问题 计算题

在一种新的“子母球”表演中,让同一竖直线上的小球A和小球B,从距水平地面高度为php>1)和h的地方同时由静止释放,如图所示。球A的质量为m,球B的质量为3m。设所有碰撞都是弹性碰撞,重力加速度大小为g,忽略球的直径、空气阻力及碰撞时间。

(1)求球B第一次落地时球A的速度大小;

(2)若球B在第一次上升过程中就能与球A相碰,求p的取值范围;

(3)在(2)情形下,要使球A第一次碰后能到达比其释放点更高的位置,求p应满足的条件。

答案

(1)A球速率 (2)1<p<5   (3)1<p<3

(1)由于两球同时释放,所以球B第一次落地时A球下落的高度为h,设此时A球的速度大小为v0,由可得,

(2)球B第一次落地并与地发生弹性碰撞后做竖直上抛运动。

若球B上升到最大高度h处时刚好与球A发生碰撞,设此时球A自由下落的时间tA,则=h,此时球A自由下落的高度。联立以上两式,可得hA=4h,则ph=hA+h=5h,所以p=5。

若球B在第一次上升过程中就能与球A相碰,则p的取值范围应为1<p<5。

(3)设球B第一次落地并与地发生弹性碰撞后又上升了时间t就与球A相碰,则球A、B在空中碰前的速度大小分别为有,设它们碰后的速度分别为,选竖直向上为正方向,两球发生弹性碰撞,根据动量守恒和能量守恒,

联立解得,

碰撞时,A球自由下落的高度,B球竖直上升的高度

联立解得,即要使球A第一次碰后能到达比其释放点更高的位置

【考点定位】考查自由落体运动、竖直上抛运动、弹性碰撞等考点,意在考查考生的分析综合能力。

选择题
阅读理解

When people want to know about the weather, they usually go to there radios, TVs, newspapers, or to the Internet. However, you can also find many weather signs among wildlife, because of their highly developed senses. Drops in air pressure(压力) produce an effect on small animals in many ways. Mice and deer are good weather indicators. People who spend a lot of time outdoors have observed that, before a storm, field mice come out of their holes and run around, Deer leave high ground and come down from the mountains.

Birds are especially good weather indicators because they also show the effect of a pressure drop in many ways. For example, some birds become irritable(急躁的)and quarrelsome and will fight over a piece of bread. Other birds chirp(叽叽喳喳)and sing just before a storm. It seems they know they won’t get another chance for an hour or two. Birds also seek safe places before a storm, You will sometimes see birds settling in trees or gathering together on a wire close to a building. Pre-storm low pressure makes the are so thin that birds have difficulty flying.

It is unusual to see many birds flying overhead in the summertime, rather than during the periods in the spring or autumn. Watch for other weather signs if you see this. If they fly in the wrong direction, they may be flying ahead of a storm.

By paying closer attention to some important signs in nature, we can become better prepared for any kind of weather.

小题1:The word“indicators”in paragraph I probably means ________.

A.maps

B.services

C.signs

D.stations小题2:There will be a storm if birds __________ .

A.make more noise than usual

B.fly in different directions

C.come down from tall trees

D.share a piece of bread小题3:How can birds sense the coming of a storm?________

A.By feeling a drop in air temperature.

B.By noticing the change of wind directions.

C.By feeling a drop in air pressure.

D.By noticing the movements of other animals.小题4:The best title for the text would be ________         .

A.Signs of a Storm

B.Drops in Air Pressure

C.Animals’Sharp Senses

D.Nature’s Weather Signs