Velocity is a relative quantity

Size: px

Start display at page:

Download "Velocity is a relative quantity"

Cori James
5 years ago
Views:

1 Veloci is a relaie quani

2 Disenangling Coordinaes PHY2053, Fall 2013, Lecure 6 Newon s Laws 2

3 PHY2053, Fall 2013, Lecure 6 Newon s Laws 3 R. Field 9/6/2012 Uniersi of Florida PHY 2053 Page 8 Reference Frames Consider wo frames of reference he O-frame (label eens according o,,,) and he O-frame (label eens according o,,,) moing a a consan eloci V, wih respec o each oher a le he origins coincide a 0. In he Galilean ransformaions he O and O frames are relaed as follows: Galilean Veloci Transformaion: V Een O: (,,,) O: (.,,) O O V V + V V + + ( 1 ) V V V Time is absolue Classical eloci addiion formula

4 Posulaes of Classical Phsics Firs Posulae of Classical Phsics ( Relaii Principle ): The basic laws of phsics are idenical in all ssems of reference (frames) which moe wih uniform (unacceleraed) eloci wih respec o one anoher. The laws of phsics are inarian under a change of inerial frame. The laws of phsics hae he same form in all inerial frames. I is impossible o deec uniform moion. O V O V Een O: (,,,) O: (.,,) Second Posulae of Classical Phsics (Galilean Transformaion): The O and O frame are relaed b he Galilean Transformaion. + V + V + V Classical eloci addiion formula R. Field 9/6/2012 PHY 2053 Page 9 PHY2053, Uniersi Fall of 2013, FloridaLecure 6 Newon s Laws 4

5 H-ITT Problem #1, 3 min Relaie Veloci 5

6 H-ITT Problem #1, 3 min Car A is driing 45 mph souh. Car B is driing 60 mph a 45º wes of souh. Wha is he magniude and direcion of he eloci of car A as seen b a passenger in car B? Direcion is epressed in angle wih respec o Eas. 1) BA 115 mph, direcion 50º 2) BA 115 mph, direcion 25º see 3) BA 100 mph, direcion 50º 4) BA 100 mph, direcion 25º 5) BA 85 mph, direcion 50 No alid soluion is lised. See following slides. PHY2053, Lecure 6, Newon s Laws 6

Broken up ino and componens, he wo eloci ecors are: ~ A [ 45 ŷ]mph ~ B [( 60 sin )ˆ +( 60 cos )ŷ]mph a Wha ecor calculaion do we wan o perform? We know he elociies of boh cars wih respec o he ground.

7 The problem is asking us o compue he magniude and direcion of a ecor. We know how o calculae hese quaniies if we know he and componens of a ecor: an a ~A a ˆ + a ŷ A ~ q a 2 + a 2 ; This means ha breaking he calculaion up b and componens will simplif soling he problem. Broken up ino and componens, he wo eloci ecors are: ~ A [ 45 ŷ]mph ~ B [( 60 sin )ˆ +( 60 cos )ŷ]mph a Wha ecor calculaion do we wan o perform? We know he elociies of boh cars wih respec o he ground. I hen makes sense o ake he reference frame fied o he ground o be he reference frame from which we are ransforming (O). We wan o know wha an obserer in car B would see. So, he reference frame of car B should be he reference frame ino which we are ransforming (O ). We defined he eloci ecor V as he eloci wih which reference frame O [car B] is moing when obsered from reference frame O[he ground], in oher words,. The relean eloci ransformaion formula is: ~V ~ B ~ A 0 ~ A V ~ hgien ~ A and V, ~ i compue ~ A. 0 PHY2053, Lecure 6, Newon s Laws 7

8 Haing broken down he elociies of car A and car B, we now do he calculaion of a b componens: ~ A 0 ~ A V ~ ~A ~ B [( 45 ŷ) [( 60 sin )ˆ +( 60 cos )ŷ]] mph [ 45 ŷ + 60 sin ˆ + 60 cos ŷ] mph [42.43 ˆ + ( ) ŷ] mph [42.43 ˆ 2.57 ŷ]mph. The magniude of he eloci wih which an obserer in car B sees car A moing (A ) is A 0 ~ A 0 hq i A, A, hp i mph mph The direcion angle can be compued from an 0 A, 0 A, an 1 0 A, A, 0 an mph mph an 1 ( 6.06) 6.05 rad 3.47 PHY2053, Lecure 6, Newon s Laws 8

9 PHY2053, LECTURE 6: Newon s Laws

10 PHY2053, Fall 2013, Lecure 6 Newon s Laws

11 Newon s Firs Law Law 1: Objecs in moion end o sa in moion, and objecs a res end o sa a res unless an ouside force acs upon hem. Noe - moion in his ranslaion implies moion wih a consan eloci along a sraigh line PHY2053, Fall 2013, Lecure 6 Newon s Laws

12 Eperimen Inerial ball

Newon s Second Law Law 2: The rae of change of he Le LAW II: II: Muaionem The aleraion mous of momenum of a bod is direcl proporionalem moion is eer proporional esse i morici o o he ne force

13 Newon s Second Law Law 2: The rae of change of he Le LAW II: II: Muaionem The aleraion mous of momenum of a bod is direcl proporionalem moion is eer proporional esse i morici o o he ne force impressae, he moie e force fieri impress d, secundum and acing on i, and he direcion of lineam is made recam in he direcion qua is illa of he he change in momenum akes imprimiur. righ line in which ha force is place in he direcion of he ne impress d. (ranslaion b Moe, 1792) force PHY2053, Fall 2013, Lecure 6 Newon s Laws

14 Force is a ecor quani Ne force Ne Force : For ssems wih consan mass, he rae of change of momenum is, so 2 nd Newon s law becomes: Mass [inerial] m is a proporionali consan beween force and acceleraion he proper of an objec o resis eloci changes PHY2053, Fall 2013, Lecure 6 Newon s Laws

15 Four Fundamenal Forces Elecromagneic Force elecrici, magneism, aoms, ligh Graiaional Force planes, galaies Weak Force nuclear deca - keeps he sars burning Srong Force proon, neuron PHY2053, Fall 2013, Lecure 6 Newon s Laws

16 PHY2053, Fall 2013, Lecure 6 Newon s Laws Normal Force No a fundamenal force Due o aomic srucure of eer-da objecs Objecs resis oher objecs ring o ener heir olume Couner-eamples: radiaion, (eoic) paricles Model wih a perfecl rigid, impenerable surface Surface eacl couners normal componen of conac force eered on i b an objec Eample: You are siing / sanding / no falling hrough he floor o he cener of he Earh righ now

17 Normal Force Eample: Incline The angle of he fricionless incline is α 30. Mass m 1 slides down he incline, saring from res. Wha is he speed of he mass afer i slid 10 meers downhill? [use g 10 m/s 2 ] PHY2053, Fall 2013, Lecure 6 Newon s Laws

Physics 101: Lecture 03 Kinematics Today s lecture will cover Textbook Sections (and some Ch. 4)

Physics 101: Lecture 03 Kinematics Today s lecture will cover Textbook Sections (and some Ch. 4) Physics 101: Lecure 03 Kinemaics Today s lecure will coer Texbook Secions 3.1-3.3 (and some Ch. 4) Physics 101: Lecure 3, Pg 1 A Refresher: Deermine he force exered by he hand o suspend he 45 kg mass as