RI Chap 6 Collisions - Lecture Notes

6 COLLISIONS H2 Physics 9478 Content Page 6.1 Impulse and Momentum Change 2 6.2 Conservation of Momentum and Energy 6 6.3 Collisions 6 6.4 Collisions with increase in total kinetic energy 12 6.5 Appendix 15 Learning Outcomes Candidates should be able to: (a) recall that impulse is given by the area under the force-time graph for a body and use this to solve problems. (b) state the principle of conservation of momentum. (c) apply the principle of conservation of momentum to solve simple problems including inelastic and (perfectly) elastic interactions between two bodies in one dimension (knowledge of the concept of coefficient of restitution is not required). (d) show an understanding that, for a (perfectly) elastic collision between two bodies, the relative speed of approach is equal to the relative speed of separation. (e) show an understanding that, whilst the momentum of a closed system is always conserved in interactions between bodies, some change in kinetic energy usually takes place.

Page | 2 Introduction In the topic Fields and Energy, we have seen that total energy is always conserved within an isolated system, and bodies within the system transfer energies between each other when they interact. During their interactions (such as in collisions), these bodies exert forces on each other, hence transferring momenta too. We will learn about the conservation law associated with momentum, and how it can be applied to interacting bodies. 6.1 Impulse and Momentum Change  Momentum and Newton’s Second Law of Motion Recall that the momentum p of a body is defined as the product of its mass m, and its velocity v. p mv= Newton’s Second Law of Motion states that the rate of change of momentum of a body is proportional to the resultant force acting on the body and is in the same direction as the resultant force. In S.I. units, the proportionality constant is 1. Hence, net dpF dt= In this topic, we will examine the effect of applying a resultant force on a body over a duration of time, and see how this concept, together with Newton’s Third Law of Motion naturally lead to the principle of conservation of momentum.  Impulse Consider a resultant force Fnet acting on a body . The graph in Fig. 6.1 shows how Fnet varies with time t. Fig. 6.1 From Newton’s Second Law, net dpF dt= . During a small time interval d t, the momentum of the body changes by netdp F dt= . t1 t2 Fnet / N Fmax t/s dt

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