2006年综合试答案2006年综合试答案.doc

Pan Pearl River Delta Physics Olympiad 2006 Q1 Kinetic energy of meson 介子动能 . Internal energy of meson介子内能 Suggested steps建议步骤: (1) Use energy and momentum conservation to obtain the speed of m2 after collision with m1.利用动量能量守恒求得m2与m1碰撞后的速度。 (2) Find the center-of-mass speed Vc of m2-m3 system (m3 is still at rest right after collision). The kinetic energy Ek of the m2+m3 system is then (m2+m3)/2 times the square of Vc. 由(1)求得m2-m3系统的质心速度Vc，进而求得其动能。 (3) The internal energy Ei can then be found using energy conservation, counting both the meson and the electron after collision, or just counting the energy m2 has after collision. 介子内能等于m2的初始动能减介子动能。 Q2 When the moment of inertia of the pulley is the largest, which means putting mass along the edge. Then use energy conservation that the initial potential energy is equal to the kinetic energy of mass m3 and that of the pulley. 由能量守恒可知，当滑轮的转动惯量最大时，重物到达地面的速度最小。因此M2应分布在轮边上。 Moment of inertia 滑轮的转动惯量 无滑动 能量守恒 答案 Q3 (10 points) (a) Pressure is proportional to depth, and the total force is found by integrating the entire depth. The force acting on the strip is 压强正比于深度 作用于条面的压力为 (b) Step-1 Find the shape of the liquid surface 第一步，求液面形状 Method-1: In the rotating reference frame the inertia force is , and the associated potential is . The liquid surface is an equal-potential surface, and the gravitation potential is gh. So the shape is a rotating parabola determined by constant. 方法-1 在转动参照系内，惯性力场为，其势能为，加上原有的重力势能gh，以及液面应是个等势面，得常数。 Method-2: The slope of the surface should be such that normal force should balance the gravity in the vertical direction, and give the concentric force for in the horizontal direction. That leads to the same answer as Method-1. 方法-2 液面的斜率应在垂直方向与重力平衡，在水平方向提供所需的向心力。 Method-3 方法-3 where其中 where 其中 where is a constant. Step-2 Determine C第二步，定常数C Consider the Volume during rotation, 液体的总体积不变。 For在 , 对条面的压力 附加的力为 Q4 (1