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子弹击中振动系统后,子弹质量对系统的影响是否可忽略不计?对这个问题试举一例分析一下。例:已知一木块质量为M,悬挂于倔强系数为K的弹簧下端,有一子弹质量为m,初速度为V_o,在垂直下方击中,并停留在木块里。 讨论: 发生碰撞后的简谐振动。 解: (1)在碰撞系统的内力远大于外力时,系统 的动量守恒。设V为子弹和木块的共同 速度,则有: mV_o=(M+m)V (2)参见图<1>设:A为弹簧原长末端的位置,定为弹性势能的零点,B为挂上木块后的平衡位置;C为振子运动的最低点,定为重力势能的零点:x_1=Mg/K;为从原平衡位置开始计起的
After the bullet hits the vibration system, can the impact of the bullet quality on the system be negligible? Give an example analysis of this issue. Example: It is known that a piece of wood of mass M is suspended from the lower end of a spring with a stubborn coefficient of K. A bullet of mass m, initial velocity v_o hits vertically below and remains in the block. Discussion: Simple harmonic vibration after collision. Solution: (1) In the collision system when the internal force is much larger than the external force, the system of conservation of momentum. Let V be the common velocity of the bullet and the wood block, then: mV_o = (M + m) V (2) See Figure <1> Let A be the position of the end of the spring’s original length, C is the lowest point of the pendulum movement and is defined as the zero point of the gravitational potential energy: x_1 = Mg / K; from the point of original equilibrium position