问题 计算题

图中有一个竖直固定在地面的透气圆筒,筒中有一劲度为k的轻弹簧,其下端固定,上端连接一质量为m的薄滑块,圆筒内壁涂有一层新型智能材料——ER流体,它对滑块的阻力可调。起初,滑块静止,ER流体对其阻力为0,弹簧的长度为L,现有一质量也为m的物体从距地面2L处自由落下,与滑块碰撞后粘在一起向下运动。为保证滑块做匀减速运动,且下移距离为时速度减为0,ER流体对滑块的阻力须随滑块下移而变。试求(忽略空气阻力):

(1)下落物体与滑块碰撞过程中系统损失的机械能;

(2)滑块向下运动过程中加速度的大小;

(3)滑块下移距离d时ER流体对滑块阻力的大小。

答案

解:(1)设物体下落末速度为v0,由机械能守恒定律

,得

设碰后共同速度为v1,由动量守恒定律

2mv1=mv0,得

碰撞过程中系统损失的机械能

(2)设加速度大小为a,有

(3)设弹簧弹力为FN,ER流体对滑块的阻力为FER,受力分析如图所示

 

FS=kx

x=d+mg/k

选择题
阅读理解

  For years scientists have been worried about the effects of air pollution on the earth’s natural conditions. Some believe the air inside many houses may be more dangerous than the air outside. It may be one hundred times worse.

  Indoor air pollution can cause a person to feel tired, to suffer eye-pain, headache and other problems. Some pollutants(污染物) can cause breathing disorders, diseases of blood and even cancer, Most scientists agree that every modern house has some kind of indoor pollution. People began to notice the problem in the early 1970s. It is that when builders began making houses and offices they did not waste energy. To do this they built buildings that limited the flow of air between inside and outside. They also began using manmade building materials. These materials are now known to let out harmful gases. As the problem became more serious, scientists began searching for a way to deal with it. They discovered a natural pollution control system for building— green plants. Scientists do not really know how plants control air pollution. They believe that a plant’s leaves absorb or take in the pollutants. In exchange the plant lets out oxygen through its leaves and through its tiny organizations on its roots. Scientists suggest that all buildings should have one large plant or several small plants inside for every nine square metres of space. Studies of different plants show that each absorbs different chemicals. So the most effective way to clean the air is to use different kinds of plants. Having green plants inside your house can make it a prettier and more healthy place.

  小题1:Generally speaking, indoor air pollution may be more harmful than the air outside because ________.

A.the man - made building materials let out dangerous gases inside houses

B.there may be more harmful gases outside houses

C.the flow of air indoors is limited

D.indoor air pollution can make a person seriously ill  小题2:The most effective way to clean the air is to use different kinds of plants because________.

A.they may let out more oxygen which people need

B.they can absorb different kinds of the harmful indoor chemicals

C.they can take in all kinds of indoor pollutants

D.they can make your house prettier and more healthy