题目内容
(15分)(1)(6分)氘核和氚核可发生热核聚变而释放巨大的能量,该反应方程为:
,式中x是某种粒子。已知:
、
、
和粒子x的质量分别为2.0141u、3.0161u、4.0026u和1.0087u;1u=931.5MeV/c2,c是真空中的光速。由上述反应方程和数据可知,粒子x是__________,该反应释放出的能量为_________ MeV(结果保留3位有效数字)
(2)(9分)如图,小球a、b用等长细线悬挂于同一固定点O。让球a静止下垂,将球b向右拉起,使细线水平。从静止释放球b,两球碰后粘在一起向左摆动,此后细线与竖直方向之间的最大偏角为60°。忽略空气阻力,求
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241343292751603.png)
(i)两球a、b的质量之比;
(ii)两球在碰撞过程中损失的机械能与球b在碰前的最大动能之比。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134329135790.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134329181399.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134329213399.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134329244438.png)
(2)(9分)如图,小球a、b用等长细线悬挂于同一固定点O。让球a静止下垂,将球b向右拉起,使细线水平。从静止释放球b,两球碰后粘在一起向左摆动,此后细线与竖直方向之间的最大偏角为60°。忽略空气阻力,求
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241343292751603.png)
(i)两球a、b的质量之比;
(ii)两球在碰撞过程中损失的机械能与球b在碰前的最大动能之比。
(1)
(或中子), 17.6
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134329400699.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134329306385.png)
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134329369788.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134329400699.png)
(1)根据核反应方程遵循的规律可得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134329462868.png)
根据爱因斯坦质能方程ΔE=Δmc2可得:
ΔE=(2.0141+3.0161-4.0026-1.0087)×931.5MeV=17.6 MeV
(2)(i)设球b的质量为m2,细线长为L,球b下落至最低点,但未与球a相碰时的速度为v,由机械能守恒定律得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134329540812.png)
式中g是重力加速度的大小。设球a的质量为m1;在两球碰后的瞬间,两球共同速度为v′,以向左为正。有动量守恒定律得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134329587743.png)
设两球共同向左运动到最高处,细线与竖直方向的夹角为θ,由机械能守恒定律得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241343296341419.png)
联立①②③式得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134329712880.png)
代入数据得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134329400699.png)
(ii)两球在碰撞过程中的机械能损失是
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241343297901190.png)
联立①⑥式,Q与碰前球b的最大动能Ek(Ek=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134329837614.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241343298681277.png)
联立⑤⑦式,并代入题给数据得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824134329369788.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
练习册系列答案
相关题目