Today: Falling. v, a

Today: Falling. v, a

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Physics of Free-fall Everyhing we ve already been doing, bu now in he verical direcion. Same equaions! Same graphing conceps! (Similar) problem-solving! Somehing in free-fall is only acceleraed by graviy. We re sill using 1d, bu now urning i in he verical direcion Definiion ime: Things freely falling can be going up or down. Pracice: 2.45, 2.47, 2.53, 2.59, 2.61, 2.63, 2.69, Muliple Choice 2.1

There s no air in his lecure! In our free-fall discussions we will assume here is no air resisance. Regarding his, here s a fundamenal BUT very common misconcepion o address firs. Which is ha: everyhing experiences he same amoun of acceleraion. Acceleraion implies change in velociy, so all hings have a velociy ha changes a he same rae. WHAT DOES THIS MEAN? When here s no air, HEAVIER THINGS DON T FALL FASTER!

There s no air in his lecure! Heavier hings DON T fall faser! (bu hings wih less air resisance do) In our free-fall discussions we will assume here is no air resisance. Regarding his, here s a fundamenal BUT very common misconcepion o address firs. Which is ha: everyhing experiences he same amoun of acceleraion. Acceleraion implies change in velociy, so all hings have a velociy ha changes a he same rae. WHAT DOES THIS MEAN? When here s no air, HEAVIER THINGS DON T FALL FASTER!

There s no air in his lecure! When Asronau David Sco dropped a feaher and a hammer on he moon, which hi he ground firs? Inroduce and show video This is also rue on Earh. DO DEMO. If you ake ou he air, everyhing falls a he same rae. The velociy of boh he penny and he feaher changes in he same way. So: ALL THINGS EXPERIENCE THE SAME ACCELERATION! David Sco hammer and feaher in a vacuum: hps://www.youube.com/wach?v=kdp1iuszw8

There s no air in his lecure! When Asronau David Sco dropped a feaher and a hammer on he moon, which hi he ground firs? Inroduce and show video This is also rue on Earh. DO DEMO. If you ake ou he air, everyhing falls a he same rae. The velociy of boh he penny and he feaher changes in he same way. So: ALL THINGS EXPERIENCE THE SAME ACCELERATION! David Sco hammer and feaher in a vacuum: hps://www.youube.com/wach?v=kdp1iuszw8

A simplifying assumpion Near Earh *, all objecs have he same consan acceleraion: g = 9.8 m/s 2 owards he cener of he Earh. *Laer we will consider exremely high aliudes (beyond amosphere) For he purposes of our work for mos of his course, his makes hings very easy: all hings are affeced by he same, consan, acceleraion. This is he acceleraion caused by he graviy of Earh, and i has a magniude of ~9.8 m/s2 TOWARDS THE CENTER OF THE EARTH. You saw his g in your homework.

0 v a +x v = v 0 + a Δx = v 0 + ½ a 2 v 2 = v 0 2 + 2aΔx Jus wan o insis how easy a ranslaion his should be for you. Ready? This is he only hing ha is changing.

Wai, wha?!? +x v a = -g = -9.8 m/s 2 0 v = v 0 + a Δx = v 0 + ½ a 2 v 2 = v 2 0 + 2aΔx Now he acceleraion is always consan We commonly call verical axis y, so you occasionally see, and in he book you will see, verical falling wrien like his. This is good pracice because in he nex weeks, we will discuss moion in boh he x and y direcion, so we will pracice doing his now. BIG THING TO NOTE: he magniude of he graviaional acceleraion is 9.8 m/s^2 bu he sign DEPENDS ON YOUR AXES!

Wai, wha?!? +y v a = -g = -9.8 m/s 2 0 v = v 0 + a Δy = v 0 + ½ a 2 v 2 = v 2 0 + 2aΔy Now he acceleraion is always consan We commonly call verical axis y, so you occasionally see, and in he book you will see, verical falling wrien like his. This is good pracice because in he nex weeks, we will discuss moion in boh he x and y direcion, so we will pracice doing his now. BIG THING TO NOTE: he magniude of he graviaional acceleraion is 9.8 m/s^2 bu he sign DEPENDS ON YOUR AXES!

Wai, wha?!? +x v a = -g = -9.8 m/s 2 0 v = v 0 + a Δx = v 0 + ½ a 2 v 2 = v 2 0 + 2aΔx Now he acceleraion is always consan We commonly call verical axis y, so you occasionally see, and in he book you will see, verical falling wrien like his. This is good pracice because in he nex weeks, we will discuss moion in boh he x and y direcion, so we will pracice doing his now. BIG THING TO NOTE: he magniude of he graviaional acceleraion is 9.8 m/s^2 bu he sign DEPENDS ON YOUR AXES!

Wai, wha?!? +y v a = -g = -9.8 m/s 2 0 v = v 0 + a Δy = v 0 + ½ a 2 v 2 = v 2 0 + 2aΔy Now he acceleraion is always consan We commonly call verical axis y, so you occasionally see, and in he book you will see, verical falling wrien like his. This is good pracice because in he nex weeks, we will discuss moion in boh he x and y direcion, so we will pracice doing his now. BIG THING TO NOTE: he magniude of he graviaional acceleraion is 9.8 m/s^2 bu he sign DEPENDS ON YOUR AXES!

+y v a = -g = -9.8 m/s 2 Cavea! The magniude of g is 9.8 m/s 2 bu he sign DEPENDS ON YOUR AXES! 0 v = v 0 + a Δy = v 0 + ½ a 2 v 2 = v 0 2 + 2aΔy +y If y poins down, a = +g If y poins up, a = -g +y BIG THING TO NOTE: he magniude of he graviaional acceleraion is 9.8 m/s^2 bu he sign DEPENDS ON YOUR AXES! This acceleraion always poins owards he Earh, so here a = -g

Velociy and Acceleraion Vecors v = + a = -g +y v = - a = -g Acceleraion is always owards Earh in free-fall 0 NOTE: If y axis were poining downward here, he signs of everyhing change! There s somehing I beg you o NOT OVERTHINK when you re wriing down he mah! This is: regardless of wheher you re on he upward or downward phase of he rip, acceleraion is always owards Earh. Everyone knows ha graviy never pushes hings upward, bu for some reason when we sar alking abou vecors people ge befuddled. Velociy vecors do wha hey do, bu graviaional acceleraion vecors alway poins downward.

No alking please! +y A 0 Q07 Wha is he velociy vecor a poin A? A. Posiive B. Negaive C. Zero Please don speak o your neighbor. Answer: C. Velociy ges smaller and smaller unil i his 0 and becomes negaive.

Le s ry i! You oss an orange and i reaches a heigh 10f above where you released i. How long does i ake o reach his heigh? 1 m = 3.28 f v = v 0 + a Δx = v 0 + ½ a 2 v 2 = v 0 2 + 2aΔx DID ON LIGHT BOARD. [soluion will be posed online]

Le s ry i! You oss an orange and i reaches a heigh 10f above where you released i. How long does i ake o reach his heigh? 1 m = 3.28 f v = v 0 + a Δx = v 0 + ½ a 2 v 2 = v 0 2 + 2aΔx DID ON LIGHT BOARD. [soluion will be posed online]

Q08 Which graph se represens he ball as shown below? +y Graphing free-fall A. B. +y +y +v +a +v +a 0 C. +y +v +a D. +y +v +a ANSWER: C. Please cha wih your neighbor. Le s ie his back o he las lecure and I wan you o ell me which graph corresponds o he moion of he ball. Things: NEGATIVE CONSTANT ACCELERATION (look a graphs).

No alking please! If you drop an objec in he absence of air resisance, i acceleraes downward a 9.8 m/s 2. If insead you hrow i downward, he magniude of is downward acceleraion afer release is A. less han 9.8 m/s 2. B. 9.8 m/s 2. C. more han 9.8 m/s 2. Q09 Answer: B.The acceleraion of graviy is a consan, independen of iniial velociy. You WILL run ino ricks like his in your homework and on es THINK and READ and DRAW if you need o!

y 10 5 y 2 = y v 1 o + oy 2 g vy = voy g 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0-5 -10-15 -20 v y 10 5 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0-5 -10-15 -20-25 Noe: y is a maximum a he same insan when v y = 0 These are no caroons. Here I ve acually ploed he moion equaions as y and v as a funcion of. Now I d like YOU o do a problem, and I s going o be a *concepual* problem.

y 10 5 y 2 = y v 1 o + oy 2 g vy = voy g 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0-5 -10-15 -20 10 5 2 a = 9.8 m/s v y 10 5 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0-5 -10-15 -20-25 Noe: y is a maximum a he same insan when v y = 0 a y (m/s 2 ) 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0-5 -10 Say i again: a y = -9.8 m/s 2 ALWAYS! (if +y up) -15 These are no caroons. Here I ve acually ploed he moion equaions as y and v as a funcion of. Now I d like YOU o do a problem, and I s going o be a *concepual* problem.

Concepual Problem A person sanding a he edge of a cliff hrows one ball sraigh up and anoher ball sraigh down a he same iniial speed. Neglecing air resisance, he ball o hi he ground below he cliff wih he greaer speed is he one iniially hrown v = v 0 + a Δx = v A. upward. 0 + ½ a 2 B. downward. v 2 = v 2 0 + 2aΔx C. neiher hey boh hi a he same speed. Q10 Answer: C. Upon is descen, he velociy of an objec hrown sraigh up wih an iniial velociy v is exacly v when i passes he poin a which i was firs released. You ll noice hese equaions keep showing up. You can be hey ll be on he es!!!

Concepual Problem A person sanding a he edge of a cliff hrows one ball sraigh up and anoher ball sraigh down a he same iniial speed. Neglecing air resisance, he ball o hi he ground below he cliff wih he greaer speed is he one iniially hrown v = v 0 + a Δx = v A. upward. 0 + ½ a 2 B. downward. v 2 = v 2 0 + 2aΔx C. neiher hey boh hi a he same speed. Jus because i s a concepual problem, doesn mean you can use a formula o help you hink abou i! Q10 Answer: C. Upon is descen, he velociy of an objec hrown sraigh up wih an iniial velociy v is exacly v when i passes he poin a which i was firs released. You ll noice hese equaions keep showing up. You can be hey ll be on he es!!!

Injury from Falling and/or a Collision When we hi a wall or he ground, acceleraion is, for a brief period, in he opposie direcion and much larger han our iniial acceleraion and velociy vecors.

Injury from Falling and/or a Collision I s no he falling ha hurs, bu he sopping. Skydiving a a = 9.8 m/s 2 is (more or less) healhy. When we sop, a is much more han 9.8 m/s 2 How do rea a problem wih 2 acceleraions? When we hi a wall or he ground, acceleraion is, for a brief period, in he opposie direcion and much larger han our iniial acceleraion and velociy vecors.

I assigned you a homework problem ha I hink is imporan for a lo of your careers and lives, especially he medical folks. I migh be a ad ricky so I waned o se i up for you so you undersand i. PADDED HELMETS no only sop your skull from cracking, bu also ease he acceleraion.

Large acceleraion causes raumaic brain injury. I assigned you a homework problem ha I hink is imporan for a lo of your careers and lives, especially he medical folks. I migh be a ad ricky so I waned o se i up for you so you undersand i. PADDED HELMETS no only sop your skull from cracking, bu also ease he acceleraion.

Large acceleraion causes raumaic brain injury. hp://www.ncbi.nlm.nih.gov/pmc/aricles/pmc155415/ Generally, an acceleraion less han 800 m/s 2 lasing for any lengh of ime will no cause injury, whereas an acceleraion greaer han 1000 m/s 2 lasing for a leas 0.001 seconds will cause injury. I assigned you a homework problem ha I hink is imporan for a lo of your careers and lives, especially he medical folks. I migh be a ad ricky so I waned o se i up for you so you undersand i. PADDED HELMETS no only sop your skull from cracking, bu also ease he acceleraion.

Acceleraing: a = -9.8 m/s 2 squishy surface Firs phase, he s in free fall.

Acceleraing: a = -9.8 m/s 2 squishy surface Phase 1 Firs phase, he s in free fall.

Deceleraing: a = Δv/Δ Iniial v=? Final v=0 squishy surface As soon as he his he surface, he s no longer in free-fall. He s going from an iniial velociy o a final velociy in a brief period of ime.

Deceleraing: a = Δv/Δ Iniial v=? Final v=0 squishy surface Phase 2: Coming o res over a given duraion and disance As soon as he his he surface, he s no longer in free-fall. He s going from an iniial velociy o a final velociy in a brief period of ime.