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Math Help - another simple statics problem

  1. #1
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    another simple statics problem

    Unfortunately, there are no examples in the book like this and I don't have any physics books.


    The answer in the back of the book says k = 11.2 lb/ft. But the spring is only stretched an additional .464 feet when theta is 30, so is that 5.104 pounds all going to the y component to hold up the rod? What is the method here, and how many "steps" does it take?

    Thanks
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  2. #2
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    Quote Originally Posted by hairy View Post
    Unfortunately, there are no examples in the book like this and I don't have any physics books.


    The answer in the back of the book says k = 11.2 lb/ft. But the spring is only stretched an additional .464 feet when theta is 30, so is that 5.104 pounds all going to the y component to hold up the rod? What is the method here, and how many "steps" does it take?

    Thanks
    seems the geometry is a bit more complex than first meets the eye ...



    stretched spring length L = \sqrt{6^2+3^2 - 2(6)(3)\cos(30)} \approx 3.718 ft

    stretch, x \approx 0.718 ft

    obtuse angle at B = 180 - \arcsin\left(\frac{3}{L}\right) \approx 126.2^\circ

    using net torque about point A ...

    kx(3)\sin(B) = 15(1.5)\sin(60)

    k = \frac{5(1.5)\sin(60)}{x\sin(B)} \approx 11.2 lbs/ft
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  3. #3
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    Quote Originally Posted by skeeter View Post
    seems the geometry is a bit more complex than first meets the eye ...



    stretched spring length L = \sqrt{6^2+3^2 - 2(6)(3)\cos(30)} \approx 3.718 ft

    stretch, x \approx 0.718 ft

    obtuse angle at B = 180 - \arcsin\left(\frac{3}{L}\right) \approx 126.2^\circ

    using net torque about point A ...

    kx(3)\sin(B) = 15(1.5)\sin(60)

    k = \frac{5(1.5)\sin(60)}{x\sin(B)} \approx 11.2 lbs/ft
    thanks a lot. i never would've gotten this. the law of cosines is not one of the first things i check out.

    edit: would you mind explaining what about this problem indicated to you that this was the strategy?
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  4. #4
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    Quote Originally Posted by hairy View Post
    thanks a lot. i never would've gotten this. the law of cosines is not one of the first things i check out.

    edit: would you mind explaining what about this problem indicated to you that this was the strategy?
    I just saw the Side-Angle-Side setup with the 6 ft horizontal spacing, angle \theta , and the 3 ft rod ... the fundamental setup for the law of cosines.
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