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    A smooth circular wire of radius a is fixed in a vertical plane with light elastic strings of natural length a and modulus lambda attached to the upper and lower extremities, A and C, of the vertical diameter. The other ends of the two strings are attached to a small ring B of mass m which is free to slide on the wire. Show that, while both strings remain taut, the equation for the motion of the ring is

    2ma \ddot{\theta}=\lambda(\cos \theta-\sin \theta)-mg\sin 2\theta, where theta is the angle CAB.

    Frankly I don't even know where to start.
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    (Original post by bbrain)
    Frankly I don't even know where to start.
    With a diagram, obviously.
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    (Original post by bbrain)
    A smooth circular wire of radius a is fixed in a vertical plane with light elastic strings of natural length a and modulus lambda attached to the upper and lower extremities, A and C, of the vertical diameter. The other ends of the two strings are attached to a small ring B of mass m which is free to slide on the wire. Show that, while both strings remain taut, the equation for the motion of the ring is

    2ma \ddot{\theta}=\lambda(\cos \theta-\sin \theta)-mg\sin 2\theta, where theta is the angle CAB.

    Frankly I don't even know where to start.

    can i know what module this is in order for me to assisst you with better guidance?
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    (Original post by study beats)
    can i know what module this is in order for me to assisst you with better guidance?
    I think this is a combination of circular motion (M3) and elastic strings also M3.
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    (Original post by bbrain)
    I think this is a combination of circular motion (M3) and elastic strings also M3.
    fun stuff mate, i am not on that yet
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    As the person above, start with a diagram. Draw one, label everything and post it here when you get as far as you can go.
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    (Original post by BabyMaths)
    With a diagram, obviously.
    (Original post by Hanvyj)
    As the person above, start with a diagram. Draw one, label everything and post it here when you get as far as you can go.



    This is my diagram. Any thoughts?


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    (Original post by bbrain)
    This is my diagram. Any thoughts?


    This was posted from The Student Room's iPhone/iPad App
    1. You have labelled both tensions as T. In general, they will be different so label them T_1 and T_2

    2. You haven't labelled the lengths of the strings. Call them l_1 and l_2.

    3. l_1 and l_2 are not independent. You need to find a relationship between them. Circle geometry, Pythagorus, and the sine rule are your friends.

    4. Angles CAB and ACB are not independent. How are they related?

    5. When you get to the point where you can express the tensions in a useful form (i.e. in terms of other things that you know already), then you should apply Newton II, resolving horizontally and vertically. Given the nice geometry of the problem, it looks like this should be pretty easy.

    6. Rearrange your equations into the desired form. This is algebraic book work.
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    (Original post by atsruser)
    5. When you get to the point where you can express the tensions in a useful form (i.e. in terms of other things that you know already), then you should apply Newton II, resolving horizontally and vertically.
    In fact, given the geometry of the problem, this should probably read "resolving tangentially and radially".
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    (Original post by bbrain)
    This is my diagram. Any thoughts?


    This was posted from The Student Room's iPhone/iPad App
    I've now had time to work through this question, so I can make a couple of other points:

    1. It will help you if you can recognise where the term 2ma\ddot{\theta} comes from.

    2. When you know where that term comes from, you should realise that \theta is the wrong angle to be working with: you need an angle that measures tangential displacement of the particle from, say, the equilibrium position of the mass.

    3. That should prompt you to draw a particular radial line on your diagram, to give you the required angle. The angle (lets call it \alpha) should have the same sense as \theta i.e. as \theta increases, so should \alpha - that keeps the application of Newton II a bit easier (I did it so my \alpha had the wrong sense, so I got the wrong answer for a bit)

    4.When you've drawn that line, some more trigonometrical possibilities arise (Hint: sine rule possibilities, to allow you to rewrite those pesky string lengths in terms of something more useful)

    5. You'll definitely have to resolve radially and tangentially. How will you resolve the weight of the mass, though? (What angle does it make with the radius?)

    6. You'll probably need to know how to work with expressions like \sin(\pi-A), \sin(\pi-2A)at some point. How can they be rewritten?
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    (Original post by atsruser)
    I've now had time to work through this question, so I can make a couple of other points:

    1. It will help you if you can recognise where the term 2ma\ddot{\theta} comes from.

    2. When you know where that term comes from, you should realise that \theta is the wrong angle to be working with: you need an angle that measures tangential displacement of the particle from, say, the equilibrium position of the mass.

    3. That should prompt you to draw a particular radial line on your diagram, to give you the required angle. The angle (lets call it \alpha) should have the same sense as \theta i.e. as \theta increases, so should \alpha - that keeps the application of Newton II a bit easier (I did it so my \alpha had the wrong sense, so I got the wrong answer for a bit)

    4.When you've drawn that line, some more trigonometrical possibilities arise (Hint: sine rule possibilities, to allow you to rewrite those pesky string lengths in terms of something more useful)

    5. You'll definitely have to resolve radially and tangentially. How will you resolve the weight of the mass, though? (What angle does it make with the radius?)

    6. You'll probably need to know how to work with expressions like \sin(\pi-A), \sin(\pi-2A)at some point. How can they be rewritten?
    Where does 2ma\ddot{\theta} come from?
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    (Original post by bbrain)
    Where does 2ma\ddot{\theta} come from?
    In a circular motion problem, where would you find a term that looks like that?
 
 
 
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