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Math Help - Vector as forces problem

  1. #1
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    Vector as forces problem

    I really need some help with this:
    A mass of 15 kg is suspended by two cords from a ceiling. The cords have lengths of 15 cm and 20 cm, and the distance between the points where they are attached on the ceiling is 25 cm. Determine the tension in each of the two cords.

    thanks in advance.
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  2. #2
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    Quote Originally Posted by Soul to soul View Post
    I really need some help with this:
    A mass of 15 kg is suspended by two cords from a ceiling. The cords have lengths of 15 cm and 20 cm, and the distance between the points where they are attached on the ceiling is 25 cm. Determine the tension in each of the two cords.

    thanks in advance.
    Start by recognising that you have a 3-4-5 triangle in there and hence a 90 degree angle at the point where the 15 kg mass is attached ....

    Note that Lami's Theorem makes the problem simple.
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  3. #3
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    Quote Originally Posted by Soul to soul View Post
    I really need some help with this:
    A mass of 15 kg is suspended by two cords from a ceiling. The cords have lengths of 15 cm and 20 cm, and the distance between the points where they are attached on the ceiling is 25 cm. Determine the tension in each of the two cords.

    thanks in advance.
    let A be the point where the 15 cm string is attached to the ceiling.
    C be the point where the 20 cm string is attached to the ceiling.
    B be the point directly above the hanging mass between A and C.
    M is the mass position.

    ABM and CBM are right triangles.

    AC = 25 cm , AB = x cm , BC = (25-x) cm

    using Pythagoras ...

    15^2 - x^2 = 20^2 - (25 - x)^2

    x = 9 ... BM = 12 cm

    let T_1 = tension in the 15 cm string
    T_2 = tension in the 20 cm string
    g = acceleration due to gravity

    system is in equilibrium ...

    \sum{F_x} = 0

    T_1 \cdot \frac{3}{5} = T_2 \cdot \frac{4}{5}

    \sum{F_y} = 0

    T_1 \cdot \frac{4}{5} + T_2 \cdot \frac{3}{5} = 15g

    solve the system for T_1 and T_2
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  4. #4
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    Thanks a lot, now I know how to solve it!
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