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Lecture 8

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  • 1. Third LawFor every action there is an equal and oppositereaction.Some action/reaction pairs:I push on the floor, the floor pushes back on mewith equal force (unless it breaks).Tug of war (when at a standstill) – west grouppulls rope with a force equal in size but oppositein direction to east group.
  • 2. Simple Rule:Action: Object A exerts a force on object BReaction: Object B exerts a force on object AA BF on Adue to BF on Bdue to A
  • 3. 3rdlaw example problemA 5 kg and a 1 kg mass collide.Which experiences the larger force?Explain.
  • 4. RollingHow does a car accelerate?The wheels are turned by the motor.What would happen if there was nofriction between road and tire?Wheel would spin but car wouldn’taccelerate.Friction between road and tire is alsoresponsible for force that keeps carturning when changing direction.F of tireon roadF of roadon tire
  • 5. RollingVideo: Cars...ON ICE!
  • 6. Action/Reaction different massesWhat happens when A and B(equal mass) collide?Which one (if any) hits harder?Now, what if A and C collidewhere C is more massive thanA?Which one hits harder?Action/Reaction forces are apair – they are always and mustalways be the same size.A BC A
  • 7. CannonAction forces and reactionforces must be the samesize.Why does the cannonballfly so fast?Why doesn’t the cannonmove as much as theball?Recall Newton’s 2ndlaw:acceleration = force/massFma = Fma =
  • 8. RocketsIf the rocket was in avacuum would it stillwork?Yes – Rockets are alittle like the cannon.(Demo)
  • 9. Wrapping up Newton’s LawsAn object will not accelerate (change directionor speed) unless acted upon by an unbalancedforce.The acceleration of an object is proportional tothe force on it and inversely proportional tomass (a = F/m).So what will happen to acceleration if you doubleforce with same mass?If you double mass with same force?If object A exerts a force on object B thenObject B exerts an equal in magnitude butoppositely directed force on A.
  • 10. Momentum
  • 11. What is momentum?Is it harder to stop something that is movingquickly or something that is moving slowly?Is it harder to stop something that has more massor something that has less mass?How difficult something is to start or stop.More than just inertia (mass)includes how quickly something is already moving.
  • 12. Momentum:Momentum = mass * velocityMomentum has a direction and thatdirection matches the direction of motion.Changing direction requires a change inmomentum.
  • 13. So objects with wildlydifferent masses andvelocities can havesame momentum.Vv
  • 14. ExampleA motorcycle of mass 200-kg travels with avelocity of 50 m/s. What is its momentum?A car of mass 1000-kg travels with a velocity of10 m/s. What is its momentum?
  • 15. Changes in MomentumWhat causes a change in velocity?An acceleration, but what causes anacceleration?A Force: The greater the force and the longer it actsthe greater the change in velocity.mv vmvmF
  • 16. ImpulseImpulse is the change in momentum.Consists of:Force (produces the velocity change)Time (how long the force was applied)
  • 17. Impulse – Momentum:Impulse = change in momentumF*t = m2*v2 – m1*v1ORF*t = Δmv
  • 18. Coming to a stop:Braking: Low force over long timeCrash: High force over short time.What is the momentum change for a truck braking to astop? For a truck hitting a wall?Result is the same: same mass, same starting velocity andfinal velocity is zero.crunch!vFvv
  • 19. Increasing MomentumLarger force applied over longer time willcause greatest increase.Rocket: tremendous force applied for severalminutes to reach escape velocity.Rifles: why is a rifle long?Why wouldn’t you use a pistol to shootsomething far away?
  • 20. Rifles:Bang!(hot gasses push)Gasses escape...Gasses escape...
  • 21. Decreasing MomentumRemember the truck: hitting a wall (fast stop)results in much more force than a controlledstop.Increasing the time a collision takes reduces theforce experienced.Can you think of any examples?Airbags, crumple zones in cars.Boxers who dodge backward as they are hit.Bungee Jumping.Examples are endless.
  • 22. Decreasing MomentumSlow change – bymoving backwardwith the hit youdecrease the force byincreasing thecontact time.Fast change – don’tmove the wrong way,you increase theforce by decreasingthe contact time.
  • 23. Demo: Fast vs. Slow changes2 meter stick, 2 100 gram weights.Weight 1 attached 90 cm from tableWeight 2 attached 10 cm from tableBoth by thin threads.What will happen when each is dropped (fromthe same height)?
  • 24. BouncingWhich results in agreater impulse:bouncingstoppingLook at momentumchange: bounce: m(v2-v1) =m(v-(-v)) = 2mvstop: 0 – m*(-v) = mvv v0vboing!
  • 25. Demo: Happy and Sad balls.One ball does not bounce.Other ball will.Which imparts more impulse? Why?
  • 26. Conservation of MomentumMomentum is conserved.In a collision or otherinteraction, momentum isneither created nordestroyed.Recall the cannon examplefrom Newton’s Third law.What was net momentumbefore cannon fired?What is net momentum(ball + cannon) after it isfired?
  • 27. Momentum before =0Momentum aftermust be 0(momentum isconserved). 0 = mc*vc + mb*vb So vc and vb will be inopposite directions tomake the sum zero.Can we figure outwhat proportion theirsizes will be?
  • 28. CollisionsImagine two 1-kgcarts.Momentum before =1kg*10m/s = 10kg*m/smomentum aftermust be equal.2 kg * v = 10 kg*m/sv = 5 m/s
  • 29. Wrapping up:Momentum is conserved (I know, I know,another conservation law – there are afew of them).Momentum is proportional to velocity andmass of the object.Impulse is a change in momentum. It isproportional to the force and the contacttime.