PHYSICS 149: Lecture 9

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1 PHYSICS 149: Lecure 9 Chaper Velociy and Acceleraion 3.3 Newon s Second Law of Moion 3.4 Applying Newon s Second Law 3.5 Relaive Velociy Lecure 9 Purdue Universiy, Physics 149 1

2 Velociy (m/s) The average velociy is he change in posiion (vecor) divided by he change in ime. x() v Δr x x = = f Δ f 0 0 Insananeous velociy is he limi of average velociy as ges small. I is he slope of he x() plo. v = lim Δ 0 Δ r Δ x() Lecure 9 Purdue Universiy, Physics Δ Δx

3 ILQ 1 A go-kar ravels around a circular rack a a consan speed. Which of hese is a rue saemen? (a) The go-kar has a consan velociy. (b) The go-kar has zero acceleraion. A) Boh (a) and (b) are rue B) Neiher (a) nor (b) is rue C) (a) D) (b) Lecure 9 Purdue Universiy, Physics 149 3

4 ILQ 2 If he average velociy of a car during a rip along a sraigh road is posiive, is i possible for he insananeous velociy a some ime during he rip o be negaive? A - Yes correc B - No The car migh have reversed If he car is raveling in a for a lile while along he rip sraigh pah he velociy creaing a negaive will always be posiive. insananeous velociy a he The car needs o ravel in poin. If he overall he opposie direcion o displacemen of he car is ge a negaive velociy. posiive for ha paricular ime inerval, han he average velociy is posiive as well. Lecure 9 Purdue Universiy, Physics 149 4

5 How o deermine x from v() The oal displacemen x during and ime is he area under he graph v() Assume 1D, and v consan: v v x Δx = v = v 1x av, x Δ Δx Δ x= v Δ 1x 1 2 Lecure 9 Purdue Universiy, Physics 149 5

6 Acceleraion (m/s 2 ) The average acceleraion is he change in velociy divided by he change in ime. a Δv = Δ v() Δv Δ Insananeous acceleraion is limi of average acceleraion as ges small. I is he slope of he v() ()plo. a = lim Δ 0 Δ v Δ v() Lecure 9 Purdue Universiy, Physics 149 6

7 Average Acceleraion Average acceleraion is he change in velociy during he ime inerval during which he velociy changed. = "change"in velociy elapsed ime The x- and y-componens of he average velociy are: Typical unis for he magniude of acceleraion are m/s 2, km/s 2, and so on. Lecure 9 Purdue Universiy, Physics 149 7

8 Insananeous Acceleraion Insananeous acceleraion is he average acceleraion we measure when he ime inerval is infiniesimally shor. The x- and y-componens of he insananeous velociy are: Lecure 9 Purdue Universiy, Physics 149 8

9 Direcion of Acceleraion If speed is increasing, v and a are in same direcion. If speed is decreasing, v and a are in opposie direcion. Lecure 9 Purdue Universiy, Physics 149 9

10 ILQ: Acceleraion If he velociy of some objec is no zero, can is acceleraion ever be zero? A) Yes B) No If he velociy is consan, he acceleraion is zero (slope of v() is 0). ) v() v() Lecure 9 Purdue Universiy, Physics

11 ILQ: Acceleraion Is i possible for an objec o have a posiive velociy a he same ime as i has a negaive acceleraion? A) Yes B) No Yes, when hey have differen signs, he objec is slowing down. v() v() Δv Δ Lecure 9 Purdue Universiy, Physics

12 Posiion vs Time Plos Gives locaion a any ime Displacemen is change in posiion Slope gives velociy x (m) 3 Posiion a =3, x(3) = 1 Displacemen beween =5 and =1. Δx = -1.0 m m m = -1.0 m -3 Average velociy beween =5 and =1. v = m/s -1 m / 4 s = m/s Lecure 9 Purdue Universiy, Physics

13 Velociy vs Time Plos Gives velociy a any ime Area gives displacemen Slope gives acceleraion v (m/s) Velociy a =2, v(2) = 3 m/s 4 Displacemen beween =0 and =3: 3: x = 75m =0 o =1: ½ (3m/s) (1 s) = 1.5 m =1 o =3: (3m/s) (2 s) = 6 m Average velociy beween =0 and =3? v= 7.5 m / 3s = 2.5 m/s Change in v beween =5 and =3. v = -2 m/s 3 m/s = -5 m/s Average acceleraion beween =5 and =3: a = -5 m/s / (2 s) = -2.5 m/s 2 Lecure 9 Purdue Universiy, Physics

14 Acceleraion vs Time Plos Gives acceleraion a any ime Area gives change in velociy a (m/s 2 ) Acceleraion a =4, a(4) = -2 m/s 2 Change in v beween =4 and =1. v = +4 m/s 2 4 =1-3: v = (3m/s 2 )(2s) = 6 m/s -3 =3-4: v = (-2m/s 2 )(1s) = -2 m/s 3 6 Lecure 9 Purdue Universiy, Physics

15 ILQ: Conceps A skydiver is falling sraigh down, along he negaive y direcion. During he iniial par of he fall, her speed increases from 16 o 28 m/s in 1.5 s. Which of he following is correc? A) v>0, a>0 v a B) v>0, a<0 C) v<0, a>0 D) v<0, a<0 correc During a laer par of he fall, afer he parachue has opened, her speed decreases from 48 o 26 m/s in 11 s. Which of he following is correc? A) v>0, a>0 B) v>0, a<0 C) v<0, a>0 D) v<0, a<0 C) v<0 a>0 correc Lecure 9 Purdue Universiy, Physics v a y

16 Dropped Ball A ball is dropped from a heigh of wo meers above he ground. Draw v y vs 3 v v v A 3 B 3 C y x v D v E Lecure 9 Purdue Universiy, Physics

17 Dropped Ball A ball is dropped from a heigh of wo meers above he ground. x v Draw v vs Draw x vs Draw a vs a Lecure 9 Purdue Universiy, Physics

18 Tossed Ball A ball is ossed from he ground up a heigh of wo meers above he ground and falls back down. y Draw v vs v v A B C v x v D v E Lecure 9 Purdue Universiy, Physics

19 Tossed Ball A ball is ossed from he ground up a heigh of wo meers above he ground and falls back down. x v Draw v vs Draw x vs Draw a vs a Lecure 9 Purdue Universiy, Physics

20 ILQ Which car has a wesward acceleraion? A) a car raveling wesward a consan speed B) a car raveling easward and speeding up C) a car raveling wesward and slowing down D) a car raveling easward and slowing down E) a car saring from res and moving oward he eas Lecure 9 Purdue Universiy, Physics

21 Newon s Second Law of Moion If here is a ne force acing on an objec, i experiences an acceleraion in he direcion of he ne force, and he magniude of he acceleraion is he ne force s magniude divided by he mass of he objec. In componen form, Unis for force: 1 N = 1 kg m/s 2 Lecure 9 Purdue Universiy, Physics

22 ILQ A single force is acing on an objec. Which ype of moion is no physically allowed? A) he objec speeds up B) he objec is a res C) he objec slows down D) he objec's moion changes direcion Lecure 9 Purdue Universiy, Physics

23 ILQ If an objec is aced on by wo finie consan forces, is i possible for he objec o move a consan velociy? A) No, i will accelerae B) Yes, he forces mus be perpendicular p C) No, i will follow a curved pah D) Yes, he forces mus be equal and opposie E) Yes, he forces mus be in he same direcion Lecure 9 Purdue Universiy, Physics

24 ILQ A force F acing on a mass m 1 resuls in an acceleraion a 1.The same force acing on a differen mass m 2 resuls in an acceleraion a 2 =2a 1. Wha is he mass m 2? m 1 m 2 F a 1 F a 2 = 2a 1 A) 2m 1 B) m 1 C) 1/2 m 1 F=ma F= m 1 a 1 = m 2 a 2 = m 2 (2a 1 ) Therefore, m 2 = m 1 /2 Or in words wice he acceleraion means half he mass Lecure 9 Purdue Universiy, Physics

The unis of mass are g, kg, and so on Objecs wih a larger amoun of ineria (large mass) are harder o change he sae of

25 Mass Mass is a measure of an objec s ineria he amoun of resisance o changes in velociy. Mass is an inrinsic propery of an objec, so mass does no change wherever he objec is (unlike weigh). The unis of mass are g, kg, and so on Objecs wih a larger amoun of ineria (large mass) are harder o change he sae of moion of compared o objecs wih a small amoun of ineria (small mass) For he same ne force, a m (= ΣF/m ) > a M (= ΣF/M ) because m < M m M Lecure 9 Purdue Universiy, Physics

26 Newon s Second Law F = ma A racor T is pulling a railer M wih a consan acceleraion. If he forward acceleraion is 1.5 m/s 2. Calculae he force on he railer M (m=400kg) due o he racor T (m=500kg). x direcion F = x ma x T = ma x 2 ( 400 kg)( 1.5 m/s ) T = T = 600 Newons N T y x W Lecure 9 Purdue Universiy, Physics

27 Example A racor T (m=500kg) is pulling a railer M (m=400kg). I sars from res and pulls wih consan force such ha afer 1 seconds is velociy is 1m/s. Calculae he horizonal force y on he racor due o he ground. x-direcion: Tracor ΣF = ma F w T = m racora F w = T+ m racor a x-direcion: Trailer ΣF = ma T = m railer a N T T N W W Combine: F w = m railer a + m racor a F w = (m railer+ m racor ) a F w x Lecure 9 Purdue Universiy, Physics

28 Example A racor T (m=500kg) is pulling a railer M (m=400kg). I sars from res and pulls wih consan force such ha afer 1 seconds is velociy is 1m/s. Calculae he horizonal force y on he racor due o he ground. Combine: F w = m railera + m racora F w = (m railer+ m racor ) a N W T T N W F w x a=δv/δ=(1m/s)/(1s)=1 m/s 2 Consan force = consan a F w =(900kg) 1 m/s 2 =900N Lecure 9 Purdue Universiy, Physics

29 ILQ A wrench has a mass of 0.75 kg here on earh. I is shipped up o be used on he Inernaional Space Saion. An asronau on he Space Saion will measure is mass o be: A) 0 kg B) 7.5 N C) 1.7 lbs D) 0.75 kg How abou is weigh? Lecure 9 Purdue Universiy, Physics

30 Relaive Velociy We ofen assume ha our reference frame is aached o he Earh. Wha happen when he reference frame is moving a a consan velociy wih respec o he Earh? The moion can be explained by including he relaive velociy of he reference frame in he descripion of he moion. The ground speed of an airplane is he vecor sum of he airspeed and he wind velociy. Using he air as he inermediae reference frame, ground speed is: v = v + v PG PA AG Example airplanes Lecure 9 Purdue Universiy, Physics

31 Relaive Velociy Wha is he relaion beween he velociy of an objec as deermined in one reference frame and he velociy of he same objec as deermined in anoher reference frame ha is moving wih respec o he firs reference frame? v AC = v AB + v BC where v AC is he velociy of A relaive o C, v AB is he velociy of A relaive o B, and v BC is he velociy of B relaive o C. Lecure 9 Purdue Universiy, Physics

32 Example where v WT is he velociy of Wanda relaive o Tim, v TG is he velociy of Tim relaive o Greg, and v WG is he velociy of Wanda relaive o Greg. Lecure 9 Purdue Universiy, Physics

=12m/so 1.2 righ. Wha is her velociy relaive o he ground?

33 ILQ As a rain ravels wih a velociy v TG = 15.5 m/s o righ, Wanda walks oward he fron of he rain wih a velociy v WT =12m/so 1.2 righ. Wha is her velociy relaive o he ground? A) 0 m/s B) 16.7 m/s, o righ C) 14.3 m/s, o righ D) impossible o ell Lecure 9 Purdue Universiy, Physics

34 ILQ: Relaive Velociy You are on a rain raveling 40 mph Norh. If you walk 5 mph sideways across he car (W), wha is your speed relaive o he ground? A) < 40 mph B) 40 mph C) >40 mph v = = 40.3mph Lecure 9 Purdue Universiy, Physics

35 ILQ: Time o Cross he River Three swimmers can swim equally fas relaive o he waer. They have a race o see who can swim across a river in he leas ime. Relaive o he waer, Beh (B) swims perpendicular o he flow, Ann (A) swims upsream, and Carly (C) swims downsream. Which swimmer wins he race? A B C Beh uses all of her force in he 'y' A) Ann direcion, he direcion of he oher bank. B) Beh Time o ge across = widh of river / C) Carly y-componen of velociy Lecure 9 Purdue Universiy, Physics

PHYSICS 220 Lecture 02 Motion, Forces, and Newton s Laws Textbook Sections

PHYSICS 220 Lecture 02 Motion, Forces, and Newton s Laws Textbook Sections PHYSICS 220 Lecure 02 Moion, Forces, and Newon s Laws Texbook Secions 2.2-2.4 Lecure 2 Purdue Universiy, Physics 220 1 Overview Las Lecure Unis Scienific Noaion Significan Figures Moion Displacemen: Δx