问题 计算题

如图所示,质量mB=3.5kg的物体B通过一轻弹簧固连在地面上,弹簧的劲度系数k=100N/m.一轻绳一端与物体B连接,绕过无摩擦的两个轻质小定滑轮O1、O2后,另一端与套在光滑直杆顶端的、质量mA=1.6kg的小球A连接.已知直杆固定,杆长L为0.8m,且与水平面的夹角θ=37°.初始时使小球A静止不动,与A端相连的绳子保持水平,此时绳子中的张力F为45N. 已知A O1=0.5m,绳子不可伸长.现将小球A从静止释放(重力加速度g取10m/s2,sin37°=0.6,cos37°=0.8)。求:

小题1:在释放小球A前弹簧的形变量;

小题2:若直线C O1与杆垂直,求物体A运动到C点的过程中绳子拉力对物体A所做的功;

小题3:求小球A运动到底端D点时的速度.

答案

小题1:0.1cm

小题2:7J

小题3:

(1)释放小球A前,物体B处于平衡状态: 得       

故弹簧被拉长了0.1cm

(2)小球从杆顶端运动到C点的过程,由动能定理:

      而

物体B下降的高度                             

由此可知,此时弹簧被压缩了0.1m,则弹簧的弹性势能在初、末状态相同。

再以A、B和弹簧为系统,由机械能守恒:                                     

对小球进行速度分解可知,小球运动到C点时物体B的速度      

由以上几式联立可得:

(3)因杆长L=0.8m,故

故DO1=AO1,弹簧的伸长量依然为0.1m.,与最初状态相比,弹簧的弹性势能相同,物体B又回到了初始位置,其重力势能也与最初状态相同。

在D点对A的速度进行分解可得: 

由机械能守恒:                                               

联立可得小球A运动到杆的底端D点时的速度:

单项选择题

Are you a man or a mouse When people ask this question they want to know (1) you think you are a (2) person or a coward. But you will never really know the answer to this question (3) you are tested in real life. Some people (4) they are brave but when they come face to face with real (5) , they act like cowards. Others think of themselves as cowards, but when they meet danger, they act like (6)

Lenny had always thought of himself as a (7) person. He got worried before examinations. He worried about his job and health. All he wanted in life was to be safe and healthy. (8) , on January 15th, 2002, a plane crashed into the Potomac River in Washington. Lenny went to the river to see what was happening. He saw a woman in the (9) water. Lenny did not feel afraid. He kept very (10) and did a very dangerous thing. He jumped into the Potomac, (11) to the woman, and kept her head (12) the water. Seventy-eight people died that day. Thanks to Lenny, it was not (13) .

When you are in a very (14) situation and feel afraid, the body automatically produces a chemical in the blood. The chemical is called adrenalin. (15) adrenalin in the blood system, you actually feel per and per and are (16) to fight or run away. However, when you are absolutely terrified, the body can produce too much adrenalin. When this (17) , the muscles become very hard and you find you (18) move at all. You are then paralyzed with fear. This is (19) when we are very frightened, we sometimes say we’re "petrified". This word comes from the Greek word "petros", which means "stone". We are (20) frightened that we become stonelike.

18()

A.needn’t 

B.can’t 

C.mustn’t 

D.shouldn’t

单项选择题