{VERSION 2 3 "APPLE_PPC_MAC" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Ohlfs" 0 12 182 136 88 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 "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 0 255 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 0 216 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 \+ Font 2" -1 257 1 {CSTYLE "" -1 -1 "Courier" 0 12 180 136 32 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 38 "Computer Intensive Physic s\nPhysics 211" }}}{EXCHG {PARA 19 "" 0 "" {TEXT -1 162 "Steven R. Dun bar\nDepartment of Mathematics and Statistics\nUniversity of Nebraska- Lincoln\nLincoln, NE, 68588\n\nsdunbar@math.unl.edu\nhttp://www.math.u nl.edu/~sdunbar" }}}{EXCHG {PARA 4 "" 0 "" {TEXT -1 240 "Topic: 1D Dy namics (No/low friction with visible applied forces)\n\nTitle: Forces that Vary with Time\n\nKeywords: F=ma, Newton's Second Law, Accelera tion, Velocity, Position\n\nAudience: Students in Computer Lab Settin g\n\nTime: 30-45 minutes" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 50 "Oly mpic Sprinters - What's their thrust function?" }}{EXCHG {PARA 256 " " 0 "" {TEXT -1 598 "The propelling force (or thrust) created by an Ol ympic-quality sprinter in the 100-meter sprint event has been measured as F = 3600*exp(-k*t) (in newtons) where k is some positive constant. \n\nThe mass of a heavily muscled competitor such as Ben Johnson is ab out 90 kg.\n\nFind the constant k so that the sprinter can finish the \+ 100-meter race in 10 seconds\n\nUsing Newton's Second Law, you can for mulate the acceleration. Remember the runner starts with no velocity and the distance down the track is measured from the starting positio n. This information will help you set up and solve the problem\n " }} {PARA 256 "" 0 "" {TEXT -1 34 "Add references to literature here." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 19 "F :=3600*exp(-k*t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "m := 90;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "a := ; # solve for a using your information" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "v := int( , t = 0..T); # find the velocity at time T" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "s := int( , T = ); # position, watch limits of integration" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "s10 := subs( T1 = 10, s);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "plot( s10, k= 1/2..5);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "fsolve( s10 = 100, k, 1..10) ;" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 39 "Jet Runways -- How long sh ould they be?" }}{EXCHG {PARA 256 "" 0 "" {TEXT -1 305 "A 727 jet need s to be traveling 90 m/s to take off. The mass of the jet is 10^5 kg. The thrust of the jet engines during take-off is 10^6*(1-exp(-t)). \+ The jet starts from rest. How long must the runway be?\n(Adapted fr om Calculus, 1st Edition, Hughes-Hallett, Gleason, et.al, Problem 50, \+ Section 6.4)" }}{PARA 256 "" 0 "" {TEXT -1 349 "Strategy: First we wi ll find the acceleration from the force. \n Then we w ill find the velocity at any time.\n Then we will find position down the runway at any time.\n We will find \+ out how long it takes to reach 90 m/s from the velocity.\n \+ Then we will find the position at that time. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "F := ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "m := ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 " a := ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "v := ;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "s := ;" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 17 "fsolve( , );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "subs( , );" }}}}}{MARK "4" 0 }{VIEWOPTS 1 1 0 1 1 1803 }