PHYS 1443 – Section 003 Lecture #15PowerLinear Momentum and ForcesConservation of Linear Momentum in a Two Particle SystemImpulse and Linear MomentumExample for ImpulseExample for ImpluseCollisionsExample for CollisionsElastic and Inelastic CollisionsElastic and Perfectly Inelastic CollisionsTwo dimensional CollisionsExample of Two Dimensional CollisionsCenter of MassCenter of Mass of a Rigid ObjectWednesday, Oct. 22, 2003 PHYS 1443-003, Fall 2003Dr. Jaehoon Yu1PHYS 1443 – Section 003Lecture #15Wednesday, Oct. 22, 2002Dr. Jaehoon Yu1. Impulse and Linear Momentum2. Collisions3. Two dimensional collisions4. Center of Mass5. Motion of a group of particlesRemember the 2nd term exam (ch 6 – 11), Monday, Nov. 3!Homework #8 is due noon, next Wednesday, Oct. 29!Remember the colloquium at 4:00pm today in Rm 103!!!Wednesday, Oct. 22, 2003 PHYS 1443-003, Fall 2002Dr. Jaehoon Yu2Power•Rate at which work is performed–What is the difference for the same car with two different engines (4 cylinder and 8 cylinder) climbing the same hill? 8 cylinder car climbs up fasterIs the amount of work done by the engines different? NOThen what is different? The rate at which the same amount of work performed is higher for 8 cylinder than 4.Average power tWPdtdWtWPt 0limInstantaneous power Unit? / WattssJ WattsHP 7461 What do power companies sell? Energy JsWat tskWH6106.3360010001 sdtdFvFcosFvWednesday, Oct. 22, 2003 PHYS 1443-003, Fall 2002Dr. Jaehoon Yu3Linear Momentum and ForcesWhat can we learn from this Force-momentum relationship?Something else we can do with this relationship. What do you think it is? vmdtddtpdF The relationship can be used to study the case where the mass changes as a function of time.Can you think of a few cases like this?Motion of a meteoriteMotion of a rocket •The rate of the change of particle’s momentum is the same as the net force exerted on it.•When net force is 0, the particle’s linear momentum is constant as a function of time.•If a particle is isolated, the particle experiences no net force, therefore its momentum does not change and is conserved.Wednesday, Oct. 22, 2003 PHYS 1443-003, Fall 2002Dr. Jaehoon Yu4Conservation of Linear Momentum in a Two Particle SystemConsider a system with two particles that does not have any external forces exerting on it. What is the impact of Newton’s 3rd Law?Now how would the momenta of these particles look like?If particle#1 exerts force on particle #2, there must be another force that the particle #2 exerts on #1 as the reaction force. Both the forces are internal forces and the net force in the SYSTEM is still 0. Let say that the particle #1 has momentum p1 and #2 has p2 at some point of time.Using momentum-force relationship 121dtpdF And since net force of this system is 0constpp 12ThereforeFThe total linear momentum of the system is conserved!!!dtpdF212and2112FF dtpddtpd12 12ppdtd0Wednesday, Oct. 22, 2003 PHYS 1443-003, Fall 2002Dr. Jaehoon Yu5Impulse 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. dtpdF Net force causes change of momentum Newton’s second lawSo what do you think an impulse is?fittpdpdtFIfittWhat are the dimension and unit of Impulse? What is the direction of an impulse vector? Defining a time-averaged force fittdtFtF1Impulse 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.dtFpd pppiffittdtFWednesday, Oct. 22, 2003 PHYS 1443-003, Fall 2002Dr. Jaehoon Yu6Example for ImpulseA golf ball of mass 50g is struck by a club. The force exerted on the ball by the club varies from 0, at the instant before contact, up to some maximum value at which the ball is deformed and then back to 0 when the ball leaves the club. Assuming the ball travels 200m, estimate the magnitude of the impulse caused by the collision. RThe range R of a projectile isConsidering the time interval for the collision, ti and tf , initial speed and the final speed areLet’s assume that launch angle i=45o. Then the speed becomes:collision) thebeforely (immediate 0ivmBvBsmgvB/441960200 Therefore the magnitude of the impulse on the ball due to the force of the club isIcollision) after thely (immediate/44 smvfpBiBfmvmv smkg /2.24405.00 mgvBB2002sin2Wednesday, Oct. 22, 2003 PHYS 1443-003, Fall 2002Dr. Jaehoon Yu7Example for ImpluseIn 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 Wednesday, Oct. 22, 2003 PHYS 1443-003, Fall 2002Dr. Jaehoon Yu8Collisions Consider a case of a collision between a proton on a helium ion. The collisions of these ions never involves a 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.fittdtFp211tFF12F21Assuming no external forces,
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