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Statics of Rigid Bodies Question - Edexcel M2

Discussion in 'Mathematics' started by chrisa86, May 7, 2017.

  1. chrisa86

    chrisa86 New commenter

    Hi
    Question from an M2 paper (June 2009):
    A uniform rod AB, of length 1.5 m and mass 3 kg, is smoothly hinged to a vertical wall at A. The rod is held in equilibrium in a horizontal position by a light strut CD as shown in Figure 1. The rod and the strut lie in the same vertical plane, which is perpendicular to the wall. The end C of the strut is freely jointed to the wall at a point 0.5 m vertically below A. The end D is freely joined to the rod so that AD is 0.5 m.
    (a) Find the thrust in CD.
    (b) Find the magnitude and direction of the force exerted on the rod AB at A.

    Please forgive my stupidity on this but I am wondering why there is no reaction at the wall at C; is the phrasing of "freely jointed" the reason? I have to admit I'm missing this and can neither convince myself nor a student as to why this is not considered and, hence, why we do not consider any thrust acting into the wall.

    Any help?
     
  2. Ezioclone

    Ezioclone New commenter

    I've never taught M2 and have had to interpret the text to determine what I believe is shown in Fig 1 but why do you think there's no reaction at C? If there's thrust in CD (as there is), then surely there has to be horizontal and vertical components in the reaction to this at C.
    Don't you simply have to take moments of AB about point A to solve this problem?.
     
  3. mike372

    mike372 New commenter

    For mechanics questions you generally show the forces acting on a single body when drawing force diagrams. Here we care about the rod so the force acting on the strut by the wall is irrelevant. But I agree that there will be force on the strut by the wall.

    For the rod to be in equilibrium, the resultant moment acting on the rod about any point must be zero. So the forces on the strut won't be included in this calculation. Another example : in ladders questions there are forces acting on the wall/floor by the ladder but you don't show these on your diagram and you don't include these forces in any calculations.
     
  4. chrisa86

    chrisa86 New commenter

    Thank you! I knew I wasn't going crazy. Being naïve, I took the diagram given in the solutions to be the full diagram but they had only considered the forces acting on the rod rather than add everything in which complicated unnecessarily.
     
  5. stewarty

    stewarty New commenter

    It's a very easy mistake to make, and one that many students make. Of course all the forces in the whole system must by in equilibrium. However its good to look at the forces acting on each parts separately.
    Its always similar when a block lies on a block on a surface. That reaction force between the blocks always catches them out
     
  6. armandine2

    armandine2 Established commenter

  7. armandine2

    armandine2 Established commenter

    before saying "freely jointed" they use to say (and draw) a pin-joint - the pin-joint with its frictionless pin cannot transmit a turning force at the pin (which a "built-in" connection can).
     
    Last edited: May 10, 2017
  8. armandine2

    armandine2 Established commenter

    upload_2017-5-23_17-26-41.png

    [A collectible "indeterminate" example - 1988 AEB]
     
  9. armandine2

    armandine2 Established commenter

    upload_2017-5-23_17-30-26.png

    [another "tricky" question, on the same paper!]
     
  10. armandine2

    armandine2 Established commenter

    upload_2017-6-12_18-12-12.png
    upload_2017-6-12_18-12-36.png
    upload_2017-6-12_18-13-7.png

    upload_2017-6-12_18-13-21.png
    upload_2017-6-12_18-14-11.png

    For the fence fans - and aspiring Engineering mathematicians - the A level Engineering Science question(s) can be done with first year mech eng mechanics of solids - and therefore A level Eng. Science - however the degree of difficulty in an already crowded 3 hour paper -> looks harsh.

    I've done both a moment area and Macauley's notation - neither were very quick. (the SF and BM diagrams at the end were for the (b) part of the question, and were for 16 marks)
     

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    Last edited: Jun 12, 2017
  11. Elfrune

    Elfrune New commenter

    One thing that kind of concerns me is that I have no idea of what this thread is about! I can cope with C1, 2, 3, 4, Stats 1, D1, a little of M1 and most of FP1, but then mathematics loses me. I have been a Head of Dept for 7 years and am now Lead Practitioner, but have never been able to take on a further group owing to not having a mathematics degree (I'm a strange convert from Law!). I would love to understand - really understand - mechanics, but don't know where to start. Is it a work through all the books sort of subject to learn (how I managed to get C1-4, S1, D1 and FP1 up to speed) or is there a more inspirational way of starting? I worked through the M1 book - but it seems Mechanics and my mind don't connect as much as the rest of maths. I think mechanics is fascinating, but can't seem to make connections as much as my mind can in the Core maths. Hard to explain - but when I see a question in, for example, C4, my mind instantly forms a picture of methods required to solve it. With mechanics, on the other hand, my mind starts doing cartwheels and goes in to a panic most of the time - and yet I would love to understand it. Is my mind being paranoid, or is Mechanics just a little different and more complex branch?
     
  12. mike372

    mike372 New commenter

    I'm sure you can become an expert if you put some time into learning it all.

    I highly recommend the ExamSolutions videos - these helped me relearn a lot of the stuff that I did at A Level. I also used to post questions in TheStudentRoom (I wouldn't say that I was a trainee teacher) when there was something that I didn't fully understand and this was very useful. To be a mechanics expert you really need to understand why everything works and how it all fits together. A lot of students go through A Level just learning the methods without fully understanding what they're doing.

    I'm going to have to start relearning stats soon :(
     
  13. armandine2

    armandine2 Established commenter

    Macaulay - not Macauley
    the rest I'd take with a big pinch of salt!
     
  14. armandine2

    armandine2 Established commenter



    use the digital learning technology -
     

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