Calculus/ Vectors

posted by .

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.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. physics

    A doubly tethered model airplane of mass 1.0 kg is attached to a vertical rod by two very light strings that are 2.0 each in length. the airplane and the the strings rotate in a horizontal circleabout the rod with both the strings …
  2. Vectors

    A mass 0f 10kg is suspended by 2 pieces of string, 30 cm and 40 cm long, from twp points that are 50cm apart and at the same level. Find the tension in each piece of string.
  3. physics

    a 10-kg mass is supported by two strings of length 5m and 7m attached to two pints in the celing 10m apart. find the tenion in each string
  4. physics

    A 0.101 kg meter stick is supported at its 40 cm mark by a string attached to the ceiling. A 0.68 kg object hangs vertically from the 6.61 cm mark. A second mass is attached at another mark to keep it horizontal and in rotational equilibrium. …
  5. Mechanics (A level), Please help

    A light string of length a is attached to two points A and B on the same level and distance b apart, where b < a. A smooth ring of weight W is threaded on the string and is pulled by a horizontal force P, so that it rests in equilbrium …
  6. Vectors

    A 10-kg mass is suspended by two strings of length 5m and 7m attached to two points in the ceiling 10 m apart. Determine the tension on each string. Round your result to one decimal place (include a vector and position diagrams)
  7. Vectors

    A 10-kg mass is suspended by two strings of length 5m and 7m attached to two points in the ceiling 10 m apart. Determine the tension on each string. Round your result to one decimal place (include a vector and position diagrams)
  8. Physics

    A 1.34‒kg ball is attached to a rigid vertical rod by means of two massless strings each 1.70 m long. The strings are attached to the rod at points 1.70 m apart. The system is rotating about the axis of the rod, both strings …
  9. Physics

    A lamp of mass 5kg is hung from two hooks 2.5cm apart on the horizontal ceiling of room by strings of length 1.5m and 2m.Find tension in the strings?
  10. physics

    a heavy rod AB of length of 5m weighs 50N.The bar is supported in a horizontal position by two vertical strings X and Y.If string X is 0.6m from B and string Y is 1.8 from A,find the tension in the strings.

More Similar Questions