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    A small particle of mass 0.2 kg is held by a light, inextensible string which makes an angle of 30\circ with the vertical axis. A force is applied on the string to keep it in equilibrium - what is the the tension in the string when this force has its least possible value? I tried to solve the question but couldn't get that at which direction is this force being applied? :confused:
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    (Original post by Zishi)
    A small particle of mass 0.2 kg is held by a light, inextensible string which makes an angle of 30\circ with the vertical axis. A force is applied on the string to keep it in equilibrium - what is the the tension in the string when this force has its least possible value? I tried to solve the question but couldn't get that at which direction is this force being applied? :confused:
    Draw a triangle of forces. You can mark on the force for the weight, you know the direction of the tension, so what would the direction of the appliied force have to be for it to be a minimum (i.e. what direction would give it a minimum length on the diagram?).
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    This is my force diagram:


    I don't understand where to put force, F. For it to be least it must be in some 'theta' direction having lowest horizontal component... :confused:
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    Hey I think I know this question. you put the force acting horizontally towards the right.

    You have to do this because otherwise the particle would swing back towards the centre so as it is equilibrium the force must holding it steady

    Good luck!
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    (Original post by MinpoloD)
    Hey I think I know this question. you put the force acting horizontally towards the right.

    You have to do this because otherwise the particle would swing back towards the centre so as it is equilibrium the force must holding it steady

    Good luck!
    Well I applied that way and took F = Tsin(theta), but it gave a wrong answer for value of T.
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    If im not mistaken it should be 0.2*9.8*sin30
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    The forces direction would have to be opposite to T otherwise the string would not be taut and there would be no tension.
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    (Original post by kiss_my_asthma_99)
    If im not mistaken it should be 0.2*9.8*sin30
    The answer is \sqrt{3}.

    (Original post by StephenP91)
    The forces direction would have to be opposite to T otherwise the string would not be taut and there would be no tension.
    But won't that just then cancel out the T to give 1=1? :eek: I'd be grateful if you could explain it using a force diagram.
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    Triangle of forces:

    When 3rd force is a minimum, it will be at right angles to the Tension, and you have the attached diagram.

    T is clearly root 3; or 2 cos 30.
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    (Original post by ghostwalker)
    Triangle of forces:

    When 3rd force is a minimum, it will be at right angles to the Tension, and you have the attached diagram.

    T is clearly root 3; or 2 cos 30.
    Thanks, but why does it have to be at right angle to tension to be minimum?
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    (Original post by Zishi)
    Thanks, but why does it have to be at right angle to tension to be minimum?
    Because that's when the length of that third side is the shortest, when it's at right angles to the side representing the tension.
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    (Original post by ghostwalker)
    Triangle of forces:

    When 3rd force is a minimum, it will be at right angles to the Tension, and you have the attached diagram.

    T is clearly root 3; or 2 cos 30.
    just a quick question, you considered g as 10, not 9.8, right?
    My mistake is i took sin instead of cos
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    (Original post by kiss_my_asthma_99)
    just a quick question, you considered g as 10, not 9.8, right?
    My mistake is i took sin instead of cos
    Yes; otherwise you won't get root 3, and that is what zishi must have done to get his 2N force.
 
 
 
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