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    I am having difficulty with this question:

    Object, of mass 40kg, is supported in equilibrium by 4 cables. The forces (in N) exerted by 3 cables are:

    F1 = 80i + 20j + 100k
    F2 = 60i - 40j + 80k
    F3 = -50i - 100j + 80k

    The unit vectors i and j are perpendicular and horizontal and the unit vector k is vertically upwards.

    Find F4, the force exerted by the 4th cable, in terms of i, j and k.
    Also find its magnitude to the nearest Newton.

    A decent method with brief explanation would be very well appreciated, and rep shall be given for your help.

    It is the weight of the object pulling vertically downwards (392 N) combined with the forces given in vectors, that throws me.
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    (Original post by bono_2)
    I am having difficulty with this question:

    Object, of mass 40kg, is supported in equilibrium by 4 cables. The forces (in N) exerted by 3 cables are:

    F1 = 80i + 20j + 100k
    F2 = 60i - 40j + 80k
    F3 = -50i - 100j + 80k

    The unit vectors i and j are perpendicular and horizontal and the unit vector k is vertically upwards.

    Find F4, the force exerted by the 4th cable, in terms of i, j and k.
    Also find its magnitude to the nearest Newton.

    A decent method with brief explanation would be very well appreciated, and rep shall be given for your help.

    It is the weight of the object pulling vertically downwards (392 N) combined with the forces given in vectors, that throws me.
    split them up into i, j and k

    draw a diagram, make sure the resultant is = 0 in every direction.

    eg(k direction) 100+80+80+f4 =392

    is that it?
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    (Original post by Ollie)
    split them up into i, j and k

    draw a diagram, make sure the resultant is = 0 in every direction.

    eg(k direction) 100+80+80+f4 =392

    is that it?
    But what about the weight of the particle.
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    (Original post by bono_2)
    But what about the weight of the particle.
    thats why 100+80+80+f4 =392
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    (Original post by Ollie)
    thats why 100+80+80+f4 =392
    I don't understand.

    Why would the sum of the k unit vector components equal 392? If the object is in equilibrium, then it must equal zero.
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    (Original post by bono_2)
    I don't understand.

    Why would the sum of the k unit vector components equal 392? If the object is in equilibrium, then it must equal zero.
    ok, only k for the moment (vertical)
    so force going down due to weight of the particle =40 x9.81 = 392.

    reaction force going up = 100+80+80+f4 (thats the force provided from the tension from the wires)

    no as you say, its not moving so the forces must equal 0.
    therefore force up = force down
    therefore force of gravity on object = force from tension of wires.

    so all those wire must add up to 392.
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    (Original post by Ollie)
    ok, only k for the moment (vertical)
    so force going down due to weight of the particle =40 x9.81 = 392.

    reaction force going up = 100+80+80+f4 (thats the force provided from the tension from the wires)

    no as you say, its not moving so the forces must equal 0.
    therefore force up = force down
    therefore force of gravity on object = force from tension of wires.

    so all those wire must add up to 392.
    Yes i completely understand Ollie, cheers.

    So far: F4 = -90i + xj + 132k

    How do I find x from this?
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    (Original post by bono_2)
    Yes i completely understand Ollie, cheers.

    So far: F4 = -90i + xj + 132k

    How do I find x from this?
    F1 = 80i + 20j + 100k
    F2 = 60i - 40j + 80k
    F3 = -50i - 100j + 80k

    same way you found the i part.

    20-40-100+f4=0

    therefore f4 = 120
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    (Original post by Ollie)
    F1 = 80i + 20j + 100k
    F2 = 60i - 40j + 80k
    F3 = -50i - 100j + 80k

    same way you found the i part.

    20-40-100+f4=0

    therefore f4 = 120
    I got the same answer, 120j, but the book says 40j, that is why I asked you to do it to see if you got the same!

    So I take it the books is wrong here?
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    (Original post by bono_2)
    I got the same answer, 120j, but the book says 40j, that is why I asked you to do it to see if you got the same!

    So I take it the books is wrong here?
    well the method must be right if the other 2 works.

    i guess its wrong :confused:
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    (Original post by Ollie)
    well the method must be right if the other 2 works.

    i guess its wrong :confused:
    So I've wasted your time basically (I got the other 2 bits right as well) although I thought I went wrong because I got 120j instead of the 40j in the back of the book (the other 2 answers are correct though).

    :mad: :mad: :mad:

    Anyway, thanks very much for your help Ollie, well appreciated.

    Rep for you tomorrow.
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    (Original post by bono_2)
    So I've wasted your time basically (I got the other 2 bits right as well) although I thought I went wrong because I got 120j instead of the 40j in the back of the book (the other 2 answers are correct though).

    :mad: :mad: :mad:

    Anyway, thanks very much for your help Ollie, well appreciated.

    Rep for you tomorrow.
    no, all seems in order, i think the books wrong, ring a friend 2mrw, see what they got.
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    (Original post by Ollie)
    no, all seems in order, i think the books wrong, ring a friend 2mrw, see what they got.
    Anyway, continuing from that.

    Find the magnitude of F4.

    F4 = sq.root (90^2 + 120^2 + 132^2)
    F4 = sq.root (39, 924)

    F4 = 200N (nearest Newton)
 
 
 
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