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

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Presentation on theme: "Page 1 Dr. Gareth J. Bennett Trinity College Dublin 1E10 Lecture in Design Mechanical & Manufacturing Engineering “Dynamics for the Mangonel”. Dr. Gareth."— Presentation transcript:

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

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

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

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

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

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

7 Page 7 Dr. Gareth J. Bennett Trinity College Dublin 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?

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

9 Page 9 Dr. Gareth J. Bennett Trinity College Dublin Derived Units Force (1N=1kgm/s 2 ) Work (1J=1Nm=1kgm 2 /s 2 ) Energy (J) Power (1W=1J/s)

10 Page 10 Dr. Gareth J. Bennett Trinity College Dublin Dynamics Starting with some basic equations Speed av =distance/time Acceleration av =velocity/time

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

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

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

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

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

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

17 Page 17 Dr. Gareth J. Bennett Trinity College Dublin Dynamics Example 2: (1-D) s=1/2at 2 t (from stopwatch) u=0 (at top) s=? 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!

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

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

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

21 Page 21 Dr. Gareth J. Bennett Trinity College Dublin Dynamics y x Not u and v now but v 1, v 2, v 3, v 4, etc….. 1 2 3 4 v1v1 v2v2 v3v3 v4v4

22 Page 22 Dr. Gareth J. Bennett Trinity College Dublin Dynamics y x We can decompose vectors (v, s, a) into x, y components 1 2 3 4 s 1x s1s1 s 1y

23 Page 23 Dr. Gareth J. Bennett Trinity College Dublin Dynamics v=u+at becomes: v x2 =v x1 +a x1 Δt v y2 =v y1 +a y1 Δt s=ut+1/2at 2 becomes: Δs x =v x1 Δt+1/2a x1 Δt 2 Δs y =v y1 Δt+1/2a y1 Δt 2 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)

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

25 Page 25 Dr. Gareth J. Bennett Trinity College Dublin Dynamics t2=t1+ Δ t

26 Page 26 Dr. Gareth J. Bennett Trinity College Dublin Dynamics x 2 =x 1 +v x1 Δ t+1/2a x1 Δ t 2

27 Page 27 Dr. Gareth J. Bennett Trinity College Dublin Dynamics y 2 =y 1 +v y1 Δ t+1/2a y1 Δ t 2

28 Page 28 Dr. Gareth J. Bennett Trinity College Dublin Dynamics v x2 =v x1 +a x1 Δ t

29 Page 29 Dr. Gareth J. Bennett Trinity College Dublin Dynamics v y2 =v y1 +a y1 Δ t

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

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

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

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

34 Page 34 Dr. Gareth J. Bennett Trinity College Dublin Assignment 1 Mangonel Dynamics Design Tool using Excel Work in groups and/or individually in computer rooms today and during week to 1.Create excel spreadsheet as demonstrated 2.Plot x versus y 3.Study effect of changing velocity 4.Study effect of changing angle An assignment will be set based on this work. Assignment to be submitted individually – no copying!


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