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UT Arlington PHYS 1441 - Lecture Notes

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PHYS 1441 – Section 501 Lecture #10Energy Diagram and the Equilibrium of a SystemGeneral Energy Conservation and Mass-Energy EquivalencePowerEnergy Loss in AutomobileLinear MomentumLinear Momentum and ForcesLinear Momentum ConservationConservation of Linear Momentum in a Two Particle SystemMore on Conservation of Linear Momentum in a Two Particle SystemExample for Linear Momentum ConservationImpulse and Linear MomentumExample 7-5Example 7-5 cont’dExample for ImpulseCollisionsElastic and Inelastic CollisionsElastic and Perfectly Inelastic CollisionsExample for CollisionsTwo dimensional CollisionsExample of Two Dimensional CollisionsCenter of MassSlide 23Center of Mass of a Rigid ObjectExample 7-11Example for Center of Mass in 2-DMotion of a Diver and the Center of MassCenter of Mass and Center of GravityMotion of a Group of ParticlesMonday, July 5, 2004 PHYS 1441-501, Summer 2004Dr. Jaehoon Yu1PHYS 1441 – Section 501Lecture #10Monday, July 5, 2004Dr. Jaehoon Yu•Energy Diagrams•Power•Linear Momentum & its conservation•Impulse & Collisions•Center of Mass •CM of a group of particlesRemember the second term exam, Monday, July 19!!Monday, July 5, 2004 PHYS 1441-501, Summer 2004Dr. Jaehoon Yu2Energy Diagram and the Equilibrium of a SystemOne can draw potential energy as a function of position  Energy DiagramsULet’s consider potential energy of a spring-ball systemA ParabolaWhat shape would this diagram be? xUs-xmxm221kxU What does this energy diagram tell you?1. Potential energy for this system is the same independent of the sign of the position. 2. The force is 0 when the slope of the potential energy curve is 0 at the position.3. x=0 is the stable equilibrium of this system where the potential energy is minimum.Position of a stable equilibrium corresponds to points where potential energy is at a minimum. Position of an unstable equilibrium corresponds to points where potential energy is a maximum. Minimum Stable equilibrium Maximum unstable equilibrium 221kxMonday, July 5, 2004 PHYS 1441-501, Summer 2004Dr. Jaehoon Yu3General Energy Conservation and Mass-Energy EquivalenceGeneral Principle of Energy ConservationThe total energy of an isolated system is conserved as long as all forms of energy are taken into account.Friction is a non-conservative force and causes mechanical energy to change to other irreversible forms of energy.What about friction?Principle of Conservation of MassEinstein’s Mass-Energy equality.However, if you add the new forms of energy altogether, the system as a whole did not lose any energy, as long as it is self-contained or isolated.In the grand scale of the universe, no energy can be destroyed or created but just transformed or transferred from one place to another. Total energy of universe is constant.In any physical or chemical process, mass is neither created nor destroyed. Mass before a process is identical to the mass after the process.2mcERHow many joules does your body correspond to?Monday, July 5, 2004 PHYS 1441-501, Summer 2004Dr. Jaehoon Yu4Power•Rate at which work is done–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 total 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 WPtD=DP �Instantaneous power Unit? / WattssJ WattsHP 7461 What do power companies sell? Energy 1kWH =0limtWtD �D=D0lim costsFtqD �D=D�rurcosF v q�ur r61000 3600 3.6 10Watts s J� = �Monday, July 5, 2004 PHYS 1441-501, Summer 2004Dr. Jaehoon Yu5Energy Loss in AutomobileAutomobile uses only at 13% of its fuel to propel the vehicle. Why?67% in the engine: 1. Incomplete burning2. Heat 3. Sound13% used for balancing energy loss related to moving vehicle, like air resistance and road friction to tire, etcTwo frictional forces involved in moving vehiclesP =1450carm kg=Coefficient of Rolling Friction; =0.01616% in friction in mechanical parts4% in operating other crucial parts such as oil and fuel pumps, etcAir Dragartfff 222647.02293.15.02121vvAvDfaTotal ResistanceTotal power to keep speed v=26.8m/s=60mi/hPower to overcome each component of resistancerP = kWvfPaa5.128.267.464 Weight =227n mg Nm m= =tf v =( )691 26.8 18.5N kW� =rf v =( )227 26.8 6.08kW� =14200mg N=Monday, July 5, 2004 PHYS 1441-501, Summer 2004Dr. Jaehoon Yu6Linear MomentumThe principle of energy conservation can be used to solve problems that are harder to solve just using Newton’s laws. It is used to describe motion of an object or a system of objects.A new concept of linear momentum can also be used to solve physical problems, especially the problems involving collisions of objects.vmp Linear momentum of an object whose mass is m and is moving at a velocity of v is defined as 1. Momentum is a vector quantity.2. The heavier the object the higher the momentum3. The higher the velocity the higher the momentum4. Its unit is kg.m/s What can you tell from this definition about momentum?What else can use see from the definition? Do you see force?The change of momentum in a given time intervalptD=Dur0mv mvt-=Dr r( )0m v vt-=Dr rvmtD=DrF�urma =rMonday, July 5, 2004 PHYS 1441-501, Summer 2004Dr. Jaehoon Yu7Linear 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?pFtD=D�ururThe 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.Monday, July 5, 2004 PHYS 1441-501, Summer 2004Dr. Jaehoon Yu8Linear Momentum Conservation221121vmvmppii'22'1121vmvmppffMonday, July 5, 2004 PHYS 1441-501, Summer 2004Dr. Jaehoon Yu9Conservation 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


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UT Arlington PHYS 1441 - Lecture Notes

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