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Math Help - Statics of a Particle

  1. #1
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    Exclamation Statics of a Particle

    Could someone help me with this problem
    A weight of 20 kg is suspended from two strings of
    length 10 cm and 12 cm, the ends of the strings being
    attached to two points in a horizontal line, 15 cm apart.
    Find the tension in each string.
    Statics of a Particle-mathspic.bmp
    The answer in the textbook is T1=14.99kg wt and T2=12.10kg wt, but i'm not sure how to get it. i tried finding the angles and then moving the vectors around but it wasn't right.
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  2. #2
    MHF Contributor arbolis's Avatar
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    I won't do it, but the book is wrong. A tension is a force and its unit is commonly in newtons ( N), not kg.
    Put the equations :
    The system is in equilibrium, so the sum of the vertical components of the tensions are equal in magnitude to the weight. Take note that the weight is a force and its unit is not in kg but in N. The object has a mass of 20 kg which means 20kg\cdot \frac{9.8m}{s^2}=196N.
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  3. #3
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    what are the vertical components of the tensions and how would you figure them out? would finding them help to solve the problem? would it be possible to use kilogram weight as the force instead of newtons, or does it have to be N? sorry but i still dont know how to work it out
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  4. #4
    MHF Contributor arbolis's Avatar
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    Quote Originally Posted by needhelpplease View Post
    what are the vertical components of the tensions and how would you figure them out? would finding them help to solve the problem? would it be possible to use kilogram weight as the force instead of newtons, or does it have to be N? sorry but i still dont know how to work it out
    I don't have the time to do it for now. I think you can work out the vertical components of the tensions by calculating the angles that are into the triangle formed by the strings and the ceiling.
    Yes, finding them would help to solve the problem. You have to put down equations.
    For example you know that the horizontal components of the tensions T_1 and T_2 are equal in magnitude and opposite in sense because the system is at equilibrium. If they are not equal in magnitude, then the system would be moving with an acceleration which is not the case.
    So put down the equations for the "x-axis" and the "y-axis" that you may want to define in the same direction than the figure is.
    On the x-axis you have that the horizontal component of T_1 times i unit vector + horizontal component of T_2 times i unit vector is equal to 0.
    I call T_{1ver} the vertical component of T_1 and T_{2ver} the vertical component of T_2. For the y-axis you have that T_{1ver}+T_{2ver}=\text{weight of the mass}.
    And I'm sorry, your book is probably right about the weight. The weight is a force and the SI unit for it is the newton, N which is worth \frac{1kgm}{s^2}, but I misread what your book says, it says kg\cdot wt. I never saw that before but it is probably a possible unit for a force. So excuse me here.
    Also pardon my poor quality answer to your problem. Maybe try to post it on http://www.physicshelpforum.com/physics-help/....
    That's a nice problem though, and I'll try to solve it maybe next week so don't wait for me. Good luck.
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