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Lecture1

Lecture1 - Location path of a particle in space HES2310...

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HES 2310 LECTURE NOTES DEVELOPED BY DR JAMAL NASER FOR HIS LECTURES HES2310 - Dynamics-1 Jamal Naser Senior Lecturer EN216 Ext: 8655 Swinburne University NB: These lecture notes are prepared from “Engineering Mechanics- Dynamics” (the book by J.L. Merium & L.G. Kraige). These notes will help the students to follow lectures in the class. Students should read the book. Students should not depend on these lecture notes only. HES 2310 LECTURE NOTES DEVELOPED BY DR JAMAL NASER FOR HIS LECTURES Location & path of a particle in space Location can be defined in rectangular cordinates by x, y, z cylindrical coordunates by r, θ , z spherical coordinates by R, θ, φ Path in space can be – constrained guided in a defined path – unconstrained no defined path HES 2310 LECTURE NOTES DEVELOPED BY DR JAMAL NASER FOR HIS LECTURES Rectilinear motion The dislacement of the particle in time t is s – hence the velocity is v=lim ( t 0) s/ t s s t=0 t=t t=t+ t -s +s a dv dt v or a d s dt s = = = = / D / DD ( ) 2 2 2 v ds dt s = = / D ( ) 1 v ds a dv or vdv ads or sds sds / / D D DD ( ) = = = 3 HES 2310 LECTURE NOTES DEVELOPED BY DR JAMAL NASER FOR HIS LECTURES Graphical relationships between s, v, a & t Tangent to curve in Fig(a) gives Velocity= v = ds/dt velocity at all ponnts determined and plotted in Fig (b) Tangent to curve in Fig(b) gives Acceleration= a =dv/dt Area under the v-t curve is: v dt = ds , on integration : ds vdt s s s s v v 1 2 1 2 2 1 = = HES 2310 LECTURE NOTES DEVELOPED BY DR JAMAL NASER FOR HIS LECTURES accelerations at all ponnts determined and plotted in Fig (c) Shaded area under the a-t curve is: adt = dv , on integration : Change in velocity dv adt v v v v t t 1 2 1 2 2 1 = = These graphical representations are important for: 1. Visualizing the relationship between s, v, a & t 2. Approximating results by graphical integration or Differencation when mathematical functions & relationships are not available HES 2310 LECTURE NOTES DEVELOPED BY DR JAMAL NASER FOR HIS LECTURES Acceleration Vs distance plot gives ads = vdv = d(v 2 /2) Integrating Net Area under a-s curve vdv ads v v v v s s 1 2 1 2 1 2 2 2 1 2 = = ( ) From the similar triangles in Fig.(b) CB/v = dv/ds CB=vdv/ds = a

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