Chapter 9 Impulse Momentum and Collisions Up to now we have considered forces which have a constant value does not depend on time throughout the motion and no explicit time duration Now lets consider a force which has a time duration usually short and with a magnitude that may vary with time examples a bat hitting a baseball a car crash a asteroid or comet striking the Earth etc It is difficult to deal with a time varying force so we might take the mean value F Favg ti tf t t Define a new quantity by multiplying the force by the time duration Favg t I Impulse a vector points in the same direction as the force has units of N s Define another quantity but which gives a measure of the motion mv p linear momentum a vector points in same direction as the velocity units of kg m s N s Example A car of mass 760 kg is traveling east at a speed of 10 0 m s The car hits a wall and rebounds moving west with a speed of 0 100 m s Determine its momentum before and after the impact Determine the impulse Solution Given m 750 kg v i 10 0 ms x v f 0 10 ms west 0 10 ms x pi mv i 750 kg 10 0 m s x 3 7 50x10 kg m s x p f mv f 750 kg 0 100 m s x 1 7 50x10 kg m s x Now rewrite Newton s 2nd Law F F v mv ma m t t p t Assume only one force acts or net force and it is the average force over the time duration then p Favg t p f pi Favg t or I p The Impulse momentum Theorem Alternatively consider the definition of acceleration v f vi mv f mv i a ma t t Favg t p f pi or I p The Impulse Momentum Theorem says that if an impulse force time duration is applied to an object its momentum changes In this example the impact of the car with the wall applies an impulse to the car car s p 3 changes I p p 75 0 x 7 50x10 x f i 7 58x10 3 kg m s x Collisions Involves two or more objects which may have their motion velocity momentum altered by collisions These concepts are applicable to the collisions of atoms billiard balls cars planetary objects galaxies etc Say we have a collection of interacting particles numbered 1 2 3 We can define the Total Momentum of the system all the particles as just the sum of all the individual momenta P pi p1 p2 p3 Imagine that these particles interact in some way collide and scatter As long as there are no net external forces acting on the system collection of objects the Total Linear Momentum does not change This means the Total Linear Momentum is the same before the collision during the collision and after the collision Pi Pf Conservation of Linear Momentum
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