PHYSICS 231 Lecture 13 Keeping momentum PHY 231 1 quiz extra credit At which point are the kinetic and potential energy highest respectively a A and B b D and E c D and A d B and A e D and D PHY 231 2 Momentum Collisions When a bullet hits the wall its velocity is very much reduced The wall does not move although the force on the bullet is the same as the force on the wall Newton s 3rd law Fwall bullet Fbullet wall Fwall bullet mbulletabullet Fbullet wall mwallawall Mbullet Mwall abullet awall PHY 231 3 Is it only the mass Vbullet 100 m s Vbullet 200 m s When the bullet gets stopped in the wall it deaccelerates from its initial velocity to 0 So its acceleration is vbullet t with t some small time Second law Fwall bullet mbulletabullet mbulletvbullet t PHY 231 4 More general and formal F ma Newton s 2nd law F m v t a v t F m vfinal vinital t Define p mv p momentum kgm s F pfinal pinitial t F p t The net force acting on an object equals the change in momentum p in a certain time period t Since velocity is a vector momentum is also a vector pointing in the same direction as v PHY 231 5 Impulse F p t p F t Definition F2 F1 Force change in mv per time period t The change in momentum equals the force acting on the object times how long you apply the force p Impulse What if the force is not constant within the time period t p F t F1 s F2 s F3 s t F1 s F2 s F3 s t tFaverage F3 s s s t p Faverage t PHY 231 6 car hitting haystack car hitting wall The change in momentum impulse is the same but the force reaches a much higher value when the car hits a wall 7 PHY 231 Some examples A tennis player receives a shot approaching him horizontally with 50m s and returns the ball in the opposite direction with 40m s The mass of the ball is 0 060 kg A What is the impulse delivered by the ball to the racket B What is the work done by the racket on the ball A Impulse change in momentum p p m vfinal vinitial 0 060 40 50 5 4 kgm s B W KEfinal KEinitial mvfinal2 mvinital2 no PE 0 060 40 2 50 2 27 J PHY 231 8 Child safety A friend claims that it is safe to go on a car trip with your child without a child seat since he can hold onto your 12kg child even if the car makes a frontal collision lasting 0 05s and causing the vehicle to stop completely at v 50 km h about 30 miles h Is he to be trusted F p t force impulse per time period m vf vi t vf 0 and vi 50km h 13 9 m s m 12kg t 0 05s F 12 13 9 0 05 3336 N This force corresponds to lifting a mass of 340 kg or about 680 pounds DON T TRUST THIS GUY PHY 231 9 question The velocity change is largest in case A B The acceleration is largest in case A B The momentum change is largest in case A B The impulse is largest in case A B PHY 231 10 accident Consider the cases A and B in which a car crashes into a wall In which case is the likelihood that the passengers are severely hurt greater A the change in impulse is largest A 9mcar B 5mcar and thus the force acting on the passengers largest PHY 231 11 Momentum p mv F p t Impulse the change in momentum p F t Demo the safe bungee jumper PHY 231 12 Conservation of Momentum F21 t m1v1f m1v1i F12 t m2v2f m2v2i Newton s 3rd law F12 F21 m1v1f m1v1i m2v2f m2v2i Rewrite m1v1i m2v2i m1v1f m2v2f p1i p2i p1f p2f CONSERVATION OF MOMENTUM PHY 231 CLOSED SYSTEM 13 momentum conservation PHY 231 14 Moving in space An astronaut 100 kg is drifting away from the spaceship with v 0 2 m s To get back he throws a wrench 2 kg in the direction away from the ship With what velocity does he need to throw the wrench to move with v 0 1 m s towards the ship a 0 1 m s b 0 2 m s c 5 m s d 16 m s e this will never work Initial momentum maivai mwivwi 100 0 2 2 0 2 20 4 kgm s After throw mafvaf mwfvwf 100 0 1 2 vwf kgm s Conservation of momentum maivai mwivwi mafvaf mwfvwf 20 4 10 2 vwf vwf 15 7 m s PHY 231 15 Types of collisions Inelastic collisions Elastic collisions Momentum is conserved Momentum is conserved Some energy is lost in the No energy is lost in the collision KE not conserved collision KE conserved Perfectly inelastic the objects stick together PHY 231 16
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