题干

一足够长的固定斜面,最高点为O点,有一长为l=1.00m的木条AB,A端在斜面上,B端伸出斜面外.斜面与木条间的摩擦力足够大,以致木条不会在斜面上滑动,只能绕O点翻转.在木条A端固定一个质量为M=2.00kg的重物(可视为质点),B端悬挂一个质量为m=0.50kg的重物.若要使木条不脱离斜面,在①木条的质量可以忽略不计;②木条质量为m′=0.50kg,且分布均匀两种情况下,OA的长度各需满足什么条件?

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答案(点此获取答案解析)

解:①当木条A端刚离开斜面时,受力情况如图所示.设斜面倾角为θ,

根据力矩平衡条件:Mg•OAcosθ=mg•OBcosθ

考虑OA+OB=l 并代入数据得:OA=0.2m    

同类题4

     What would you do if you found a snake in your house? Many people might be afraid or try to kill it. However, if you live in North Carolina in the USA, one thing you can do is to call the Snake Catchers.
    The Snake Catchers are four men who love snakes, even poisonous ones. Their newspaper advertisement says, “Snake Catchers: free snake removal(除去)一Please do not kill them — Call us. ”
    The Snake Catchers, who started their service in 1998, don't charge anything for helping people. “We do this as a hobby,” explained Fred Johnson, one of the Snake Catchers.
    Because of their love of snakes, the Snake Catchers try to keep them alive. “One man asked us to kill a python(蟒蛇), so he could make a pair of boots from the skin. We refused, because we like snakes, and we don't want to see them killed, ” said Fred.
Some of the snakes that they catch are kept as pets; some are given to the North Carolina State University. Most, including the poisonous snakes, are set free in the wild, usually in a national park.
    Fred suggests that people should treat snakes with care. “Actually snakes are very shy and gentle creatures. They only attack if they are frightened. However, you have to know how to treat a snake properly!”
    According to one happy family, the Snake Catchers are good. One day, the Greenwood family found a snake skin in the kitchen. They looked very carefully and saw a snake sleeping behind a cupboard. They thought about what to do. Then Steve Greenwood remembered the advertisement for the Snake Catchers. He called them.
  “The Snake Catchers arrived within an hour and they finished the job quickly too,” said Steve Greenwood. “One of them went into the kitchen, found the snake and took it out alive. The Snake Catchers did a very good job.”
Last year, the Snake Catchers removed more than seventy snakes from houses in North Carolina.