问题 计算题

(18分)如图(甲)示,光滑曲面MP与光滑水平面PN平滑连接,N端紧靠速度恒定的传送装置,PN与它上表面在同一水平面.小球A在MP上某点静止释放,与静置于PN上的工件B碰撞后,B在传送带上运动的v-t图象如图(乙)且t0已知,最后落在地面上的E点.已知重力加速度为g,传送装置上表面距地面高度为H.

(1)求B与传送带之间的动摩擦因数μ;

(2)求E点离传送装置右端的水平距离L;

(3)若A、B发生的是弹性碰撞且B的质量是A的2倍,要使B始终落在E点,试判断A静止释放点离PN的高度h的取值范围.

答案

见题目分析

题目分析:

(1)由v-t图象知,在t0时间内,B的加速度大小①(1分)

B所受滑动摩擦力大小  f="2" μmg            ②(1分)

又由牛顿第二定律可知B所受合力大小    f=2ma ③(1分)

解得 :    ④(1分)

(2)由v-t图象知,小球在传送带上最后的运动阶段为匀速运动,即与传送装置已达到共同速度,它从传送装置抛出的速度vB1=, 由平抛物体运动规律:

  ⑤(1分)

 ⑥(1分)

由①②,代入vB1=,得:    ⑦(1分)

(3)若使B始终落到地面上E点,也必须是以相同速度离开传送装置;设B离开传送带时的速度为,即有 ⑧(1分)

由图象可求出B在传送带上运动时的对地位移始终为⑨(1分)

设A的质量为m,碰前速度为v,碰后速度vA;B质量为2m,碰后速度vB.

A下滑过程机械能守恒(或动能定理)  mgh=      ⑩(1分)

A、B碰撞过程,由A、B系统动量守恒   mv = mvA+2mvB ⑪(1分)

A、B系统机械能守恒           ⑫(1分)

联立⑩⑪⑫可解得⑬(1分)

B始终能落到地面上E点,有以下两类情形:

ⅰ.若,B进入传送带上开始匀减速运动,设B减速到经过位移为S1,有

 ⑭(1分),则应满足

联立①⑧⑨⑬⑭式,可得 ⑮(1分)

ⅱ.若,B以速度vB进入传送带上匀加速至,设此过程B对地位移为S2,有

 ⑯ (1分),且恒有

联立①⑧⑯式,得 ⑰(1分),即恒成立,

综上所述,要使工件B都落在地面的E点,小球A释放点高度h必须满足条件:

⑱(1分)

【评分说明:①②③④⑤⑥⑦⑧⑨⑩⑪⑫⑬⑭⑮⑯⑰⑱各1分,共18分。】

单项选择题
阅读理解

The devastation caused by Hurricane Katrina is a wake-up call. It is a call for every American to pay attention to the destruction we risk by allowing human-induced(导致的) climate change to continue. It is impossible to prove that Hurricane Katrina was caused by global warming, or even that human activities made the storm more severe. However, a paper published in the scholarly journal Nature reports that the force of dangerous hurricanes has increased by 50% during the last 50 years. It also reports that a global warming-induced rise in temperature near the ocean’s surface has probably contributed to this increase in dangerous storms, and thus to property(财产) damage and human death.

On August 30, the Los Angeles Times summed up(总结) the view of many scientists who agree that if the frequency of hurricanes does not decrease in the next few years, then we will be fairly certain that humans, and not natural storm cycle, are at the root of the problem. I believe there is at least a chance that by reducing U.S. reliance on fossil fuels for energy, we can prevent future tragedies like Hurricane Katrina. Let the change begin now.

There are many ways to reduce the volume of greenhouse gas emissions. My family drives the most fuel-efficient car we can afford, but I prefer to take public transportation whenever possible. My family buys locally grown food instead of produce that was transported thousands of miles on fuel-burning vehicles. We also replaced our incandescent light bulbs(白炽灯泡)with more energy-efficient compact fluorescents(荧光灯). This might sound like a trivial move, but the Union of Concerned Scientists reports that if every household in the United States replaced one incandescent bulb with a compact fluorescent, it would have the same effect on U.S. carbon-dioxide emissions as removing 7.5 million cars from the roads. Now think if every household replaced not just one but all of their incandescent bulbs!

The United States, with just five percent of the world’s population, is responsible for close to one quarter of greenhouse gas emissions worldwide, yet our country is doing far less than most European nations to fight global warming. We don’t have to sacrifice our lifestyles; Europeans enjoy the same standards of living as Americans. So what are we waiting for? It is time to act.

小题1: Which of the following is a fact?

A.Hurricane Katrina was caused by global warming.

B.Human activities made the storm more severe.

C.The force of dangerous hurricanes has increased by 50 percent during the last 50 years.

D.A global rise in temperature near the ocean’s surface accounts for more dangerous storms.小题2:From Paragraph 2 we can infer that many scientists agree ________.

A.it might be human activities that lead to global warming.

B.natural storm cycles have caused global warming.

C.hurricanes are likely to come more frequently.

D.burning fossil fuels for energy is a better alternative.小题3: If every household in the U.S. replaced all their incandescent bulbs, ________.

A.it would have the same effect as removing 7.5 million cars from the roads.

B.it would save 7.5 million tons of carbon-dioxide from going into the air.

C.this would reduce the total output of CO₂emissions in huge amounts.

D.cars will be much more environmentally friendly.小题4: According to the writer,_______in reducing the volume of greenhouse gas emissions.

A.Europe does a better job.

B.Europe should follow the example of America.

C.he, as an European, wants to see more efforts made by Americans.

D.Europeans should shoulder a greater responsibility.