问题 计算题

如图所示,质量为 m =10 kg的小球挂在倾角θ=37°的质量为M=40 kg的光滑斜面的固定铁杆上,当斜面和小球以a1=0.5g的加速度向右匀加速运动时,小球对绳的拉力和对斜面的压力分别为多少?当斜面和小球都以的加速度向右匀加速运动时,小球对绳的拉力和对斜面的压力又分别是多少?(取g= 10 m/s2

答案

解:先求出临界状态时的加速度,这时FN =0,小球受力如图甲所示,故有Fsinθ= mg(竖直),Fcosθ= ma0(水平), 所以

当斜面和小球以a1=0.5g向右做匀加速运动时,由于a1< a0,可知这时小球与斜面间有弹力,所以其受力如图乙所示,故有F1cosθ-FNsinθ= ma1(水平),F1sinθ+FNcosθ=mg(竖直),所以F1=100N,FN= 50 N.

 当斜面和小球以向右做匀加速运动时,由于a2>a0, 可知这时小球已脱离斜面,所以其受力如图丙所示,故有F2 sinα=mg(竖直),F2 cosα= ma2(水平),

两式平方相加,可得

所以当小球和斜面以加速度a1运动时,小球对绳的拉力为 100 N,对斜面的压力为50 N;当小球和斜面以加速度a2运动时,小球对绳的拉力为200 N,对斜面的压力为0.

听力题

完成句子

小题1:“They didn’t take measures in time”, the expert said firmly and angrily, “otherwise the explosions ________________.” (happen)

“他们没有及时采取措施,”专家坚定且愤怒地说道,“否则爆炸不会发生。”

小题2:Soon after getting off his horse, the captain appeared at the second storey windows, _______________ nothing but trees. (see)

下马不久,上尉就出现在二楼的窗口了, 从那里除了树木他什么也没看到。

小题3:Rosalyn loves sports. She is proud ________________ competitions and to have broken a record by running 800 meters this year. (participate)

罗莎琳热爱运动。她为今年参加比赛并打破800米赛跑的记录而感到骄傲。

小题4:____________________ should be no reason for treating one’s neighbors as strangers. (occupy)

工作繁忙不应该成为“对面不相识”的借口。

小题5:He went on a bus tour with a group of people, ________________ before. (travel)

他和一群人乘坐巴士旅行,这群人中的大多数以前从没旅行过。

小题6:My son has been away from home for about 2 weeks. I’m looking forward to ___________. (hear)

我儿子离家差不多两周了。我盼望着收到他的来信。

小题7:I think that only in this way ______________ the knowledge and skills needed for my job. (acquire) 我认为只有通过这种方式我才能获得工作所需要的知识与技能。

小题8: _______________ that China produces one third of the world’s cigarettes. (astonish)

令人震惊的是全世界三分之一的香烟是由中国生产的。

小题9:Even though Tony had been so clever, he would have to be rebuilt— you cannot have _________

with machines.(fall)

尽管托尼很聪明,他还得作一番改造——总不能允许女人与机器人相爱吧。

小题10:It’s time for me to quit smoking, for I do hope to live as __________________as my grandfather has. (healthy)

我该戒烟了,因为我真的希望能过着像我的祖父一样长寿健康的生活。

单项选择题