问题 计算题

(18分)如图所示,质量为的滑块(可视为质点)自光滑圆弧形槽的顶端A处无初速度的滑下。槽的底端与水平传送带相切于左传导轮顶端的B点,A、B的高度差为.传导轮半径很小,两个轮之间的距离为,滑块与传送带间的动摩擦因数.右端的轮子上沿距离地面的高度为.()

(1)若槽的底端没有放滑块,传送带静止不转,滑块滑过C点时的速度大小

(2)若下滑前将质量为的滑块(可视为质点)停放在槽的底端。下滑后与发生弹性碰撞,且碰撞后速度方向不变,则应该满足什么条件?

(3)若在(2)的前提条件下,若传送带顺时针运转,且速度为m/s。求滑块落地点间的最大距离

答案

 (1) (2)   (3)

题目分析:(1)滑块由A点滑至B点过程,由机械能守恒定律: 

解得:       (2分)

滑块由B点滑至C点过程,由动能定理:  (2分)

解得:         (1分)

或全过程研究: (4分), 解得:(1分)]

(2)滑块停放在槽的底端,滑块下滑后与发生弹性碰撞,

由动量守恒定律:         (2分)

由能量守恒定律:         (2分)

解得: 、 (此结果可以不解,解错扣1分))

据题意,碰撞后的速度方向不变,即,则:         (2分)

(3) 仅当时,滑块碰撞后的速度相差最大,经过传送带后速度相差也最大,两滑块的落点有最大距离。       (1分)

           (1分)

          (1分)

滑块经过传送带后做平抛运动,,解得:t=0.6s。      (1分)

由于滑块与传送带速度相同,不受摩擦力,水平射程: 

滑块与传送带间有摩擦力作用,由动能定理:  (1分)

解得:       (1分)

水平射程:   

滑块落地点间的最大距离:  (1分)

阅读理解

Chinese White Collars(白领) Go Down on the Farm

The latest craze among China’s white collar workers, reported in the British newspaper the Daily Telegraph, is an online virtual agricultural game called “Happy Farm.” Virtual farmers can visit each other’s farm, trade livestock and can use real cash to buy virtual (虚拟的) items such as special tools, quality seeds, and animals. The free game is played through social networking sites like kaixin001.com, Face book or xiaonei.com.

Urban office workers can escape the pressures and stresses of everyday life and enter a peaceful virtual existence where players can grow vegetables, practice animal farming and receive satisfaction that comes with a hard-won harvest. Because most Chinese white collars have little amusement after work, Happy Farm gives them a virtual world to make their dreams come true.

Global Times, an English language daily based in Beijing, recently reported that there are more than 15 million Chinese urbanites spending more than five hours a day on their virtual “farms.”

According to the English language website of the People’s Daily newspaper, the increased interest in farming among some urban office workers has resulted in some of them becoming real hobby farmers, tending small plots of land in their free time. Mr. Liu, a white collar worker, has rented a piece of farmland for RMB 3000. Mr. Liu and his family like to drive down to their farm on the weekend and do different farming tasks such as watering, weeding, fertilizing and worming. Later on, cabins will be built on agricultural land making it possible for part-time farmers like Mr. Liu to stay on their land for two weeks enabling them to get a little taste of a farmer’s life.

It is a rather interesting social development that some of urban office workers are becoming interested in farming and agriculture, while large numbers of farmers and agricultural workers continue to move to the cities.

小题1:What is “Happy Farm”? (No more than 7 words)

小题2:Why do more and more Chinese white collars go down on Happy Farm?

(No more than 14 words)

小题3:List 4 farming tasks Mr. Liu and his family do on their farms. (No more than 5 words)

小题4:How long do Chinese urbanites spend on their virtual farms every day? (No more than 4 words)

单项选择题