（9分）如图，在竖直平面内有一固定光滑轨道，其中AB部分是倾角_爱下问搜题

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问题计算题

（9分）如图，在竖直平面内有一固定光滑轨道，其中AB部分是倾角为37°的直轨道，BCD部分是以O为圆心、半径为R的圆弧轨道，两轨道相切于B点，D点与O点等高，A点在D点的正下方。质量为m的小球在沿斜面向上的拉力F作用下，从A点由静止开始做变加速直线运动，到达B点时撤去外力。已知小球刚好能沿圆轨道经过最高点C，然后经过D点落回到A点。已知sin37°=0．6，cos37°=0．8，重力加速度大小为g。求

（1）小球在C点的速度的大小；

（2）小球在AB段运动过程，拉力F所做的功；

（3）小球从D点运动到A点所用的时间。

答案

（1）（2）（3）

题目分析：（1）小球刚好能沿圆轨道经过最高点C，即在C点，重力提供向心力

得

（2）根据几何关系如下图

OB之间的高度为，B到AD的水平距离为，那么AB的高度即

从A点到C点，只有重力和AB段的拉力做功，根据动能定理

整理得

（3）从C点到D点，根据定能定理有，得

从D点到A点的高度

从C点到A点，根据动能定理有，得

从D点到A点为匀加速直线运动，有

整理解得

完形填空

完形填空（20小题；每小题1.5分，满分30分）
阅读下面短文，从短文后所给各题的四个选项A，B，C，D中选出能填入相应空白处的最佳选项，并在答题卡上将该项涂黑。
A very little boy was spending his Saturday morning playing in his sandbox. He had with him a plastic pail (桶) and a shiny, red plastic shovel (铲). In the   36  of creating roads and tunnels in the sand, he   37  a large rock in the middle of the sandbox.
The boy dug around the rock,   38  to move it off the dirt. At first, he wanted to carry it out of the sandbox with his hands; however, it was too heavy. Later, with much   39 , he pushed the rock across the sandbox by   40  his hands. When the boy got the rock to the   41  of the sandbox, he found that he couldn’t roll it up and   42  the little wall.   43 , the little boy pushed, but every time he thought he had made some   44 , the rock tipped (翻滚) and then fell back into the sandbox. The little boy pushed and pushed, but his only   45  was to have the rock roll back.
Finally he   46  tears. All this time the boy’s father watched from his living room window   47  the drama was unfolded. The moment the tears fell, a large   48  appeared across the sandbox. It was the boy’s father. Gently but   49 , he said, “Son, why didn’t you use all the strength that you had?”
Defeated, the boy   50  back, “I did! I did! I used all the strength that I had!”
“No, you didn’t. You didn’t ask me for help.” The father   51  down, picked up the rock and dropped it off the sandbox.
Do you have “rocks” in your life that need to be   52 ? Are you discovering that you don’t have   53  it takes to lift them? There is someone who is willing to give us the   54  we need. Maybe, it’s sometimes a good idea to ask others for   55  when we meet difficulties we can’t overcome.

D．controlling

D．rushed into

A．surprisingly

单项选择题

设“A班有学生不是壮族人”为假，不可推出（）

A.并非该班学生都不是壮族人

B.该班学生不都是壮族人

C.该班学生张某是壮族人

D.该班有学生是壮族人

E.该班没有学生不是壮族人