PHYS 100: Lecture 2. Motion at Constant Acceleration. Relative Motion: Reference Frames. x x = v t + a t. x = vdt. v = adt. x Tortoise.

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1 a PHYS 100: Lecure 2 Moion a Consan Acceleraion a 0 0 Area a 0 a 0 v ad v v0 a0 v 0 x vd 0 A(1/2)( v) Area v 0 v v-v 0 v 0 x x v + a Relaive Moion: Reference Frames x d Achilles Toroise x Toroise Reference frame Earh Reference frame Achilles

2 Music Who is he Aris? A) Areha Franklin B) Dinah Washingon C) Mary Wells D) Ea James E) Koko Taylor The Classic Why? She passed las Friday. Jazz from Ea Physics 100 Lecure 2, Slide 2

3 Rope Around he World The Earh has an equiorial radius of 3963 miles. There are 5280 fee in one mile. Imagine a rope wraped around he equaor of a perfecly smooh Earh. Suppose we now add 15 fee o he rope and shape his longer rope ino a smoooh circle wih is cener a he cener of he Earh. How far will he rope now sand away from he surface of he Earh? For now jus use your inuiion.. Don calculae anyhing, we will do ha nex. (A) < 1mm (B) ¼ inch (C) (D) 2 f (E) 15 f 2 inches Physics 100 Lecure 1, Slide 3

4 Rope Around he World The Earh has an equiorial radius of 3963 miles. There are 5280 fee in one mile. Imagine a rope wraped around he equaor of a perfecly smooh Earh. Suppose we now add 15 fee o he rope and shape his longer rope ino a smoooh circle wih is cener a he cener of he Earh. How do we sar his calculaion? Which of he following opions would you do firs? (A) Use your calculaor o conver radius of Earh o fee. (B) Use your calculaor o deermine he iniial lengh of rope in miles (C) Use your calculaor o conver 15 fee ino miles (D) Wrie down a mahemaical expression ha relaes he radius of he Earh o he original lengh of rope WHY? Always THINK firs Numbers can be subsiued in a he end (IF NEEDED) Physics 100 Lecure 1, Slide 4

5 Rope Around he World The Earh has an equaorial radius of 3963 miles. There are 5280 fee in one mile. Imagine a rope wraped around he equaor of a perfecly smooh Earh. Suppose we now add 15 fee o he rope and shape his longer rope ino a smoooh circle wih is cener a he cener of he Earh. Which of he following equaions relaes R E, he radius of he Earh, o L, he iniial lengh of rope? (A) R E L 2 (B) R E L π L (C) R E L 2π (D) none of hese R E L is circumference of circle of radius R E : L 2πR E Physics 100 Lecure 1, Slide 5

6 Rope Around he World The Earh has an equiorial radius of 3963 miles. There are 5280 fee in one mile. Imagine a rope wraped around he equaor of a perfecly smooh Earh. Suppose we now add 15 fee o he rope and shape his longer rope ino a smoooh circle wih is cener a he cener of he Earh. Which of he following equaions relaes L (he exra 15 fee) o R (he amoun he new rope sands above he surface of he Earh)? (A) R R E L L (B) R L (C) L R L E R L 2π L+ L 2π ( R E (D) + R) none of hese L + L R E L 2π R E R E R 2π R L R R - R E L 15 f R π 2π f Look Ma, No Calculaor!! Physics 100 Lecure 1, Slide 6

7 Rope Around he World The Earh has an equiorial radius of 3963 miles. There are 5280 fee in one mile. Imagine a rope wraped around he equaor of a perfecly smooh Earh. Suppose we now add 15 fee o he rope and shape his longer rope ino a smoooh circle wih is cener a he cener of he Earh. How far will he rope now sand away from he surface of he Earh? (A) < 1mm (B) ¼ inch (C) 2 inches (D) 2 f (E) 15 f NOTE: Example of relevance of calculus: L 2πR dr dl 1 2π 1 R L 2π 15 f 2 π 2.4 f THIS IS A GREAT EXAMPLE OF USING MATH AS A TOOL NOTE THE VALUE OF USING SYMBOLS Physics 100 Lecure 1, Slide 7

8 1-D Moion Example: Consan Acceleraion An Example of Applicaion of Kinemaic Definiions ha ARE ALWAYS TRUE!!! Acceleraion: a dv d Everyhing we did las week used ONLY hese definiions Velociy: v dx d SPECIAL CASE Assume consan acceleraion a a 0 a a 0 Area a 0 a 0 v 0 SPECIAL CASE v v-v 0 A(1/2)( v) Area v 0 v 0 0 v ad v v0 a0 x vd 0 x x v + a v v0 + a0 v 2 v a0( x x0) x x v a 0 Physics 100 Lecure 2, Slide 8

9 CheckPoins 1.1 & 1.3 A dragser sars from res and moves wih consan acceleraion and crosses he finish line (1/4 mile) in 3 seconds.. 1. I will reach half of is maximum speed a he 1/8 mile mark. 3. I will reach half of is maximum speed in 1.5 seconds. (A) Boh True (B) Boh False (C) 1 True 3 False QUESTION: Wha are possible problems wih hese explanaions? (D) 1 False 3 True yes because if i is consanly speeding up from res i should equal ou o half he maximum speed half way hrough he race Since he car acceleraes a a consan rae, i will reach half of is maximum speed halfway hrough he race. ANSWER: Halfway Poin : halfway in ime is no same as halfway in disance!! YOU CAN CHECK THIS WITH MOVING MAN!! Download from hp://phe.colorado.edu/en/simulaion/moving-man Physics 100 Lecure 2, Slide 9

10 CheckPoins 1.1 & 1.3: Takeaway Message? BE CAREFUL! Posiion, Velociy, Acceleraion, Time are differen quaniies. e.g., halfway poin NOT well-defined Halfway in Time Posiion is NOT linear in ime Halfway in Posiion Half posiion DOES NOT occur a half ime Velociy is linear in ime Halfway in Speed Half speed occurs a half ime Physics 100 Lecure 2, Slide 10

11 Follow Up A dragser sars from res and moves wih consan acceleraion and crosses he finish line (1/4 mile) in 3 seconds.. 1. I will reach he 1/8 mile mark when i reaches half of is maximum speed. 3. I will reach he 1/8 mile mark in 1.5 seconds. (A) Boh True (B) Boh False 1 True (C) 3 False Time for Half Speed (D) 1 False 3 True Time for Half Posiion Halfway in Posiion Halfway in Speed Physics 100 Lecure 2, Slide 11

12 Relaive Moion: Reference Frames There is only one equaion: v TA v T v A Check his ou a he Achilles/Toroise link in he Lecure column of he Course Planner Physics 100 Lecure 2, Slide 12

13 CheckPoin 2 x 0 QUESTIONS ABOUT 0 in reference frame of B (A) x A < 0 (B) x A 0 (C) x A > 0 x A -d (A) v A < 0 (B) v A 0 (C) v A > 0 v A +5 m/s Physics 100 Lecure 2, Slide 13

14 CheckPoin 2 x A -d v A +5 m/s QUESTIONS ABOUT 0 in reference frame of B (A) x C < 0 (B) x C 0 (C) x C > 0 x C +d (A) v C < 0 (B) v C 0 (C) v C > 0 v C -4 m/s Physics 100 Lecure 2, Slide 14

15 CheckPoin 2 A 0: x A -d v A +5 m/s x C +d v C -4 m/s Which ball (A or C) will hi B firs? (A) (B) (C) A his B before C his B C his B before A his B C his B a he same ime as A his B Le s draw his from he 5 m/s 4 m/s reference frame of B! A B C d d Physics 100 Lecure 2, Slide 15

16 CheckPoin 2 Which of he graphs o he righ represen he moion of balls A and C as observed in he reference frame of ball B? A 0: Suden reasons: x A -d v A +5 m/s x C +d v C -4 m/s (e) None of he above Ball C is coming from a posiive direcion, hus he line should be above he -axis. Ball A is coming from he negaive direcion, hus should be below he -axis. C has a greaer velociy han A+B hus i should reach ball B sooner. In B's reference frame, C is posiive so i sars above he axis and he opposie is said for A. B "sees" A coming a i wih 5m/s and "sees" C moving oward i wih 4m/s. So A will have a seeper slope han C A B C D E Physics 100 Lecure 2, Slide 16

17 CheckPoin 2 Which of he graphs o he righ represen he moion of balls A and C as observed in he reference frame of ball B? A 0: x A -d v A +5 m/s x C +d v C -4 m/s (e) None of he above WHAT DOES MOTION LOOK LIKE IN REFERENCE FRAME OF B? v A > 0 and v C < 0 A 5 m/s 4 m/s B C velociy slope of x vs plo Speed(A) > Speed(C) d d speed magniude of slope of x vs plo Physics 100 Lecure 2, Slide 17

18 Noes Web Homework 2 DUE TUESDAY 8am Office Hours on Monday (consul Websie for hours) Online Quiz 2 DUE THURSDAY 8pm Prelecure 3 and CheckPoin 3 DUE FRIDAY 8am Physics 100 Lecure 1, Slide 18