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1E10 Lecture in Design Mechanical & Manufacturing Engineering

1E10 Lecture in Design Mechanical & Manufacturing Engineering. “Dynamics for the Mangonel”. Dr. Gareth J. Bennett. Objective. A small model Mangonel. Objective. Can we predict the distance?. Objective. A larger version!. Objective.

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1E10 Lecture in Design Mechanical & Manufacturing Engineering

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  1. 1E10 Lecture in DesignMechanical & Manufacturing Engineering “Dynamics for the Mangonel”. Dr. Gareth J. Bennett Dr. Gareth J. Bennett Trinity College Dublin

  2. Objective A small model Mangonel Dr. Gareth J. Bennett Trinity College Dublin

  3. Objective Can we predict the distance? Dr. Gareth J. Bennett Trinity College Dublin

  4. Objective A larger version! Dr. Gareth J. Bennett Trinity College Dublin

  5. Objective What are the factors that control the distance? (The dynamics) Dr. Gareth J. Bennett Trinity College Dublin

  6. Modelling Bigger means further? Some of the issues related to scaling up are discussed in Prof. Fitzpatrick’s lecture! (Reflect on these) Dr. Gareth J. Bennett Trinity College Dublin

  7. Modelling For a given “size”, can we maximise the distance? What are the key parameters that control the distance? Can we formulate a model that will help us design our Mangonel? Dr. Gareth J. Bennett Trinity College Dublin

  8. Fundamentals • force = mass x acceleration (ma) • work = force x distance (Fs) • energy== work • power = rate of work (work/time) Dr. Gareth J. Bennett Trinity College Dublin

  9. Derived Units • Force (1N=1kgm/s2) • Work (1J=1Nm=1kgm2/s2) • Energy (J) • Power (1W=1J/s) Dr. Gareth J. Bennett Trinity College Dublin

  10. Dynamics • Starting with some basic equations • Speedav=distance/time • Accelerationav=velocity/time Dr. Gareth J. Bennett Trinity College Dublin

  11. Dynamics • Can derive equations for linear motion (for constant acceleration) • v=u+at • s=ut+1/2at2 • v2=u2+2as u=initial velocity v=final velocity t=time duration a=acceleration s=distance travelled Dr. Gareth J. Bennett Trinity College Dublin

  12. Dynamics • Example 1: (1-D) • Kick a ball straight up. Given a given initial velocity, how high will it go? Dr. Gareth J. Bennett Trinity College Dublin

  13. a=-g Dynamics v=0 (at top) • Example 1: (1-D) • Use equation: • v2=u2+2as • s=u2/2g s=? u Dr. Gareth J. Bennett Trinity College Dublin

  14. Dynamics • Example 2: (1-D) • Drop a rock from a cliff. How long will it take to hit the ground/sea? Dr. Gareth J. Bennett Trinity College Dublin

  15. Dynamics • Example 2: (1-D) Dr. Gareth J. Bennett Trinity College Dublin

  16. Dynamics u=0 (at top) • Example 2: (1-D) • Use equation: • s=ut+1/2at2 • s=1/2at2 s=? t (from stopwatch) Dr. Gareth J. Bennett Trinity College Dublin

  17. u=0 (at top) s=? t (from stopwatch) Dynamics • Example 2: (1-D) • s=1/2at2 Example Result: t=3s =>s=44m However! t=2.5s =>s=31m t=3.5s =>s=60m Sensitive to error: proportional to square of t! Dr. Gareth J. Bennett Trinity College Dublin

  18. Dynamics • Can we use these equations to model the trajectory of the missile? • And hence predict the distance? A 2-D problem! Dr. Gareth J. Bennett Trinity College Dublin

  19. Dynamics y x Dr. Gareth J. Bennett Trinity College Dublin

  20. Dynamics 4 3 2 y s 1 x Discretise the curve Dr. Gareth J. Bennett Trinity College Dublin

  21. Dynamics 4 3 v4 2 v3 y v2 1 x v1 Not u and v now but v1, v2, v3, v4, etc….. Dr. Gareth J. Bennett Trinity College Dublin

  22. Dynamics 4 3 2 y s1y s1 1 x s1x We can decompose vectors (v, s, a) into x, y components Dr. Gareth J. Bennett Trinity College Dublin

  23. Dynamics • v=u+at becomes: • vx2=vx1+ax1Δt • vy2=vy1+ay1Δt • s=ut+1/2at2 becomes: • Δsx=vx1Δt+1/2ax1Δt2 • Δsy=vy1Δt+1/2ay1Δt2 Acceleration is constant (for no drag of lift – we’ll return to this point later) ax=0! ay=-g t2-t1= Δt (keep time interval constant) Dr. Gareth J. Bennett Trinity College Dublin

  24. Dynamics – Assignment1 Use Excel to study trajectory of missile Dr. Gareth J. Bennett Trinity College Dublin

  25. Dynamics t2=t1+Δt Dr. Gareth J. Bennett Trinity College Dublin

  26. Dynamics x2=x1+vx1Δt+1/2ax1Δt2 Dr. Gareth J. Bennett Trinity College Dublin

  27. Dynamics y2=y1+vy1Δt+1/2ay1Δt2 Dr. Gareth J. Bennett Trinity College Dublin

  28. Dynamics vx2=vx1+ax1Δt Dr. Gareth J. Bennett Trinity College Dublin

  29. Dynamics vy2=vy1+ay1Δt Dr. Gareth J. Bennett Trinity College Dublin

  30. Dynamics Const=0! Dr. Gareth J. Bennett Trinity College Dublin

  31. Dynamics Const=-g Dr. Gareth J. Bennett Trinity College Dublin

  32. Dynamics Copy formula down Dr. Gareth J. Bennett Trinity College Dublin

  33. Dynamics Plot x versus y using chart wizard Dr. Gareth J. Bennett Trinity College Dublin

  34. Assignment 1 • Mangonel Dynamics Design Tool using Excel • Work in groups and/or individually in computer rooms today and during week to • Create excel spreadsheet as demonstrated • Plot x versus y • Study effect of changing velocity • Study effect of changing angle • An assignment will be set based on this work. Assignment to be submitted individually – no copying! Dr. Gareth J. Bennett Trinity College Dublin

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