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Physics 101:  Lecture 19  Elasticity and Oscillations Exam III
Hour exam results
Hour exam results Avg (ex 1&2), max grade, median grade, min grade 53- 56  C-,  D-,  F  N: 10 57- 60  C,  D+,  F  N: 18 61- 64  C+,  D+,  F  N: 19 65- 68  B+,  C,  D  N: 37 69- 72  A-,  C,  D-  N: 52 73- 76  A-,  C+,  D-  N: 52 77- 80  A,  B,  D-  N: 55 81- 84  A+,  B+,  C-  N: 39 85- 88  A+,  A-,  D-  N: 47 89- 92  A+,  A,  C  N: 32 93- 96  A+,  A+,  A-  N: 22 97-100  A+,  A+,  A+  N: 03
Overview ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Springs ,[object Object],[object Object],18 relaxed position F X  = 0 x x=0
Springs ACT ,[object Object],[object Object],[object Object],[object Object],x relaxed position x=0 F X  = - kx < 0 ,[object Object]
Springs ,[object Object],[object Object],relaxed position F X  = –kx > 0  x ,[object Object],x=0 18
Potential Energy in Spring ,[object Object],[object Object],[object Object],[object Object],[object Object],Force x work
Young’s Modulus ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Simple Harmonic Motion ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Spring ACT II ,[object Object],[object Object],[object Object],[object Object],F=ma +A t -A x CORRECT
Springs and Simple Harmonic Motion X=0 X=A X=-A X=A ;  v=0 ;  a=-a max X=0 ;  v=-v max ;  a=0 X=-A ;  v=0 ;  a=a max X=0 ;  v=v max ;  a=0 X=A ;  v=0 ;  a=-a max
***Energy *** ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],m x x=0 0 x PE S
Preflight 1+2 ,[object Object],[object Object],[object Object],[object Object],“ At x=0 all spring potential energy is converted into kinetic energy and so the velocity will be greatest at this point.”  Its 5:34 in the morning. Answer JUSTIFIED.  +A t -A x CORRECT
Preflight 3+4 ,[object Object],[object Object],[object Object],[object Object],The energy changes from spring to kinetic but is not lost. +A t -A x CORRECT
What does  moving in a circle  have to do with moving back & forth  in a straight line  ?? R  8 7 8 7 x y x -R R 0  1 1 2 2 3 3 4 4 5 5 6 6 x  =  R cos   =   R cos (  t ) since     =     t
SHM and Circles
Simple Harmonic Motion: x(t) =  [A]cos(  t) v(t) = -[A  ]sin(  t) a(t) = -[A  2 ]cos(  t) x(t) =  [A]sin(  t) v(t) = [A  ]cos(  t) a(t) = -[A  2 ]sin(  t) x max  = A v max  = A  a max  = A  2 Period = T  (seconds per cycle) Frequency = f = 1/T  (cycles per second) Angular frequency =    = 2  f = 2  /T For spring:   2  = k/m OR
Example ,[object Object],[object Object],[object Object],[object Object],We are told at t=0, x = +5 cm.  x(t) = 5 cos(  t) only one that works.
Example ,[object Object],[object Object],[object Object],E = U + K At t=0, x = 5 cm and v=0:  E = ½ k x 2  + 0 = ½ (24 N/m) (5 cm) 2 = 0.03 J
Example ,[object Object],[object Object],[object Object],E = U + K When x = 0, maximum speed:  E = ½ m v 2  + 0 .03 = ½ 3 kg v 2 v = .14 m/s
Example ,[object Object],[object Object],[object Object],   = sqrt(k/m) = sqrt(24/3) = 2.83 radians/sec Returns to original position after 2    radians T = 2    /    = 6.28 / 2.83 = 2.2 seconds
Summary ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],50

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Lecture19

  • 1. Physics 101: Lecture 19 Elasticity and Oscillations Exam III
  • 3. Hour exam results Avg (ex 1&2), max grade, median grade, min grade 53- 56 C-, D-, F N: 10 57- 60 C, D+, F N: 18 61- 64 C+, D+, F N: 19 65- 68 B+, C, D N: 37 69- 72 A-, C, D- N: 52 73- 76 A-, C+, D- N: 52 77- 80 A, B, D- N: 55 81- 84 A+, B+, C- N: 39 85- 88 A+, A-, D- N: 47 89- 92 A+, A, C N: 32 93- 96 A+, A+, A- N: 22 97-100 A+, A+, A+ N: 03
  • 4.
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  • 7.
  • 8.
  • 9.
  • 10.
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  • 12. Springs and Simple Harmonic Motion X=0 X=A X=-A X=A ; v=0 ; a=-a max X=0 ; v=-v max ; a=0 X=-A ; v=0 ; a=a max X=0 ; v=v max ; a=0 X=A ; v=0 ; a=-a max
  • 13.
  • 14.
  • 15.
  • 16. What does moving in a circle have to do with moving back & forth in a straight line ?? R  8 7 8 7 x y x -R R 0  1 1 2 2 3 3 4 4 5 5 6 6 x = R cos  = R cos (  t ) since  =  t
  • 18. Simple Harmonic Motion: x(t) = [A]cos(  t) v(t) = -[A  ]sin(  t) a(t) = -[A  2 ]cos(  t) x(t) = [A]sin(  t) v(t) = [A  ]cos(  t) a(t) = -[A  2 ]sin(  t) x max = A v max = A  a max = A  2 Period = T (seconds per cycle) Frequency = f = 1/T (cycles per second) Angular frequency =  = 2  f = 2  /T For spring:  2 = k/m OR
  • 19.
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  • 21.
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  • 23.

Hinweis der Redaktion

  1. 1
  2. Example: Given m,k and A and x(0), choose x(t), v(t), a(t), Calculate v_max and a_max, period, energy, K, U
  3. Example: Given m,k and A and x(0), choose x(t), v(t), a(t), Calculate v_max and a_max, period, energy, K, U
  4. Example: Given m,k and A and x(0), choose x(t), v(t), a(t), Calculate v_max and a_max, period, energy, K, U
  5. Example: Given m,k and A and x(0), choose x(t), v(t), a(t), Calculate v_max and a_max, period, energy, K, U