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Math Help - resolving forces

  1. #1
    Senior Member furor celtica's Avatar
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    resolving forces

    a lamp is supported in equilibrium by two chains fixed to two points A and B at the same level; the lengths of the chains are 0.3m and 0.4m and the distance between A and B is 0.5m. Given that the tension in the longer chain is 36N, show by resolving horizontally that the tension in the shorter chain is 48N,. By resolving vertically, find the mass of the lamp.
    I havent gotten past the first problem, proving that the tension in the first chain is 48N. I'm guessing that geometry comes in somewhere cos they gave the lengths of the chains but i couldnt say how, and i dont comprehend the relationship between the tensions in the chains; how is the lamp in horizontal equilibrium?
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    1st step --> draw the diagram

    2---> Look closely into it you would be able to see a right angel triangle with sides in familiar ratio of 3:4:5 and corresponding angles as 37,53,90.

    3---> the triangle mentioned in (2) is triangle ABC ...C being the point where the two chains start

    4---> Observe things closely you will get two equations
    36cos(37) = T_2 cos(53)

    cos(37) = 4/5 & cos(53) = 3/5

    You will get your first answer


    5----> Along Vertical

    Mg = 36sin(37) + 48 sin( 53)

    XXX Game Over XXX
    _________________________
    I wanted to attach the diagram
    My MS paint isn't working so I tried to walk on Soroban's foot-print

    and the result was as bright as coal but I would paste it here...don't keep laughing at it

    angle CAB will be 37 degree
    Angle CBA is 53 degree

    Spoiler:

    ..........C.................
    ........./\............
    ......../...\..........
    ......./......\........
    ....../.........\........
    ...../_______\......
    ....B..............A.........
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