{VERSION 2 3 "IBM INTEL NT" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Ohlfs" 0 12 0 0 0 0 2 2 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }1 0 0 0 6 6 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 4 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 3 " 4 5 1 {CSTYLE "" -1 -1 "" 1 12 0 0 0 0 1 0 0 0 0 0 0 0 0 }0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 " " 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "Title" 0 18 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 1 0 0 0 0 0 0 }3 0 0 -1 12 12 0 0 0 0 0 0 19 0 }{PSTYLE "Author" 0 19 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 8 8 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Times" 0 12 0 0 0 0 2 2 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Fo nt 2" -1 257 1 {CSTYLE "" -1 -1 "Courier" 0 12 0 0 0 0 2 1 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 40 "Computer Intensive Physic s\nPhysics 211\n\n" }}}{EXCHG {PARA 19 "" 0 "" {TEXT -1 164 "Steven R. Dunbar\nDepartment of Mathematics and Statistics\nUniversity of Nebra ska-Lincoln\nLincoln, NE, 68588\n\nsdunbar@math.unl.edu\nhttp://www.ma th.unl.edu/~sdunbar\n\n" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 365 "Hom ework 2: 1D Dynmaics (Invisible Forces)\n\nTopic: 1D Dynamics (verti cal fall from constant gravitational force with drag as a passive forc e)\n\nTitle: airresis.ms : Free fall with air resistance (coffee filt er drop)\n\nKeywords: gravity, drag, air resistance, free-body diagra m, differential equation\n\nAudience: Students, Homework using comput er lab\n\nTime: 30-50" }}}{EXCHG {PARA 5 "" 0 "" {TEXT -1 152 "The go al of this computer lab is to derive the motion of a body falling with air resistance, and to measure the effect of mass on the terminal vel ocity." }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 52 "Situation 1: Air Resis tance Proportional to Velocity" }}{EXCHG {PARA 256 "" 0 "" {TEXT -1 354 "Use Newton's Force Law: \n \n mass * acceleration = net total \+ of all forces \n\nto derive a differential equation for velocity.\n\nR emember a differential equation involves the derivative of a function \+ and the function itself.\n\nHint 1: What is the relation between velo city and acceleration?\nHint 2 : Assume the drag force is proportiona l to the velocity." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "force _eqn_1 := ;" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 111 "What is the ini tial velocity? \n\n Use this information to write down the (named) ini tial condition for velocity." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "ic_1 := " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "soln_1 := \+ dsolve( \{ , \}, );" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "vel_1 := rhs( );" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 130 "After a reasonable amount of time, what is t he approximate velocity of the falling object?\n(This is called the te rminal velocity.)" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 50 "How does t he teminal velocity vary with the mass? " }}{PARA 256 "" 0 "" {TEXT -1 0 "" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 63 "Situation 2: Air Res istance Proportional to Square of Velocity" }}{EXCHG {PARA 256 "" 0 " " {TEXT -1 408 "Second Situation\nAgain use Newton's Force Law: \n \n \+ mass * acceleration = net total of all forces \n\nto derive a secon d different differential equation for velocity.\n\nRemember a differen tial equation involves the derivative of a function and the function i tself.\n\nHint 1: What is the relation between velocity and accelerat ion?\nHint 2 : Assume the drag force is proportional to the square of the velocity." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "force_eqn _2 := ;" }}{PARA 11 "" 1 "" {XPPMATH 20 ">%,force_eqn_2G/*&%\"mG\"\" \"-%%diffG6$-%\"vG6#%\"tGF.F',&*&F&F'%\"gGF'F'*&%\"kGF'F+\"\"#!\"\"" } }}{EXCHG {PARA 256 "" 0 "" {TEXT -1 43 "What is the initial condition \+ for velocity?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "ic_2 := ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "soln_2 := dsolve( ,);" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "vel_2 := rhs();" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 156 "Let's investigate the (slightly exotic ) function tanh(z), it's called the \"hyperbolic tangent\".\n\nThe bes t way to investigate a new function is with a graph!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "plot( tanh(t), t = );" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 130 "After a reasonable amount of time, what is t he approximate velocity of the falling object?\n(This is called the te rminal velocity.)" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 50 "How does t he teminal velocity vary with the mass? " }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 15 "Data Comparison" }}{EXCHG {PARA 256 "" 0 "" {TEXT -1 534 "Some real data collected by one of the student teams for a seuqnce of \"coffee-filter objects\"\n\nThe mass of one filter is about 0.0011 \+ kg.\n\nNumber max velocity\nof filters in \+ m/s\n1 1.18\n2 1.5 9\n3 1.92\n4 2.36 \n5 2.64\n6 2.94\n 7 3.15\n8 3.32\n9 \+ 3.54\n10 3.80" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 119 "data := [[1,1.18], [2, 1.59 ], [3, 1.92], [4, 2.36], [5, 2.64],\n[6, 2.94], [7, 3.15], [8, 3.32], \+ [9, 3.54], [10, 3.80]];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 " plot( data, scaling=constrained);" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 160 "If the mass is increased by a facotr of 4, how much does the v elocity increase?\n\nIf the mass is increased by a factor of 9, how mu ch does the velocity increase?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 88 "Which of the tow mod els for air resistance is the more reasonable, ccording to the data?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 99 "Extra Credit: Using the data above can you derive t he drag coefficient for a coffee-filter object?" }}}}{MARK "5 3 0 0" 43 }{VIEWOPTS 1 1 0 1 1 1803 }