问题 计算题

如图所示,斜面和水平面由一小段光滑圆弧连接,斜面的倾角为37°,一质量为0.5kg的物块从斜面上距斜面底端B点5m处的A点由静止释放.已知物块与水平面和斜面的动摩擦因数均为0.3。(sin37°=0.6,cos37°=0.8,g=10m/s2

(1)物块在水平面上滑行的时间为多少?

(2)若物块开始静止在水平面上距B点10m 的C点处,用大小为4.5N的水平恒力向右拉该物块,到B点撤去此力,物块第一次到A点时的速度为多大?

(3)若物块开始静止在水平面上距B点10m 的C点处,用大小为4.5N的水平恒力向右拉该物块,欲使物块能到达A点,水平恒力作用的最短距离为多大?

答案

(1)2s ;(2) 6m/s ;(3)  8m

题目分析: (1)物块先沿斜面匀加速下滑,设AB长度为L,动摩擦因数为μ,

下滑的加速度mgsinθ-μmgcosθ=ma

解得:a=gsinθ-μgcosθ=3.6m/s2

到达B点时速度

在水平面上物块做匀减速运动,则有:μmg=ma′

解得:a′=μg=3m/s2

在水平面上运动的时间

(2)设CB距离为,全过程用动能定理,

则有:(F-μmg)-mgLsin37°-μmgLcos37°=

解得:v′=6m/s;

(3)设力作用的最短距离为′,

根据动能定理可得:F′-μmg-mgLsin37°-μmgLcos37°=0

解得:′=8m,

完形填空

阅读下面的短文并用英语回答问题,然后将答案写到答题卡相应的位置上(请注意问题后的字数要求)。

[1] Nowadays the cost of a new car has fallen in real terms so that it is cheaper than ever to own one, and better road conditions have also attracted more drivers. The result is overcrowding on the road system, which is one of the problems the local governments are faced with.

[2] When people travel to other towns, the problem might be relieved by getting them to park outside the town. Buses could be provided to take them into the centre. These Park and Ride projects are increasingly popular in the UK. At Southerton, for example, a council-funded project led to a 15% drop in city centre traffic over five months.

[3] What the council found, though, was that the project proved somewhat unpopular with shop owners in the area outside the centre. Many of their shops relied on passing car drivers for some of their trade. As the number of people driving past dropped, so did their incomes.

[4] Making car driving expensive is another way of ____________. Road taxes tend to mean that people use their cars less. Fining drivers who are in areas where cars have been banned can also tend to encourage them to leave their cars behind.

[5] However, one thing has to be got right for any solution to succeed. If we expect people to give up the habit of driving, we must give them an alternative they can rely on. Constant delays, unannounced changes to the timetable and sudden cancellations all discourage people from using public transport. People will only see it as a real choice if the buses and trains are on time.

小题1:What causes overcrowding on the road system according to Paragraph 1? (no more than 12 words)

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小题2:What should people do when traveling to other towns according to the Park and Ride projects? (no more than 10 words)

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小题3:Why were some shop owners unhappy about the project? (no more than 10 words)

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小题4:Fill in the blank in Paragraph 4. ( no more than 8 words)

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小题5:Why are people unwilling to use public transport according to Paragraph 5? (no more than 8 words)

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读图填空题