Dynamic We can see that in the case of a large velocity of motion the magnitude of the instantaneous force can is very large up to a surprising value even if the mass of the body is very small When a flying bird of weight 17 8N collides with a flying plane the velocity of which is 800km/h(for a modern plane this is only of medium velocity) the force of impact can reach 3.56x10N I e, the force of impact is 20 thousand times larger than the weight of the bird. This is the reason of so called bird disaster in aviation As to impacts Harmful aspects are bird disasters, damages of mechanisms and apparatuses caused by impact etc Advantageous aspects are to use to use impacts to perform useful work as, for example, forging, driving piles etc The study of impact: phenomena has the aim to undress and laws in order to make positive use of its advantageous aspects and in order to avoid its dangerous and harmful aspects
11 We can see that in the case of a large velocity of motion the magnitude of the instantaneous force can is very large up to a surprising value even if the mass of the body is very small. When a flying bird of weight 17.8N collides with a flying plane ,the velocity of which is 800km/h (for a modern plane this is only of medium velocity) the force of impact can reach 3.56105N.I.e.,the force of impact is 20 thousand times larger than the weight of the bird.This is the reason of so called bird disaster in aviation. As to impacts :Harmful aspects are “bird disasters”,damages of mechanisms and apparatuses caused by impact etc. Advantageous aspects are to use to use impacts to perform useful work as,for example , forging, driving piles etc . The study of impact：phenomena has the aim to undress and laws in order to make positive use of its advantageous aspects and in order to avoid its dangerous and harmful aspects
学 可见,即使是很小的物体,当运动速度很高时,瞬时力 可以达到惊人的程度。有关资料介绍,一只重178N的飞鸟 与飞机相撞,如果飞机速度是800kmh,(对现代飞机来说, 这只是中等速度),碰撞力可高达3.56×105N,即为鸟重的2 万倍!这是航空上所谓“鸟祸”的原因之一。 害的一面:“鸟祸”、机械、仪器及其它物品由于碰撞损坏等。 利的一面:利用碰撞进行工作,如锻打金属,用锤打桩等 硏究碰撞现象,就是为了掌握其规律,以利用其有利的 面,而避免其危害
12 可见，即使是很小的物体，当运动速度很高时，瞬时力 可以达到惊人的程度。有关资料介绍，一只重17.8N的飞鸟 与飞机相撞，如果飞机速度是800km/h，（对现代飞机来说， 这只是中等速度），碰撞力可高达3.56105N，即为鸟重的2 万倍！这是航空上所谓“鸟祸”的原因之一。 害的一面： “鸟祸”、机械、仪器及其它物品由于碰撞损坏等。 利的一面：利用碰撞进行工作，如锻打金属，用锤打桩等。 研究碰撞现象，就是为了掌握其规律，以利用其有利的一 面，而避免其危害
Dynamic 819-2 Fundamental theorems of the theory of impact Two basic premises: (1) Compared with forces of impact ordinary forces as gravity elastic forces etc are is very small during the impact. Such forces can be neglected But it is must be noted that the action of conventional forces on the change of the state of motion of bodies before and after an impact cannot be neglected (2) Because the impact time is very small but the changes of velocities are finite quantities the displacement of a body during an impact is a very small quantity which can be neglected in practice. I e, the position of the body at the beginning of an impact is the same as that at the end of the impact 13
13 §19-2 Fundamental theorems of the theory of impact (1) Compared with forces of impact ordinary forces as gravity ,elastic forces etc.are is very small during the impact . Such forces can be neglected .But it is must be noted that the action of conventional forces on the change of the state of motion of bodies before and after an impact cannot be neglected. (2) Because the impact time is very small but the changes of velocities are finite quantities ,the displacement of a body during an impact is a very small quantity which can be neglected in practice .I, e.,the position of the body at the beginning of an impact is the same as that at the end of the impact . Two basic premises：
学 §192用于碰撞过程的基本定理 两个基本假设: (1)在碰撞过程中,重力、弹性力等普通力与碰撞力相比 小得多,其冲量可以忽略不计。但必须注意,在碰撞前和碰撞 后,普通力对物体运动状态的改变作用不可忽略。 (2)由于碰撞时间极短,而速度又是有限量,所以物体在 碰撞过程的位移很小,可以忽略不计,即认为物体在碰撞开始 时和碰撞结束时的位置相同
14 §19-2 用于碰撞过程的基本定理 (1)在碰撞过程中，重力、弹性力等普通力与碰撞力相比 小得多，其冲量可以忽略不计。但必须注意，在碰撞前和碰撞 后，普通力对物体运动状态的改变作用不可忽略。 (2)由于碰撞时间极短，而速度又是有限量，所以物体在 碰撞过程的位移很小，可以忽略不计，即认为物体在碰撞开始 时和碰撞结束时的位置相同。 两个基本假设：
Dynamic TTwo basic theorems: In theoretical mechanics we are mainly concerned with the change of the velocity of a body under the action of a force of impact. So the momentum and the angular momentum theorem become the main tools for investigating impact phenomena 1. The momentum theorem applied to an impact. Theorem of impulse. Let the mass of a particle be m, its velocity before the impact is v and i at the end of the impact the impact in Neglecting the moment a of the convention al pulse iss forces, momentum the theorem in integral form becomes nmu-ny= (19-1 15
15 Two basic theorems： In theoretical mechanics we are mainly concerned with the change of the velocity of a body under the action of a force of impact. So ,the momentum and the angular momentum theorem become the main tools for investigating impact phenomena. 1. The momentum theorem applied to an impact. Theorem of impulse. Let the mass of a particle be m，its velocity before the impact is ,and at the end of the impact, the impact impulse is . Neglecting the moment a of the convention al forces ,momentum the theorem in integral form becomes. v u S mu−mv=S (19-1)