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Calculus/ Vectors

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A 10kg mass is supported by two strings of length 5 m and 7 m attached to two points in the ceiling 10 m apart. Find the tension in each string.

Help will be much appreciated! :)

  • Calculus/ Vectors -

    first draw a position diagram, a horizontal line 10 m, and two sides of 5 m and 7 ml to get triangle ABC
    where b = 10, a=7, and c=5

    by the cosine law,
    5^2 = 10^2 + 7^2 - 2(10)(7)cosC
    cosC = 124/140
    angle C = 27.66°

    by the Sine Law
    sinA/7 = sin27.66/5
    angle A = 40.54

    now draw a vector diagram, triangle PQR
    where PR = 10 and a vertical line, P above R
    PR represents the 10 kg mass

    Using the above results,
    angle P = 62.34
    angle Q = 40.54+27.66 = 68.20
    angle R = 49.46

    by sine law:
    PQ/sin 49.46 = 10/sin68.20
    PQ = 8.18

    QR/sin62.34 = 10/sin68.2
    QR = 9.54

    the tension is the 7 m string is 8.18 kg
    the tension in the 5 m string is 9.54 kg

    check my arithmetic

    draw PQ parallel to BC and QR parallel to AB
    angle QPR = 90-27.66 = 62.34°

  • retyped - Calculus/ Vectors -

    the last two line got displaced, should have been:

    first draw a position diagram, a horizontal line 10 m, and two sides of 5 m and 7 ml to get triangle ABC
    where b = 10, a=7, and c=5

    by the cosine law,
    5^2 = 10^2 + 7^2 - 2(10)(7)cosC
    cosC = 124/140
    angle C = 27.66°

    by the Sine Law
    sinA/7 = sin27.66/5
    angle A = 40.54

    now draw a vector diagram, triangle PQR
    where PR = 10 and a vertical line, P above R
    PR represents the 10 kg mass

    draw PQ parallel to BC and QR parallel to AB
    angle QPR = 90-27.66 = 62.34°



    Using the above results,
    angle P = 62.34
    angle Q = 40.54+27.66 = 68.20
    angle R = 49.46

    by sine law:
    PQ/sin 49.46 = 10/sin68.20
    PQ = 8.18

    QR/sin62.34 = 10/sin68.2
    QR = 9.54

    the tension is the 7 m string is 8.18 kg
    the tension in the 5 m string is 9.54 kg

    check my arithmetic

  • Calculus/ Vectors -

    Hey the guy above is totally right. Except for the fact that is screwed up the Lenght of PR. To get the right answer you have to do 10kg * 9.8N = 98N. Which is the length of PR. Now use 98 with sine law as Rimey did above and you shall get 80 and 94 for your two tensions.

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