TJC Unit 6 Collisions

Unit 06: Collisions ASSESSMENT OBJECTIVES Students 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.

Collisions occur when one object strikes another. It is the event in which two or more bodies exert forces on each other in about a relatively short time. 1.1 Impulse LO(a) Impulse is the product of the force acting on a body and the time interval during which the force is exerted. Consider a constant force F acting on an object for a time interval t as shown by the force–time graph in (a). The impulse is given by product of force and time interval = F t. (a) constant force (b) varying force In general, the force need not be constant, as shown in (b). Then impulse = dt F  = <F>t, where <F> is the average force. The average force <F> is defined as that constant force, which when acting over the same time interval t as the actual time-varying force, produces the same impulse and change in momentum. Graphically, the area under the average force–time graph is equal to the area under actual force– time graph. By Newton’s 2nd Law, dt dpF  => F t = p = mv The impulse of the force acting on a body is equal to the change in momentum of the body. Impulse is a vector quantity. Its unit is the same as momentum : kg m s-1 or N s. Example 1: Use the concept of impulse to explain: (a) "Follow through" when striking a tennis ball (b) Use of a seat belt in a car (c) Crumple zones of a car (a) The "follow through" increases the impact time of the racket and the ball. The impulse and hence the change in momentum is increased. Thus the ball goes off with a higher velocity. F/N Fmax <F> t/s t/s F/N F t t

(b) The seat belt extends slightly before arresting the forward lunge of the passenger. This increases the time at which the momentum of the passenger is brought to zero. The average force on the passenger is thus reduced. (c) The crumple zones of the car helps to increase the impact time as the momentum of the crashing car is brought to zero, thus reducing the average force o