问题 计算题

(10分)刀、斧、凿、刨等切削工具的刃都叫做劈,劈的截面是一个等腰三角形,如图所示,使用劈的时候,在劈背上加力F,这个力产生的作用效果是使劈的两侧面推压物体,把物体劈开.设劈的纵截面是一个等腰三角形,劈背的宽度是d,劈的侧面的长度是L.通过计算说明为什么劈的两个侧面之间的夹角越小(即越锋利的切削工具)越容易劈开物体。

答案

见答案

题目分析:根据力F产生的作用效果,可以把力F分解为两个垂直于侧面的力

如图所示,

由对称性可知,=.根据力三角形△OF与几何三角形△ACB相似可得= 

所以==F 由于F1=F2=

F1=F2=F.

所以两个侧面之间的夹角越小(即越锋利的切削工具)越容易劈开物体。

点评:本题考查了力的分解,根据题意利用角度小的正切值等于正弦值,将本题化简得出比较容易接受的表达式。

阅读理解
Peter,Helen,Catherine,Elizabeth和Levin想根据各自在环保方面的兴趣进行案例研究。阅读下面某杂志的专题报道摘要(A、B、C、D、E和F),选出适合他们研究的最佳案例,并在答题纸上将相应选项的标号涂黑。选项中有一项是多余选项。
_____小题1:Peter: Reducing plastic and other wastes through DIY
_____小题2:Helen: Making use of the heavy traffic to produce electricity
_____小题3:Catherine: Building a community without private cars
_____小题4:Elizabeth: Building houses with recycled materials and energy-efficiency systems
_____小题5:Levin: Developing a new type of urban car which burns less gas
     A
    B
Vauban
We know cars are terrible polluters, but would you give yours up? Vauban, a community in southwestern Germany, did just that, and its 5,000 citizens are doing fine. Most streets are free of vehicles, and there are generous green spaces and good public-transport links, including fast buses and bicycle paths.  When people must drive, they can turn to car-sharing clubs.  “All the citizens had the chance to plan their own city,” says Andreas Delleke, an energy expert, “and it's just how we wanted it to be.”
Denmark
During the period of gas shortage in the early 70s, Denmark decided to become self-sufficient ( 自足). So they began a few projects making smart investments along the way.
On the island of Samsoe, local families, fishermen and farmers bought wind turbines (涡轮机) to produce their own energy. Within seven years these turbines were completely paid for. And can you believe just one of wind turbines produces enough electricity for 600 households?
     C
     D
Trey Parker and Matt Stone
Trey Parker and Matt Stone, creators of South Park, have built a sustainable castle with outer siding and inner flooring of recycled wood, recycled carpeting, high-efficiency boiler systems.
“I think more and more today, people are willing to make a statement about the Earth and how they want to protect it,” Michael Rath, home designer and builder says. "For high-end homes in this valley, this is entirely consistent with what they cost."
P-NUT
Who doesn't love the name P-NUT—short for Personal-Neo Urban Transport? It's Honda's latest attempt to create a tiny footprint for a new urban vehicle.
This little P-NUT is unique. With a central driving position, the car is designed to move in tight settings. The  11-foot micro car will seat three with two rear-seat passengers behind the driver.
“The P-NUT concept explores the packaging and design potential for a vehicle designed for the city lifestyle,” said  Dave Marek, a Honda design Spokesman.
E
F
Israel Company
Is it possible that annoying rush hour traffic could become a source of renewable energy?
Israel's Technion Institute of Technology claims that if we placed special generators ( 发电机 ) under roads, railways, and runways—we could harvest enough energy to mass-produce electricity. A trial process has been used on a smaller scale, in dance clubs for instance, where the pounding feet of dancers light up the floor.
"We can produce electricity anywhere there is a busy road using energy that normally goes to waste," said Uri Amit, chairman of Israel's Technion Institute  of Technology.
Coffee
Coffee. Some of us can't start our day without it, and we don't mind waiting 10 minutes in line for it.
Here is the most effective tip to make you a superstar in environment protection.
Get a coffee machine for your home or office, or persuade your company into buying one.  (Tell them it will improve productivity. ) Skip the coffee line on the way to work and make something that is better-tasting and much better for your wallet.
Plus, you won't need those plastic cups or carrying cases that just get thrown away. Better yet, use your favorite travel mug.
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