问题 计算题

如图所示,一小球从倾角θ为37º的足够长的斜面顶端作平抛运动,初速度为8m/s,A点是小球离斜面最远点。(1)求小球从抛出到再次落到斜面上的时间?(2)求A点离斜面的距离?(3)将A点前后足够小的一段轨迹视为圆弧,求这段圆弧的半径(曲率半径)及小球在A点的向心加速度(法向加速度)与切向加速度?(第三问仅实验班的同学做,不计入总分)

答案

解决平抛运动的方法是把平抛运动分解到水平方向和竖直方向去研究,水平方向做匀速直线运动,竖直方向做自由落体运动,两个方向上运动的时间相同.

(1)设距离为L,则:水平方向:Lcosθ=V0t   竖直方向:Lsinθ=gt2

联立解得:t=1.2s

(2)将小球的运动分解为沿斜面和垂直于斜面两个分运动,当垂直斜面方向速度降为零时,小球的速度方向一斜面平行,此时小球与斜面的距离达最大

(3)由题目的介绍可知,求曲率半径也就是求在该点做圆周运动的半径,利用向心力的公式就可以求得.

在A点,把物体的运动看成圆周运动的一部分,物体的重力分力作为向心力,

由向心力的公式得,所以在其轨迹A处的曲率半径是r=12.5m

向心加速度,切向加速度

点评:本题就是对平抛运动规律的直接应用.

单项选择题
单项选择题

Caesar was right. Thin people need watching. I’’ve been watching them for most of my adult life, and I don’’t like what I see. When these narrow fellows spring at me, I quiver to my toes. Thin people come in all personalities, most of them menacing. You’’ve got your "together" in person, your mechanical thin person, your condescending thin purism, your tsk-tsk thin person, your efficiency-expert thin person. All of them are dangerous.In the first place, thin people aren’’t fun. They don’’t know how to goof off, at least in the best, fat sense of the word. They’’ve always got to be adoing. Give them a coffee break, and they’’ll jog around the block. Supple them with a quiet evening at home, and they’’ll fix the screen door and lick S & H green stamps. They say things like "there aren’’t enough hours in the day". Fat people never say that. Fat people think the day is too damn long already.Thin people make me tired. They’’ve got speedy little metabolisms that cause them to bustle briskly. They’’re forever rubbing their bony hands together and eyeing new problems to "tackle". I like to surround myself with sluggish, inert, easygoing fat people, the kind who believe that if you clean it up today, it’’ll just get dirty again tomorrow.Some people say the business about the jolly fat person is a myth, that all of us chubbies are neurotic, sick, sad people. I disagree. Fat people may not be chortling all day long, but they’’re a hell of a lot nicer than the wizened and shriveled. Thin people turn surly, mean, and hard at a young age because they never learn the value of a hot-fudge sundae for easing tension. Thin people don’’t like gooey soft things because they themselves are neither gooey nor soft. They are crunchy and dull, like carrots. They go straight to the heart of the matter while fat people let things stay all blurry and hazy and vague, the way things actually are. Thin people want to face the truth. Fat people know there is no truth. One of my thin friends is always staring at complex, unsolvable problems and saying, "The key thing is fat people never say that." They know there isn’’t any such thing as the key thing about anything.

When it comes to looking at things, fat people and thin people never come to terms with each other because________.

A.in nature thin people have less sensational inclination than most fat people who are always at the mercy of fat

B.in essence thin people are less emotional and touchy than fat people who are too impulsive

C.in nature thin people look at things in rose-colored spectacles whereas fat people always take a dim view of the objects

D.In essence thin people are too quick on the trigger whereas fat people are slow at picking up subtle things