Slide 1Impulse and Linear MomentumAnother Example for ImpulseCollisionsElastic and Inelastic CollisionsElastic and Perfectly Inelastic CollisionsExample for CollisionsTwo dimensional CollisionsExample for Two Dimensional CollisionsCenter of MassMotion of a Diver and the Center of MassExample 9-12Center of Mass of a Rigid ObjectExample for Center of Mass in 2-DExample of Center of Mass; Rigid BodyCenter of Mass and Center of GravityMotion of a Group of ParticlesMonday, Oct. 25, 2004 PHYS 1443-003, Fall 2004Dr. Jaehoon Yu11. Impulse and Momentum Change2. Collisions3. Two Dimensional Collision s4. Center of Mass5. CM and the Center of Gravity6. Fundamentals on Rotational MotionPHYS 1443 – Section 003Lecture #17Monday, Oct. 25, 2004Dr. Jaehoon Yu2nd Term Exam Monday, Nov. 1!! Covers CH 6 – 10.5!!Monday, Oct. 25, 2004 PHYS 1443-003, Fall 2004Dr. Jaehoon Yu2Impulse and Linear Momentum By integrating the above equation in a time interval ti to tf, one can obtain impulse I.Impulse of the force F acting on a particle over the time interval t=tf-ti is equal to the change of the momentum of the particle caused by that force. Impulse is the degree of which an external force changes momentum.The above statement is called the impulse-momentum theorem and is equivalent to Newton’s second law. d pFdt=ururNet force causes change of momentum Newton’s second lawSo what do you think an impulse is?What are the dimension and unit of Impulse? What is the direction of an impulse vector? Defining a time-averaged force 1iiF F tt� DD�ur urImpulse can be rewritten tFI If force is constant tFI It is generally assumed that the impulse force acts on a short time but much greater than any other forces present.d p Fdt=ur urfittd p =�urf ip p- =ur urpD =urfittFdt =�urIrMonday, Oct. 25, 2004 PHYS 1443-003, Fall 2004Dr. Jaehoon Yu3Another Example for ImpulseIn a crash test, an automobile of mass 1500kg collides with a wall. The initial and final velocities of the automobile are vi= -15.0i m/s and vf=2.60i m/s. If the collision lasts for 0.150 seconds, what would be the impulse caused by the collision and the average force exerted on the automobile?ipLet’s assume that the force involved in the collision is a lot larger than any other forces in the system during the collision. From the problem, the initial and final momentum of the automobile before and after the collision is Therefore the impulse on the automobile due to the collision isThe average force exerted on the automobile during the collision isFIivm smkgii / 225000.151500 fpfvm smkgii / 390060.21500 pippf smkgi / 225003900 smkgismkgi / 1064.2/ 264004tp150.01064.24N 1076.1/ 1076.1525ismkgi Monday, Oct. 25, 2004 PHYS 1443-003, Fall 2004Dr. Jaehoon Yu4Collisions Consider a case of a collision between a proton on a helium ion. The collisions of these ions never involve no physical contact because the electromagnetic repulsive force between these two become great as they get closer causing a collision.Generalized collisions must cover not only the physical contact but also the collisions without physical contact such as that of electromagnetic ones in a microscopic scale.211d p F dt=ur urtFF12F21Assuming no external forces, the force exerted on particle 1 by particle 2, F21, changes the momentum of particle 1 by Likewise for particle 2 by particle 1 122d p F dt=ur urUsing Newton’s 3rd law we obtain So the momentum change of the system in the collision is 0 and the momentum is conserved2d purd pur12F dt=ur21F dt=-ur1d p=-ur1 2d p d p= +ur ursystemp21pp constant0Monday, Oct. 25, 2004 PHYS 1443-003, Fall 2004Dr. Jaehoon Yu5Elastic and Inelastic Collisions Collisions are classified as elastic or inelastic based on the conservation of kinetic energy before and after the collisions.A collision in which the total kinetic energy and momentum are the same before and after the collision. Momentum is conserved in any collisions as long as external forces are negligible.Elastic CollisionTwo types of inelastic collisions:Perfectly inelastic and inelastic Perfectly Inelastic: Two objects stick together after the collision, moving together at a certain velocity.Inelastic: Colliding objects do not stick together after the collision but some kinetic energy is lost.Inelastic CollisionA collision in which the total kinetic energy is not the same before and after the collision, but momentum is.Note: Momentum is constant in all collisions but kinetic energy is only in elastic collisions.Monday, Oct. 25, 2004 PHYS 1443-003, Fall 2004Dr. Jaehoon Yu6Elastic and Perfectly Inelastic Collisions In perfectly Inelastic collisions, the objects stick together after the collision, moving together. Momentum is conserved in this collision, so the final velocity of the stuck system isHow about elastic collisions?iivmvm2211In elastic collisions, both the momentum and the kinetic energy are conserved. Therefore, the final speeds in an elastic collision can be obtained in terms of initial speeds as iivmvm2211 21211 fivvm fifivvmvvm222111iifvmmmvmmmmv22121212112fvmm )(21)(212211mmvmvmviifffvmvm22112222112121iivmvm 2222112121ffvmvm 22222 fivvm fifivvvvm11111 fifivvvvm22222From momentum conservation aboveiifvmmmmvmmmv22121121122What happens when the two masses are the same?Monday, Oct. 25, 2004 PHYS 1443-003, Fall 2004Dr. Jaehoon Yu7Example for CollisionsA car of mass 1800kg stopped at a traffic light is rear-ended by a 900kg car, and the two become entangled. If the lighter car was moving at 20.0m/s before the collision what is the velocity of the entangled cars after the collision?ipThe momenta before and after the collision areWhat can we learn from these equations on the direction and magnitude of the velocity before and after the collision?m120.0m/sm2vfm1m2Since momentum of the system must be conservedfipp The cars are moving in the same direction as the lighter car’s original direction to conserve momentum. The magnitude is inversely proportional to its own mass.Before collisionAfter collisioniivmvm2211ivm220 fpffvmvm2211
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