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Math Help - Vector forces on ring

  1. #1
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    Vector forces on ring

    The question is:- Four given pulls and thrusts act on a ring. Find their equilibrant. The pulls and thrusts are as follows:
    N = 58 - thrust
    M = 105 - pull
    L = 40 - thrust
    K = 72 - pull
    Angles are as follows:
    NM - 73 deg
    NL - 149 deg
    NK - 194 deg

    The methodology I have used is calculate the equilibrium for the pulls and thrusts separately. Then subtract the thrusts from the pulls. The answer I get is 60.36, however the answer given is 88.5. Where have I gone wrong?
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  2. #2
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    Hello p75213

    Welcome to Math Help Forum!
    Quote Originally Posted by p75213 View Post
    The question is:- Four given pulls and thrusts act on a ring. Find their equilibrant. The pulls and thrusts are as follows:
    N = 58 - thrust
    M = 105 - pull
    L = 40 - thrust
    K = 72 - pull
    Angles are as follows:
    NM - 73 deg
    NL - 149 deg
    NK - 194 deg

    The methodology I have used is calculate the equilibrium for the pulls and thrusts separately. Then subtract the thrusts from the pulls. The answer I get is 60.36, however the answer given is 88.5. Where have I gone wrong?
    If a force F acts outwards from the origin O along a line that makes a direction \theta measured anticlockwise from the positive direction of Ox, then its components along Ox and Oy are
    F\cos\theta and F\sin\theta, respectively
    Since the angles are measured from the direction of N, I assume they are all in the same sense (e.g. all anticlockwise). So we can write down the components along and perpendicular to ON, where O is the ring, as follows:

    Along ON:
    N: -58

    M: 105\cos73^o = 30.70

    L: -40\cos149^o=34.29

    K: 72\cos194^o =-69.86
    Perpendicular to ON:
    N: 0

    M: 105\sin73^o=100.41

    L: -40\sin149^o=-20.60

    K: 72\sin194^o=-17.42
    We find the resultant force by summing these components:
    Along ON: -62.87

    Perpendicular to ON: 62.4
    The magnitude of the resultant is therefore \sqrt{62.87^2+62.4^2}=88.58.

    Grandad
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  3. #3
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    Thanks Grandad. Simple when somebody shows you where you were going wrong ie. Thrusts are negative and pulls are positive.
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