题干

有一只小虫重为G,不慎跌入一个碗中,如图所示.碗内壁为一半径为R的球壳的一部分,其深度为D.碗与小虫脚间的动摩擦因数为μ,若小虫可以缓慢顺利地爬出碗口而不会滑入碗底.试问D的最大值为多少?(最大静摩擦力大小等于滑动摩擦力大小)

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对小虫受力分析,受到重力、支持力和静摩擦力,到碗口时,最容易滑下,此时静摩擦力最大,等于滑动摩擦力,如图根据平衡条件,有F=mgsinθ ①N=mgcosθ ②其中F=μN ③cosθ= ④由①②③④解得:

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    California has become the first U.S. state to approve plans to require newly-built homes to include solar equipment.

    The state's Energy Commission voted 5-0 to approve the new rules, which are to take effect in 2020. The rules will deal with most newly-built residential (住宅的) buildings up to three stories high.

    The move is California's latest step aimed at reaching renewable energy targets and reducing greenhouse gas emissions.

    California has set a goal of filling half of its electricity needs with renewable energy by 2030. Officials said they had reached 30 percent by the end of 2017. The state's Governor, Jerry Brown, plans to hold an international climate meeting in September.

    ①The Energy Commission said the cost of adding solar equipment to a single-family home would be about $9,500. But, the group added that homeowners would save at least $19,000 in energy costs over 30 years.

    Robert Raymer is the technical director for the California Building Industry Association. He says the action is a step forward for the wider use of solar power in the U.S. "You can bet every other of the 49 states will be watching closely to see what happens," he told the Associated Press.

    ②Solar companies praised the new requirements, which officials have said will likely raise demand for solar equipment in California by 10-15 percent.

    The Solar Energy Industries Association called it a "historic decision for the state and the U.S." It estimated the action would produce "huge economic and environmental benefits," including bringing tens of billions of dollars into California.

    ③Some legislative and community leaders argued that Californians cannot afford to pay any more for housing in what is already an extremely high-priced market.

    "That's just going to drive the cost up and make California, once again, not affordable to live in," said California Assemblyman Brian Dahle.

    ④Severin Borenstein is an energy economist at the University of California, in Berkeley. He sent an email to the head of California's Energy Commission to urge the state to reconsider its decision.

    He expressed his belief that it is a mistake for California to approve such a policy instead of centering on efforts to develop large solar farms to produce renewable energy. He said these farms would cost much less to operate.

    "Every energy economist I know is shaking their head at this," he told the Wall Street Journal. "In many ways, this is setting the wrong example," he added.