Presentation on theme: "Review Chap. 8 Momentum, Impulse, and Collisions"— Presentation transcript:
1 Review Chap. 8 Momentum, Impulse, and Collisions PHYS 218 secReviewChap. 8Momentum, Impulse, and Collisions
2 What you have to know Momentum and impulse Momentum conservation Various collision problemsThe typical examples where momentum conservation is used are collisions!Center of massSection 8.6 is not in the curriculum.
3 Newton’s 2nd law of motion This cannot be applied to the problems where mass m is changing.E.g.Rocket propulsion problem. (See Sec 9.6)Original form of the 2nd law of motion written by NewtonMomentum is a vector quantity.
4 Impulse-momentum theorem The impulse-momentum theoremImpulseImpulse is a vector quantity.Impulse-momentum theoremThe change in momentum of a particle during a time interval equals the impulse of the net force.
5 Impulse-momentum theorem General definitionImpulse-momentum theoremImpulse: area under the curve of net force in F-t graphLarge force for a short timeSmalle force for a longer timeSame areaSame impulse
6 identical Momentum vs. Kinetic Energy Integral form of Newton’s 2nd lawidenticalDifferential form of Newton’s 2nd law
8 First decompose the momentum into x and y directions Ex 8.3This is a 2-dim. motion.First decompose the momentum into x and y directionsAfterBefore
9 Conservation of Momentum External force Internal forcesIsolated system: External force = 0Newton’s 2nd lawNewton’s 3rd lawYou can add these forces to obtain the net (internal) force for the systemThe sum of these forces cannot be applied to a single object.
10 Conservation of Momentum Total momentum of an isolated system is conserved.Total momentumMomentum conservation gives a vector equation.
11 Note that momentum conservation is valid for an isolated system. Ex 8.4Recoil of a rifleRifle + bulletBeforeNote that momentum conservation is valid for an isolated system.So it is useful when the system changes. Therefore, draw diagrams for “before” & “after” the eventAfterRiflebulletThe negative sign means that the rifle is moving back!change the unit so that the both masses have the same unit
12 The sum of these two momenta vanishes as it should be. Ex 8.4 (cont’d)The sum of these two momenta vanishes as it should be.The kinetic energy is NOT conserved.The kinetic energy before the event was 0.
13 Collision along a straight line Ex 8.5Collision along a straight lineBeforeABAfterIf you have a collision problem, always use momentum conservation.AB
14 Collision in a horizontal plane Ex 8.6Collision in a horizontal planeBeforeAfterAgain, we use momentum conservation.Also note that momentum is a vector quantity.Use the numbers above
15 Momentum conservation and collisions The key to solve collision problems is Momentum conservation.At the instant of collision, very complex and very large forces are acting on the bodies.Then the other forces can be neglected and the system is almost an isolated system. g momentum conservation can be appliedThe forces are very complex and we do not know much about the forces. g momentum conservation can give useful information for the motions of the colliding bodiesElastic collisionIf the forces between the colliding bodies are conservative, no mechanical energy is lost The total kinetic energy of the system is conserved.For elastic collisions, the total momentum and the total kinetic energy of the system are conserved.
16 Completely inelastic collision In this collision, the total kinetic energy of the system after the collision is less than before the collision.The forces during the collision are non-conservative.Completely inelastic collisionThis is a special case of inelastic collisions.This is where the colliding bodies stick together and move as one body after the collision.
17 Completely inelastic collisions What happens to momentum and kinetic energy in a completely inelastic collision of two bodiesBeforeABAfterConsider a 1-dim collision where vB1 = 0AB
18 (A) (B) Ex 8.8 The ballistic pendulum This is a device which can measure the speed of a bullet.(A)(B)Before collisionImmediately after collisionSwing of the body after collisionCollision processOne-body motionThis gives a relation between v1 and v2.This gives a relation between v2 and the height y.So, if you know y, you can know v2 and v1Analyze this event in two stages !
19 By measuring the height y, you can know the speed of the bullet Ex 8.8 (cont’d)The first stage: (A) collisionThe second stage: (B) one-body motionCombining the twoBy measuring the height y, you can know the speed of the bullet
20 Ex 8.9Automobile collisionCompletely inelastic collisionAfterBefore
21 Consider 1-dim elastic collision. Elastic collisionsConsider 1-dim elastic collision.BeforeABAfterABThese give TWO equations.You now have TWO unknowns (the final velocities).Therefore, you can completely determine the unknowns.
22 Elastic collisions: one body initially at rest rearrangerearrangeBeforeABAfterAB
23 The motion of the heavy object doesn’t change. BeforeABeforeBBAAfterAfterABBAThe motion of the heavy object doesn’t change.The light object moves in the direction of the heavy one but (two times) faster than the heavy one.The motion of the heavy object doesn’t change.The light object moves to the opposite direction but with same speed.
24 Elastic collisions & relative velocity The velocity of B relative to A after the collisionThe negative of the velocity of B relative to A before the collisionIf you watch the motion of A sitting on B, then you will see:A is approaching to B with speed v before the collision.After the collision, A is moving away from B with the same speed
25 Two-dim elastic collision (If this is a head-on collision, it is the same as the 1-dim collision.)Ex 8.12BeforeFOUR unknowns after collision(two velocity vectors)AfterMomentum conservation gives two eqs.Kinetic energy conservation gives one eq.So totally THREE equations.To uniquely determine the final velocities, we need ONE more information for the final velocities