nnouncements: Today HW#3 due by 8:00 am Wednesday Exam #1 on Thusday /11 No class on Thusday /4 Taveling a Poblem fom HW# Gavity The Newtonian Woldview Vectos (Hints fo the boat poblem) ISP09s10 Lectue 5-1- Homewok Poblem Taveling a 1st sketch the speed vs. time gaph Then, use the speed gaph to sketch the acceleation vs. time gaph ISP09s10 Lectue 5 -- Homewok Poblem Taveling a Homewok Poblem Taveling a The egions in ed have a constant slope (ate of change) ISP09s10 Lectue 5-3- Regions,,, each have constant velocity, hence zeo acceleation ISP09s10 Lectue 5-4-
Homewok Poblem Taveling a Homewok Poblem Taveling a Looking at the slopes (no need to calculate), we In the black elbow egions, the slope itself changes fom point-to-point. Thee is non-zeo acceleation have V < V < V <V ISP09s10 Lectue 5-5- ISP09s10 Lectue 5-6- Homewok Poblem Taveling a Homewok Poblem Taveling a Slowing own Slowing own Speeding up Speeding up In the black elbow egions, the slope itself changes fom point-to-point. Thee is non-zeo acceleation ISP09s10 Lectue 5-7- The fist elbow is shape than the second one. I.e., its slope is changing faste as you go aound the bend. ISP09s10 Lectue 5-8-
Homewok Poblem Taveling a Slowing own Speeding up Theefoe, the magnitude of acceleation in the fist elbow is GRETER than that of the nd elbow. ISP09s10 Lectue 5-9- Histoy of astonomy in 1 slide Ptolomy: Eath-centeed model of the motion of planets that woked well enough using epicycles. openicus: 1st Sun-centeed model **. Much simple than Ptolomy s w/equal accuacy ** In 300., istachus had the same idea! ahe: geatly impoved accuacy of measuements and thus showed deficiencies in pevious models Keple: devised his thee laws of planetay motion with the Sun at the cente but discaded pevious assumptions (e.g., cicula obits, constant speed) Newton: unified Keple s Planetay Motion w/his Univesal Law of Gavitation (along w/ eathly motion like falling apples) ISP09s10 Lectue 5-10- Newton s Univesal Law of Gavity pplies to any objects w/mass (Univesal) Gm m F =! 1 ; G = 6.673E 11 Nm kg The Law of Gavity What is the foce of gavity on a 90 kg pofesso standing on the suface of the Eath? Gm m F =! 1 ; G = 6.673E 11 Nm kg is the distance sepaating the centes of the two masses Stange because the objects aen t touching WHY? HOW? ISP09s10 Lectue 5-11- e ISP09s10 Lectue 5-1-
The Law of Gavity What is the foce of gavity on a 90 kg pofesso standing on the suface of the Eath? Gmpm F = ' Nm $ % 6.673E ( 11 " 90kg! 5.974E4kg & kg = # e = e ( 6.378E6 m) 88 N Weight and Gavity Wait a second! Last class, you told us that an object s weight On the suface of the eath was given by: F gavity = w = mg (whee g = 9.8 m/s ) ut in the pevious poblem we used a diffeent equation! ata: eath = 6.378E+6 m, m eath = 5.974E+4 kg The pofesso exets the same 88 N foce on the eath. That is Newton s thid law. Recall, the foce of gavity on the pofesso is called his Weight ISP09s10 Lectue 5-13- Nothing ticky. Plug in values fo Gm e / e gives 9.8 m/s ISP09s10 Lectue 5-14- Two examples using the Law of Gavity What would happen if the adius of the Eath wee doubled, but the mass was the same? Foce of gavity on an astonaut What is the foce if the 90 kg pofesso is in the space shuttle at 300 km above the Eath? Gm m Gm m e p e p F = = =! ( e ) 4( e ) 4 1 ISP09s10 Lectue 5-15- F e obit Same as befoe, but now we use R = eath + obit in the eqn. whee obit = distance above eath ISP09s10 Lectue 5-16-
Foce of gavity on an astonaut What is the foce if the 90 kg pofesso is in the space shuttle at 300 km above the Eath? 1000m 300 km = 300km! = 3.00E5 m km ' 6.673E 11Nm $ 90kg! 5.974E4kg Gmem % ( p kg " F = = & # = e ( 6.378E6 m + 3.00E5 m) e + obit 804 N Weid! Why ae the astonauts in the pictue floating if thei Weight is not zeo? ISP09s10 Lectue 5-17- nswe to the iddle stonauts obiting the eath ae actually in fee-fall. Like this poo fellow in the falling Elevato! In both cases, you would feel weightless, but gavity Is still acting on you (and weight is defined as the Gavitational foce acting on you). ISP09s10 Lectue 5-18- n answe to anothe iddle F Gavity = mg (mass & adius of Eath ae inside the g) lso F Gavity = ma gavity by Newton s nd Law. Theefoe, neglecting othe foces like ai esistance mg = ma gavity Note how the m cancels out, ie. a gavity = g This is why a tennis ball falls at the same ate as a bowling ball! ISP09s10 Lectue 5-19- Pe-Newtonian Philosophy and Science efoe the Newtonian ea, the Westen woldview was a combination of medieval histianity, eath-centeed astonomy, and istotle s physics. ll wee believed to act togethe, as humankind fulfilled the pupose of eation. Eath and humans ae special (diffeent fom othe planets and species) since God ceated them. ISP09s10 Lectue 5-0-
Newtonian View of the Univese Natue was thought to be 100% undestood The Mechanical Univese o Eveything is Pedictable Suppose we know the positions and velocities of evey atom in the univese at some instant ccoding to Newton s laws of motion, the futue behavio of the univese can be exactly pedicted fo all time. If thoughts and feelings ae educible to the motion of the atoms in ou bains, it follows that all futue thoughts, feelings, and actions ae entiely pedetemined and pedictable! Loss of fee will Fom 1894: "The moe impotant fundamental laws and facts of physical science have all been discoveed, and these ae now so fimly established that the possibility of thei eve being supplanted in consequence of new discoveies is exceedingly emote... Ou futue discoveies must be looked fo in the sixth place of decimals." - lbet.. Michelson, speech at the dedication of Ryeson Physics Lab, U. of hicago 1894 cold, clockwok univese Natual Law and democacy ISP09s10 Lectue 5-1- The Quantum and Relativistic Revolutions ISP09s10 Lectue 5 -- The Quantum and Relativistic Revolutions Just when many thought thee was nothing else to discove thanks to Newton s theoies Evidence stats to emege that Newtonian Physics fails in cetain situations: 1) ) 3) 4) Fom 1900: "Thee is nothing new to be discoveed in physics now. ll that emains is moe and moe pecise measuement" - Lod Kelvin High Speeds Tiny distances Huge distances Huge masses The Newtonian Univese is only an appoximation. Reality is much stange as we will see ISP09s10 Lectue 5-3- ISP09s10 Lectue 5-4-
Hints fo the boat poblem Vecto ddition and Subtaction Questions like: What diection of owing cosses the ive in the shotest time? Rowing in iection is longe/shote/the same time as Rowing in iection K, etc ISP09s10 Lectue 5-5- ddition Subtaction ISP09s10 Lectue 5-6- Example of the use of vectos How long to coss the ive? Rive Rive Rive Rowing velocity ctual Velocity Rowing velocity distance acoss the ive time = owing speed ctual Velocity Velocity of steam ISP09s10 Lectue 5-7- Velocity of steam The owing speed is the magnitude of the component of the boat s total velocity that is diected towad the opposite bank. ISP09s10 Lectue 5-8-
Vectos Vectos ae want to be ae ive want to be K ISP09s10 Lectue 5-9- ISP09s10 Lectue 5-30- Vectos Vectos ae ive want to be Which way will get you acoss the ive in the quickest time, the Red o lue choice? ISP09s10 Lectue 5-31- ISP09s10 Lectue 5-3-
Vectos distance acoss the ive time = owing speed Noth The owing speed is the magnitude of the component of the boat s total velocity that is diected towad the opposite bank (I.e., East). East ISP09s10 Lectue 5-33-