Theoretical Mechanics Chapter 19: Impact
1 Theoretical Mechanics
里论力学 第十撞
2
Dynamic In the preceding chapters the velocities of all points of a body under the action of forces al ways change continuously and gradually. In the present chapter we will study another mechanical phenomenon-wimpact. When bodies collide the velocities of all point of a body suffer a finite change in a very small time interval. The main subject here is to study collision phenomena, the fundamental theorems of the theory of impact, the loss in the kinetic energy of bodies during impact, the center of impact, etc 3
3 In the preceding chapters the velocities of all points of a body under the action of forces always change continuously and gradually . In the present chapter we will study another mechanical phenomenon——impact. When bodies collide the velocities of all point of a body suffer a finite change in a very small time interval .The main subject here is to study collision phenomena ,the fundamental theorems of the theory of impact ,the loss in the kinetic energy of bodies during impact , the center of impact ,etc
学 在前面讨论的问题中,物体在力的作用下,运动速度都 是连续地、逐渐地改变的。本章研究另一种力学现象—碰 撞,物体发生碰撞时,会在非常短促的时间内,运动速度突 然发生有限的改变。本章研究的主要内容有碰撞现象的特征, 用于碰撞过程的基本定理,碰撞过程中的动能损失,撞击中 心
4 在前面讨论的问题中，物体在力的作用下，运动速度都 是连续地、逐渐地改变的。本章研究另一种力学现象——碰 撞，物体发生碰撞时，会在非常短促的时间内，运动速度突 然发生有限的改变。本章研究的主要内容有碰撞现象的特征， 用于碰撞过程的基本定理，碰撞过程中的动能损失，撞击中 心
Chapter 19: Impact 819-1 Impact phenomenon and its fundamental characteristics. force of impact D819-2 Fundamental theorems of the theory of impact 8 19-3 Impact of a particle on a fixed plate. Coefficient of restitution D819-4 Direct Central impact of two bodies. Loss in kinetic energy. 回§19-5 The action of an impact force on a rigid body rotating about a fixed axis.The center of impact Small Summary
5 §19–1 Impact phenomenon and its fundamental characteristics. force of impact. §19-2 Fundamental theorems of the theory of impact §19–3 Impact of a particle on a fixed plate. Coefficient of restitution . §19–4 Direct Central impact of two bodies.Loss in kinetic energy. §19–5 The action of an impact force on a rigid body rotating about a fixed axis.The center of impact Small Summary Chapter 19 : Impact
第十九章碰撞 §19-1碰撞现象及其基本特征·碰撞力 §19-2用于碰撞过程的基本定理 §19-3质点对固定面的碰撞·恢复系数 §19-4两物体的对心正碰撞·动能损失 §19-5碰撞冲量对绕定轴转动刚体的作用 撞击中心 小结
6 §19–1 碰撞现象及其基本特征 碰撞力 §19-2 用于碰撞过程的基本定理 §19–3 质点对固定面的碰撞 恢复系数 §19–4 两物体的对心正碰撞 动能损失 §19–5 碰撞冲量对绕定轴转动刚体的作用 撞击中心 小结 第十九章 碰撞
Dynarnics 819-1 Impact phenomenon and its fundamental characteristics: force of impact Impact: The phenomenon that the velocities of the points of a body suffer sharp changes in a very small time interval if the moving body is suddenly subjected to a collision (including switched on or switched off forces of constraints)is called impact Fundamental characteristics of an impact phenomenon The velocities or moment a of the points of a body suffer finite changes in a very small time interval during impact. The impact time is very short measured to be of the order of one thousandth or even acceleration and of the acting forces are very large glues of the of one ten-thousandth of a second Therefore the val Force of impact: The forces occurring during an impact are called forces of impact. They are also called instantaneous forces because the action time is very short 7
7 §19-1 Impact phenomenon and its fundamental characteristics : force of impact Fundamental characteristics of an impact phenomenon： The velocities or moment a of the points of a body suffer finite changes in a very small time interval during impact .The impact time is very short ,measured to be of the order of one thousandth or even of one ten-thousandth of a second. Therefore ,the values of the acceleration and of the acting forces are very large . Impact：The phenomenon that the velocities of the points of a body suffer sharp changes in a very small time interval if the moving body is suddenly subjected to a collision (including switched on or switched off forces of constraints)is called impact. Force of impact ：The forces occurring during an impact are called forces of impact. They are also called instantaneous forces because the action time is very short
力单 §19-1碰撞现象及其基本特征碰撞力 碰撞:运动着的物体在突然受到冲击(包括突然受到约 束或解除约束)时,其运动速度发生急剧的变化,这种现象 称为碰撞。 碰撞现象的基本特征:物体的运动速度或动量在极短的 时间内发生有限的改变。碰撞时间之短往往以千分之一秒甚 至万分之一秒来度量。因此加速度非常大,作用力的数值也 非常大。 碰撞力(瞬时力):在碰撞过程中出现的数值很大的力 称为碰撞力;由于其作用时间非常短促,所以也称为瞬时力
8 §19-1 碰撞现象及其基本特征 碰撞力 碰撞现象的基本特征：物体的运动速度或动量在极短的 时间内发生有限的改变。碰撞时间之短往往以千分之一秒甚 至万分之一秒来度量。因此加速度非常大，作用力的数值也 非常大。 碰撞：运动着的物体在突然受到冲击（包括突然受到约 束或解除约束）时，其运动速度发生急剧的变化，这种现象 称为碰撞。 碰撞力（瞬时力）：在碰撞过程中出现的数值很大的力 称为碰撞力；由于其作用时间非常短促，所以也称为瞬时力
D Ilustration of the characteristics of the forces of impact by the example of a hammer hitting iron Let a hammer of weigh 10n hit a block of iron with v,=6m/s, the impact time is [=1/1000s and the hammer is rebounded with v2=1. 5m/s after impact Determine the average value of the force of impact F Take the hammer as the object to be studied mv -mv=s He ence (15+6)= s and S=7.65Ns g z-1 The general time-behavior of the change of the force of impact is shown in diagram The average value of the force of impact is F*=S/T=7650N 9 being 765 times larger than the weight of the hammer
9 Let a hammer of weigh 10N hit a block of iron with v1=6m/s , the impact time is =1/1000s and the hammer is rebounced with v2=1.5m/s after impact .Determine the average value of the force of impact. The general time-behavior of the change of the force of impact is shown in diagram . The average value of the force of impact is , being 765 times larger than the weight of the hammer. F* =S/ =7650N Illustration of the characteristics of the forces of impact by the example of a hammer hitting iron： mv2 −mv1 =S . (1.5 6) S=7.65 N s 10 + =S g Take the hammer as the object to be studied . and Hence,
学 以榔头打铁为例说明碰撞力的特征: 设榔头重10N,以v16m/s的速度撞击铁块,碰撞时间z 1/1000s,碰撞后榔头以v2=1.5ms的速度回跳。求榔头打击铁块 的力的平均值。 以榔头为研究对象,根据动量定理 m2m1=S的投影形式得 (1.5+6)=S;∴S=765NS 碰撞力的变化大致情况如图所示。 平均打击力F*=S/z=7650N,是榔头重的765倍。 10
10 设榔头重10N，以v1=6m/s的速度撞击铁块，碰撞时间 =1/1000s , 碰撞后榔头以v2=1.5m/s的速度回跳。求榔头打击铁块 的力的平均值。 mv2 −mv1 =S 的投影形式得 (1.5 6) ; 7.65 N s 10 + =S S= g 碰撞力的变化大致情况如图所示。 平均打击力 F* =S/ =7650N ，是榔头重的765倍。 以榔头打铁为例说明碰撞力的特征： 以榔头为研究对象，根据动量定理