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by: Carlotta Dare DVM


Carlotta Dare DVM
GPA 3.68


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Class Notes
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This 6 page Class Notes was uploaded by Carlotta Dare DVM on Saturday September 12, 2015. The Class Notes belongs to Physics 3 at University of California - Irvine taught by Staff in Fall. Since its upload, it has received 41 views. For similar materials see /class/201926/physics-3-university-of-california-irvine in Physics 2 at University of California - Irvine.




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Date Created: 09/12/15
Physics 3A Energy 3980 far we have explored motion using velocity acceleration forces I Forces cause changes in motion gt accelerations which are changes in velocities IWe can apply another approach to motion which in many cases is much simpler than forces accelerations etc I This uses the concept of energy I It won39t tell us all the details but is still very useful ITo use energy we must separate the things we want to analyze from those outside that we don39t want to analyze I Define the System as being the things we want to study I A single object or particle I A collection of objects or particles I A region ofspace I It can vary in size and shape I Define the environment to be everything else outside the system Shoup 7 113 Physics 3A Energy IWork I We use the term work frequently in everyday life I In physics we de ne work differently and more precisely I Consider You just ran out of gas and have to push your car to t e gas station I Case 1 I You push your car with a force of 50 N for 100 m I Physics says you just did a signi cant amount of work 39 on the car I Case 2 I You push and push on your car with a 50 N force but the car never moves I Physics says you did zero work quoton the car even though you might have exerted a lot of effort Shoup 7 120 Physics 3A Energy 39Examples of systems and environments I Choice 1 I system is ball I environment is everything else I the environment in uences the system by the tension in the rope 8 by gravity I Choice 2 I system is the ball block rope and pulley I environment is everything else I so tension in rope is now an internal force not external I earth39s gravity in uences the system by external forces on both the block and ball smup7 119 Physics 3A Energy IIn physics we define work as for constant forces quotThe work done by an agent exerting a constant force on a system is the product ofthe component Fcos ofthe force along the direction of the displacement ofthe point of application of the force and the magnitude r of the displacementquot I in equation form W Arcos0 61 I some properties ofwork 2 2 I Dimensions ML T Units N In Joule J I Vector or scalar scalar I if component ofF in direction of displacement is zero then work is zero Sh up 7 m Physics 3A Energy 39Question Order the following situations in order of decreasing work done on block displacement is always to right F F L F a b C d c a d 1 zero work positive work negative work Shoup 7 12 Physics 3A Energy 39Work as a Scalar Product dot product I Recall the scalar product of two vectors A EEABCOSlB I From the previous de nition of work we can express it as the scalar product of the two vectors F and Ar as WEFAICOS0 64 Shoup 7 12 Physics 3A Energy 3915 work done by and if so is it positive or negative I You on a heavy box as you lift it Yes positive I Gravity on the box while you lift it Yes negative I Gravity on the box as you carry it No I You on the box as you carry it No I You on the box as you lower it to the ground Yes negative I Gravity on the box as you lower it to the ground Yes positive I Frictional force between a car39s tires and the road No on a car as it undergoes uniform circular motion Sh up 7 in Physics 3A Energy ISome properties of scalar product KEEABCOSW I commutative law I distributive law I unit vectors I Component form we 2 2 2 2 I Special case A A AxAvAI A Sh up 7 us Physics 3A Energy IEquation 61 is only valid if the force is constant 39What are some situations where the force is not constant m 1 z I Gravity Fg kg 11qu I I Electrostatic force Fe I Springs Fykx IIn these situations we need to extend our mathematics 39Consider Fx on a block moving in xedirection Shoup 7 us Physics 3A Energy IWe can generalize further to case where force and displacement are not parallel I can break into x 8 yif convenient WWXWy 1 V wxj Fx dx wyj Fyldy x V INote IfW is to be the total work done then F in above is the resultant net force ICan compute work done by individual forces as well snoup7iza Physics 3A Energy IWe break motion into tiny pieces where force is almost constant W1FXAX x v ISum up all pieces WNZ FKAX 1 x K ITake the limit as AX goes to zero W lim 2 FxAxfodx Axm Kl Kl Sh up 7 127 Physics 3A Energy 39Example I Consider case of a block attached to a spring horizontally I de ne x0 when spring not compressed or stretched equilibrium I pull block to right stretches spring and spring pulls to left I pull block to left compresses spring and spring pushes to right I spring force always forces block back to equilibrium position I thus spring force is called a restoring force I measurements show that if displacement x is small force is 613 k gt spring constant or force constant Sh up 7 129 Physics 3A Energy 39Lets compute the work done by spring on block as it moves from 7x to O max Shoup 7 130 Physics 3A Energy Lets look at how the work done on an object changes the object39s motion 39 This approach will allow us to solve problems easily which would have been hard using Newton39s second law Consider a block moving horizontally with a net horizontal force o ifo Xfixl then the r work is waffzmx 39 We can use Newton39s 2 1 law to replace 2F ma xl Shoup 7 13 Physics 3A Energy For an arbitrary move from xl to xi we get x 71 quot 1 1 wsxl rkxdx17kxllx4 kx kxh 39What work do we do to stretch a spring 39 assume no acceleration thenF iF App 5 39 SO km was Fwdx CI a smupr 131 Physics 3A Energy 39But a dvdt so A x39 dv x39 dv dx Wnctxfma dx Wnct ni tdxVWHCE WEde V 1 z 1 z 1 z W mvdv mv mv 7 mv f net J llz 2 r 2 1 v39 dx WMF imEdv 617 IWe de ne 12 mv2 as the kinetic energy ofthe block 618 Sh upr l Physics 3A Energy 3980 now we see that the net work done on an object goes into changing the object39s kinetic energy K 619 Kmvz amp Kfmvf This is called the workkinetic energy theorem quotWhen work is done on a system and the only change in the system is in its speed the work done by the net force equals the change in kinetic energy of the systemquot 39 Note Ifwork done is positive kinetic energy increases and so does speed If work done is negative kinetic energy decreases and so does speed 39 Also note that this only involves scalars not vectors 3 m aoupr Physics 3A Energy Nonisolated Systems I Any system which is quotin uencedquot by its environment Examples 39 Book pushed on a table 39 Pencil picked up by you after you drop it Here the quotin uencequot causes a change in the system 39 In our current context the change in the system is its quotenergyquot energy is either transferred into or out of the system 39 This transfer of energy is the work done on the system I We can expand our concept of the system39s energy from just kinetic energy to include both kinetic and internal energy 39 nternal energy 7 related to system39s temperature it is motion of system39s quotinternal partsquot shoup7ias Physics 3A Energy 3But wait Is the workkinetic energy theorem always valid Consider book sliding across a table with friction 39 Frictional force does work on book changing its kinetic energy 9 But doesn39t friction also do work on the table Does the table39s kinetic energy change smup7 13 Physics 3A Energy 3980 system39s energy now is Em Internal Energy K Kinetic Energy For nonisolated systems energy can be transferred into or out of the system by the environment 39 Types of energy transfers are Wor Pushing your out7of7gas car 39 Mechanical waves 7 propagation ofa disturbance in a media 5 h as air or water sound waves from your radio transferring energy into your ear 39 Heat 7 transfer ofinternal energy Placing your hand on the campfire to see if it is hot I Matter transfer 7 matter crosses the system boundary quotfuelquot into your car or quotexhaustquot out of a rocket Electrical transfer 7 electrical current owing from your kitchen wall outlet into your nger 39 Electromagnetic 7 radio waves received from local statiggr m up Physics 3A Energy 39Once we include internal energy and other forms of energy transfer can revive the quotworkekinetic energy theoremquot into the concept of quotConservation of Ener Energy cannot be created or destroyed it can only change forms or be transferred into or out of a system ie 39 where 2H is the sum of all the ways energy can be transferred into or out of the system EHWQH H H H MW MT Er It wor heat electromagnetic h 1 radiation mec amca mass electrical wave tranSfer transmission WNW Physics 3A Energy 39Using the above equations substitute into 621 Vf Vl Axvlvft t K f AxrnaA xfgtkaxmVV kaxm VF VVVf4 f AxlmV vflmv lmvfAK 2 2 2 622 VVft Sh up 7 14a Physics 3A Energy 39We said that frictional forces can change the internal energy of a a system and the quotoldquot workekinetic energy theoremquot doesn39t hold 39Lets see how to relate a frictional force to this change in energy Consider the book sliding across a table aApply Newton39s 2 1 law fkrna multiplybyAx kaXInaAx 39From chapter 2 1 a VFV AX VVft t smuprm Physics 3A Energy 39Ifother forces also act on the book then 623 39Now consider the book and the table as the system 39 no external forces do any work on the system and so 2H O in 620 8 so A KA Emt 0 kaxAEm0 624 The kinetic frictional force transforms kinetic energy into internal energy Shoup 7 m


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