问题 问答题

.如图6-2-21,细绳上端固定于O点,下端系一质量m="1" kg的小球P,且小球P处于静止状态.小球P与平台的B点接触,但对平台无压力,绳长L="0.5" m,平台高h="0.8" m.另有一质量M="2" kg的小球Q沿平台自左向右运动到B处与P球发生正碰,碰后P球在绳的约束下做圆周运动且恰好能过最高点,而Q球落在水平地面上的C点,DC间的距离s="2.4" m,不计空气阻力,取g="10" m/s2,求:

图6-2-21

(1)Q球与P球碰前速度v0的大小;

(2)系统在两球发生碰撞过程中损失的机械能.

答案

(1)v0="8.5" m/s (2)23.75 J

(1)设QP碰后,P的速度为v1,Q球速度为v2g取10 m/s2

P做圆周运动,且恰好过最高点和机械能守恒,选P作零势能面

mg =mvA2/L 

代入数据得v1="5" m/s

QBC做平抛运动,由平抛运动的规律得v2t=s gt2/2=h

代入数据得v2="6" m/s

取向右为正方向,由动量守恒定律得

Mv0=mv1 +Mv2

代入数据得v0="8.5" m/s.

(2)由能量守恒定律得

Mv02/2 =mv12/2 + Mv22/2 +E

代入数据得E="23.75" J.

单项选择题 案例分析题
阅读理解

What science fiction once told of other worlds far away, is now a fact. Astronomers prove the existence of another solar system like ours with some planets in the constellation Andromeda(仙女座) .
Geoffrey Marcy is a professor of astronomy and physics at San Francisco State University and says, “What we have found now, for the first time ever, is indeed a fully-grown system of planets around the star Upsilon Andromeda, in which there are three planets, one close in, one at a middle distance, and one farther out.” The star is slightly larger than our sun. The planets are huge, like our Jupiter (木星)
Marcy’s partner in this research, Debra Fischer, describes the solar system, “Here’s the inner planet that goes around every 46 days, the middle planet that goes around every 242 days, and then the outer planet that goes around every three and a half to four years.”
Astronomically, it’s not far away, 44 light years. The sun of that solar system, Upsilon Andromeda, is so near and bright that it can be seen by using no equipment during summer and fall.
For twelve years astronomers searched the skies in the belief that if our sun has planets around it, surely others do, too. Geoffery Marcy says, “And then starting three and a half years ago, we began finding for the first time planets singly, one planet here around one star.”
“When I look up at the stars now at night, I can imagine easily that every one of them has planets around them,” says Debra Fischer.
It was the tremble in the star that led Marcy to discover the planets. “The star rocks around due to the gravity of the planet much like a dog owner gets pulled around by a little dog.”
Can they support life? We don’t know, because present technology is not advanced enough to determine what the planets are made of. That, Marcy says, is astronomy’s next challenge.
75. Which of the following can best show the relationship between Andromeda (A), Upsilon Andromeda system (U) and the three mentioned planets (P) ?
 
A                       B                     C                   D
76. What led to Marcy’s discovery of the planets?
A. That he found a dog owner was pulled by his dog.
B. The tremble of Upsilon Andromeda
C. That any planet has gravity
D. That he believes any star has its planets
77. We can infer from the text that scientists are _______________
A. to find out whether the planets can support life
B. to find means to communicate with the living beings on the planets
C. to find means to travel to the planets
D. soon to be able to find another planet for life to live on