问题 问答题

如图所示,一质量M=2.0kg的长木板静止放在光滑水平面上,在木板的右端放一质量m=1.0kg可看作质点的小物块,小物块与木板间的动摩擦因数为μ=0.2.用恒力F=10N向右拉动木板使木板在水平面上做匀加速直线运动,经过t=1.0s后撤去该恒力,此时小物块恰好运动到距木板右端l=1.0m处.在此后的运动中小物块没有从木板上掉下来.(g=10m/s2)求:

(1)恒力撤去前,小物块和长木板的加速度各多大,方向如何?

(2)刚撤去F时,小物块和长木板的速度各多大?

(3)长木板的长度至少是多少?

答案

(1)对木块,只受摩擦力作用,µmg=ma1     a1=2m/s2 方向向右,

对木板,受拉力和摩擦力作用,F-µmg=Ma2   a2=4m/s2 方向向右,

(2)F作用时间为1s,

对木块:v1=a1t=2m/s

对木板:v2=a2t=4m/s

(3)撤去F后木块和木板组成的系统动量守恒,木块达到木板左端时二者恰好达到共同速度,这过程中木块对地位移为s,设最后共同速度为v

Mv2+mv1=(M+m)v

如图,设撤去F时,木块距木板左端为L1

分别以木块和木板为研究对象,由动能定理得:

μmgs=

1
2
mv2-
1
2
m
v21

-μmg(s+L1)=

1
2
Mv2-
1
2
M
v21

解得L1=

2
3
m

故木板长度为1+

2
3
≈1.67m

答:(1)恒力撤去前,小物块和长木板的加速度各2m/s2,方向向右和4m/s2,方向向右.

(2)刚撤去F时,小物块和长木板的速度各2m/s和4m/s.

(3)长木板的长度至少是1.67m.

单项选择题

Questions 16-20 are based on the following passage.
What is intelligence, anyway When I was in the army, I received a kind of aptitude test that all soldiers took and, against a normal of 100, scored 160. No one at the base had ever seen a figure like that, and for two hours they made a big fuss over me. (It didn’t mean anything. The next day I was still a buck private with KP—kitchen police—as my highest duty. )
All my life I’ve been registering scores like that, so that I have the complacent feeling that I’m highly intelligent, and I expect other people to think so, too. Actually, though, don’t such scores simply mean that I am very good at answering the type of academic questions that are considered worthy of answers by the people who make up the intelligence tests—people with intellectual bents similar to mine
For instance, I had an auto-repair man once, who, on these intelligence teste, could not possibly have scored more than 80, by my estimate. I always took it for granted that I was far more intelligent than he was. Yet, when anything went wrong with my car I hastened to him with it, watched him anxiously as he explored its vitals, and listened to his pronouncements as though they were divine oracles—and he always fixed my car.
Well, then, suppose my auto-repair man devised questions for an intelligence test.Or suppose a carpenter did, or a farmer, or, indeed, almost anyone but an academician. By every one of those thests, I’d prove myself a moron. And I’d be a moron, too. In the world where I could not use my academic training and my verbal talents but had to do something intricate or hard, working with my hands, I would do poorly. My intelligence, then, is not absolute but is a function of the society I live in and of the fact that a small subsection of that society has managed to foist itself on the rest as an arbiter of such matters.
Consider my auto-repair man, again. He had a habit of telling me jokes whenever he saw me. One time he raised his head from under the automobile hood to say: "Doc, a deaf-and-mute guy went into a hardware store to ask for some nails. He put two fingers together on the counter and made hammering motions with the other hanD.The clerk brought him a hammer. He shook his head and pointed to the two fingers he was hammering. The clerk brought him nails. He picked out the sizes he wanted, and left. Well, doc, the next guy who came in was a blind man. He wanted scissors. How do you suppose he asked for them "
In dulgently, I lifted my fight hand and made scissoring motions with my first two fingers. Whereupon my auto-repair man laughed and said, "Why, you dumb jerk, he used his voice and asked for them. " Then he said smugly, "I’ve been trying that on all my customers today. " "Did you catch many " I askeD."Quite a few," he said, "but I knew for sure I’d catch you. " "Why is that " I askeD."Because you’re so goddamned educated, Doc, I knew you couldn’t be very smart. "
And I have an uneasy feeling he had something there.

What is the message of this article

A.A person becomes more intelligent when he receives more education.

B.A person who scores high on an aptitude test is also smart on other matters.

C.Intelligence test is relative because it takes different forms in different situations.

D.A person who scores low on an aptitude test is unlikely to be able to repair a car.

选择题