绕地球运动的最大速度,故这些卫星的运行速度均小于7.9km/s,故C错误

D、根据万有引力提供向心力G

Mm
r2
=mrω 2,ω=
GM
r3
,GM=gR2

所以A由位置运动到位置B所需的时间t=

2πr
5R
r
g
,故D正确

故选D.

阅读理解

阅读理解

       Moreno, Stanley, and 23 other st udent s f rom Westf ield State College were on vacation in

Acapulco, Mexico. This was the last night in the hotel. It was 4 am, Moreno and Stanley came back

from a party.

       Just as Stanley went to sleep, he heard loud noise outside. From the balcony (阳台) of their

fourth-floor room,  Moreno and Stanley saw black smoke out of one window and heard people

shouting.

       Moreno ran out into the corridor and began knocking on doors and shouting, "Fire!" After that,

he went upstairs in a hurry to tell other people.  At the same time,  Stanley was downstairs helping

people get through the smoke-filled room. There he joined forces with Nalewanski, a 21-year-old

boy who had a room on the second floor.

       "Let's go," Nalewanski said. He and Stanley wet their shirts in the bathroom and put them around

their mouths and noses so they could breathe.  Then they ran up the stairs. On the fourth floor they

found Moreno feeling terrible (Moreno had made it up to the eighth floor before turning back). But

after making sure he could get back down on his own, they continued upstairs, knocking on the doors

on every floor.

       In the end, no one was seriously hurt. Moreno said, "There were hundreds of people in the hotel.

It was our duty to help them."

1. students from Westfield State College were on       vacation in Acapulco, Mexico.

A. Twenty-three          

B. Twenty-four

C. Twenty-five            

D. Twenty-six

2. Which floor does Stanley live on?

A. The second floor.        

B. The fourth floor.

C. The seventh floor.        

D. The eighth floor.

3. Nalewanski and Stanley put their wet shirts around their mouths and noses in order to     .

A. make them cool

B. stop the smoke from going into lungs ( 肺)

C. let people find them

D. play a joke with other people

4. What is the correct order?

a. Moreno told other people.

b. No one was seriously hurt.

c. Nalewanski joined them to save people.

d. Stanley and Moreno saw the smoke.

A. d-b-c- a              

B. d-a-c-b

C. a-d-c-b                

D. c-d-b-a

5. From the fourth paragraph, we can know     .

A. the three boys are brave

B. Moreno died in the fire

C. the reason of the fire

D. Nalewanski called the police for help

单项选择题