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# MECHANICS PHYS 218

Texas A&M

GPA 3.77

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This 36 page Class Notes was uploaded by Miss Elbert Nader on Wednesday October 21, 2015. The Class Notes belongs to PHYS 218 at Texas A&M University taught by Rupak Mahapatra in Fall. Since its upload, it has received 23 views. For similar materials see /class/225900/phys-218-texas-a-m-university in Physics 2 at Texas A&M University.

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Date Created: 10/21/15

Physucs 218 Chapter 10 Prof Rupak Mahapa39l39r39a Chapter 10 Momentum Want to deal with more complicated sys l39ems Collisions Explosions Newton39s laws still work but we need some new ideas Physics 218 Lecture XVI 2 Today39s Lecture Different style than in The Textbook Begin with a definition of Linear Mame1 fum Then show 39l39ho39l39 conserva on of momem um helps us solve cer39l39oin Types of problems 771th colliding Thin 5 ex loa ina Physics 218 Lecture XVI 3 Definition of Linear Momentum Vector equation gt P ml system Physics 218 Lecture XVI 4 Resfm ing Newton39s Second Law quotThe rare of change of momenfum of an objecf is equal fa fhe nef force appfed f0 if 2F Do a check for cansfanf mass d3 dmV df df m m5 If we CXCI39I u nef force on a body fhe momenfum of fhe body changes Whaf if ZF0P If SF0 Then dpdf 0 p cons ran39r Mame7 fum does7 139 change v I I I momentum before momentum offer Physics 218 Lecture XVI 6 Conservation of Momentum orasgsem y Newto39s laws F0 Conserva an of Momen rum I Z I I l i Sum of all Sum of all momentum before momentum after True in X and Y directions separately Physics 218 Lecture XVI b39 an For Conservation of Momentum problems 1 BEFORE and AFTER 2 Do X and Y Separa39l39ely Physics 218 Lecture XVI 8 So who 7 Momentum is useful when we don39t know anything about the forces Examples from everyday life When ice ska ting if you push someone why do you go backwards Why does a gun recoil when you shoot if Physics 218 Lecture XVI 9 E Verj do EX erience Question Why do you go backwards when ou ush someone on fhe ice Newton39s Law39s answer When you exert a force on another person then by Newton39s law The person exerts an equal and opposite force on you Physics 218 Lecture XVI 10 Ever do Ex erience Cont Question Wh do you go backwards 14 en you push someone on the ice Momentum Conservation Answer Before The system starts with zero momentum nobody is moving After The system ends with zero momeh tum you and your friend move 11 030051 te direc tons Physics 218 Lecture XVI 11 im le Gun Exam le A gun of mass M5 is sitting at rest with a bullet of mass MB inside it You shoot the gun and the bullet comes out with a speed V at angle 0 hat is the recoil velocif o the gun Physics 218 Lecture XVI 12 Weird example Ball of mass m is dropped from a heigh l 1 Whaf 12 fhe momen fum before release Whaf 12 fhe momen fum before if hifs fhe ground Is momen fum conserved Physics 218 Lecture XVI 13 What if we add The Earth What 1339 fhe force on fhe ball Whaf 129 the force on the earfh Is fher39e any nef force in 1129 sysfem Z39s momen rum conserved Physics 218 Lecture XVI 14 Momentum for a system is Conserved Momentum is AL WAYS conserved for o SYSTEM you just have to look at a big enough system to see it correctly Not conserved tor a single boll A ball falling is not a big enough system You need to consider what is making it fall Newton39s Law For every acfian there is an equal and opposite reacfian Add up all the momentums in the problem The forcg39 and the forcee Physics 218 Lecture XVI 15 Energy and Momentum in Collisions Definitions 33 2 6 Elos c collision kine l39ic a Approach energy is conserved Inelastic collision kinetic energy is n01 conserved b C0111s10n L03 Ee Vi Momenfum conserved anemic Tofa Energy conserved I I V40 912 d If inelastic Physics 218 Lecture XVI 16 Inelastic Collisions B deinition Inelastic mechanical energy not conserved kinetic energy not conserved Inelastic Example Two trains which collide and stick together Physics 218 Lecture XVI 17 Colliding Trains 1 Dimension The train car on the lefEl39 mass m1 is moving with speed V0 when it collides with a stationary car of mass mg The two stick together 1 Whaf 12539 fheir speed affer fhe cal1251b 2 Is it elastic collision Show your work u 1 ii 1 b Aftercollislon Physics 218 Lecture XVI 18 Ballistic Pendulum A bullet of ma veloci l39y Va plows info a block of wood with mass M which is par l39 of a pendulum Is fhe collision or inelas c How high I block of woar M Physics 218 Lecture XVI 19 Bottom line When to use Momentum When you do39 forces in the system When you are studying all of the pieces of the system which are doing the or39cind Before and After Problems Physics 218 Lecture XVI 20 Head On Collision A ball of mass m1 collides head on elasTically wiTh a second ball aT r39esT and rebounds goes in The opposiTe direcTion wiTh speed equal To of iTs original speed WhaT is The mass of The second ball m2 Physics 218 LecTure XVI 21 Two Balls Collide Two billiard balls of equal and known mass m are Traveling with known velocities V1 and V2 They collide elastically What are the velocities after the collision Physics 218 Lecture XVI 22 A Ball collides with o Stationary We have two billiard balls ofdiffer39ent and known masses m1 and ma Ball one is Traveling with known velocity V1 They collide elastically What are the velocities after the collision Physics 218 Lecture XVI 23 Pla39 in Pool 2 Dimensions Before the collision ball 1 moves with y speed V1 in the x direction while ball 2 is at rest Both have equal mass After the collision the balls go off at angles 9 and What are v 1 and v 2 aftrth lliinr Physics 218 Lecture XVI Quiz Particle Collision A Proton traveling W1 velocity v1 knocks out a neutron from a stationary target A set of springs ks are arranged at 10degree intervals to be used as detectors The proton is observed to snow up on a spring at an angle 01 degrees and compresses the spring by an amount d1 Determine the which spring angle on the lower right hand quadrant will see the neutron and how much the compression will be Assume elastic collision y Lx Physics 218 Lecture XVI 25 Cem er of Mass CMV What is The C39em er of Mass More impor39l39arrl39ly quotWhy do we care Ims IS a specual pomT In space where quotifis as if fhe objecf could be replaced by all fhe mass af fhaf one liffe poim Physics 218 Lecture XVII 26 CenTer of Mass CMV ConT Examples where This is useful We can model The earTh moving around The sun as a sinle oinT aT quotThe cen fer of The earfh AT some le been assuming These Things for doing problems all semesTer Physics 218 LecTure XVII 27 Center of Mass CM Cont Yet another example there are only a couple of points on a ruler that you can put your finger under and hold it up Your finer rovides the normal force Physics 218 Lecture XVII 28 Visual Examples The center of mass hs The serge Trajectory as a point since both have The same OCCZIZI OTIOH O d I ITIOI VZIOCITY I HYSICS 16 LCCTLIF39C AVLJ as How do you calculate CM 1 Pick an origin 2 Look at each piece of massquot and figure out how much mass it has m how far it is vector displacement from the origin Take mass times position 3 Add them all up and divide out by the sum of the masses The center of mass is a displacement vector 39t39eafgve f0 someIoryh hysics 218 Lecture XVI S ellin out The math X mjxj mgx2 cm for 2 parfIces m m2 X mjxj max m3x3 cm for 3 parfices m mg m3 efc No fe fhaf A7 is fhe 3 D vecfor a IZS39pacemmf Physics 218 Lecture XVII 31 ZD Example Three balls wi39l39h masses m 2 and m3 are CIIEe loaded 0139 39I h poin39l39s given to 39l39he righ l Where 129 fhe cem er of 39 Physics 218 Lecture XVII 32 0 wmf 2 wazs to solve collisionexplosion pro lems 1 Conservation of Momentum in all directions 2 WaTChll39Ig the center or Mass Need to be able to do both Pick easier method Physics is the same Physics 218 Lecture XVII 33 Two balls in ouTer space Two balls are moving in ouTer space They have known mosses 2M and 3M and speeds 4V and 2V respectively and They collide IT The origin The directions are as shown in The figure AfTer The collision The Two balls sTick TogeTher and form a blob Whaf is The final velocify of The blob y Speed 4V i nore rovi I PX 9 9 W peed 2v Physics 218 LecTure XVII 34 Toy Rocket Problem Your friend fires a toy rocket into the air with an unknown velocity You observe that at the peak of its trajectory It has traveled a distance d in the X direction It then breaks into two e Vual mass 7 ieces Part I falls straii ht down with no initial velocity Where does 72 23974 haf of 72 fay end up Two Balls in Two Dimensions Before a collision ball 1 moves with y speed V1 in the x 1 direction while ball x I 2 is at rest Both V 0 have the same mass Q 1gt f I After the collision the balls 90 off at angles and Q V392 Whaf are the veloci es V391 and VIZ affer the collision Physics 218 Lecture XVII 36

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