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如图12所示，在距水平地面高为h处有一半径为R的1/4圆弧轨道，圆弧轨道位于竖直平面内，轨道光滑且末端水平，在轨道的末端静置一质量为m的小滑块A。现使另一质量为m的小滑块B从轨道的最高点由静止释放，并在轨道的最低点与滑块A发生碰撞，碰后粘合为一个小滑块C。已知重力加速度为g。求：

(1)滑块C对轨道末端的压力大小。

(2)滑块C在水平地面上的落地点与轨道末端的水平距离。

 

答案

（1） 3mg      （2）

(1)滑块B沿轨道下滑过程中，机械能守恒，设滑块B与A碰撞前瞬间的速度为v1，则                                                                   mgR=。…………1分

滑块B与滑块A碰撞过程沿水平方向动量守恒，设碰撞后的速度为v2，则

               mv1=2mv2 。     …………1分

设碰撞后滑块C受到轨道的支持力为N，根据牛顿第二定律，对滑块C在轨道最低点有                                                                N-2mg=2mv/R ，…………1分

联立各式可解得，                                    N=3mg。 …………1分

根据牛顿第三定律可知，滑块C对轨道末端的压力大小为N′=3mg。…………1分

(2)滑块C离开轨道末端做平抛运动，设运动时间t，根据自由落体公式，

     h=gt2 。…………1分

滑块C落地点与轨道末端的水平距离为s=v2t ，…………1分

联立以上各式解得s=。 …………1分

单项选择题 A型题

脘痞，嗳腐吞酸，多见于（）

A.食积胃脘

B.湿邪困脾

C.饮邪停胃

D.脾胃气虚

E.胃阴亏虚
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单项选择题

Young girls at high risk for depression appear to have a malfunctioning reward system in their brains, a new study suggests. The finding comes from research that (1) a high-risk group of 13 girls, aged 10 to 14, who were not depressed but had mothers who (2) recurrent depression and a low-risk group of 13 girls with no (3) or family history of depression. Both groups were given MRI brain (4) while completing a task that could (5) either reward or punishment.

(6) with girls in the low-risk group, those in the high-risk group had (7) neural responses during both anticipation and receipt of the reward. (8) , the high-risk girls showed no (9) in an area of the brain called the dorsal anterior cingulated cortex (背侧前扣带皮质), believed to play a role in (10) past experiences to assist learning.

The high-risk girls did have greater activation of this brain area (11) receiving punishment, compared with the other girls. The researchers said that this suggests that high-risk girls have easier time (12) information about loss and punishment than information about reward and pleasure.

"Considered together with reduced activation in the striatal (纹状体的) areas commonly observed (13) reward, it seems that the reward-processing system is critically (14) in daughters who are at elevated risk for depression, (15) they have not yet experienced a depressive (16) ," wrote Ian H. Gotlib, of Stanford University, and his colleagues. " (17) , longitudinal studies are needed to determine whether the anomalous activations (18) in this study during the processing of (19) and losses are associated with the (20) onset of depression," they concluded. The study was published in the April of the Archives of General Psychiatry.

19（）

A.criticisms

B.punishments

C.rewards

D.allowances
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