问题 计算题

(10分)如图甲所示为一皮带传送装置,皮带保持匀速率运动,货物由静止放到皮带顶端,被皮带向下传送,其运动的v—t图象如图乙所示,g=10m/s2

求:(1)皮带的速率;(2)皮带与水平面间的夹角(及货物与皮带之间的动摩擦因数);(3)如果货物是用麻袋装载的石灰粉,当第一件货物被运送后,发现皮带上留有一段8.0m长的白色痕迹,请由此推断每件货物的传送时间和传送距离。

答案

⑴ 6.0m/s  ⑵ 30°  ⑶ 3s  23m

题目分析:(1)货物先加速,当货物的速度与传送带速度相等时,由于货物重力的下滑分力大于滑动摩擦力,继续加速,但加速度减小,皮带的速度为6.0 m/s,方向沿斜面向下.

(2)由货物运动的v-t图象得:a1=="6.0" m/s2,a2=="4.0" m/s2

在0~1.0 s:皮带对物体的滑动摩擦力沿斜面向下,

由牛顿第二定律得:mg•simθ+μmg•cosθ=ma1

在1.0 s~2.0 s:皮带对物体的滑动摩擦力沿斜面向上,

由牛顿第二定律得:mg•sinθ-μmg•cosθ=ma2

联立得:θ=30°,μ=

(3)由v-t图象知货物在1.0时间内加速到与皮带相同的速度6.0 m/s,皮带发生的位移s=v1t="6.0" m,货物发生的位移s=="3.0" m,此时间内皮带上痕迹的长度:△s=s-s="3.0" m<l="8.0" m.

此后货物速度超过皮带速度,物体向底端运动过程中发生的位移比皮带多8.0 m(其中有3.0 m为痕迹重叠区域).设从1.0秒末开始,货物的传送到底端的时间为t1、货物到底端的距离为S,则:

对皮带S-8=v1t1,对货物S=v1t1+a2t12,联立以上两式得:t1=2s  s=20m

故每件货物的传送时间:T=t1+t=(1+2)s=3s

传送距离:L=s+S=23m.

阅读理解

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Is there anything more important than health? I don’t think so.“Health is the greatest wealth,” wise people say. __小题1:___

If you have a headache, toothache, backache, or bad pain in the stomach, if you complain of a bad cough, or if you suffer from high or low blood pressure, I think you go to the doctor.

The doctor will examine your throat, test your blood pressure, take your temperature, sound your heart and lungs, check your teeth or have your chest X-rayed. __小题2:___The only thing you have to do is to follow his advice.

__小题3:___

An old gentleman came to see the doctor.The man was very ill.He told the doctor about his weakness, memory loss and serious problems with his heart and lungs.The doctor examined him and said there was no medicine for his disease.He told his patient to go to a quiet place for a month and have a good rest.__小题4:__In other words, the doctor advised him to follow the rule: “Eat at pleasure, drink with measure and enjoy life as it is.” The doctor also said that if the man wanted to be well again, he shouldn’t smoke more than one cigarette a day.

A month later the gentleman came into the doctor’s office.__小题5:__He thanked the doctor and said that he had never felt a healthier man.

“But you know, doctor,” he said, “it’s not easy to begin smoking at my age”

A.He also advised him to eat a lot of meat, drink two glasses of red wine every day and take long walks.

B.You can’t be good at your studies or work well when you are ill.

C.After that he will advise some treatment or some medicine.

D.All these will cost a lot of money. E.He looked cheerful and happy.

F.He was more worried about his illness.

G.Speaking about doctor’s advice, I can’t help telling you a funny story.

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