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Math Help - Circular-rectilinear transfer

  1. #1
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    Circular-rectilinear transfer

    Hi, I'm Tim for Quebec, Canada and I'm having a hard time grasping the whole problem and how to solve it. I'd appreciate it a lot if you could help me with this one. Thank you very much and best regards.

    P.S. I translated the problem from French to English the best I could and I couldn't find a proper way to translate part b) so I'm sorry for the hard time I'm causing you. I hope you understand what I wrote.

    Circular-rectilinear transfer
    The metal bar of length l on the figure has an extremity fixed on point P on a circle of the radius a. The other extremity of the bar, point Q, moves in a rectilinear horizontal trajectory.


    a) By finding x, the distance between O and Q, determine x in function of angle θ.


    b) Supposing that the lengths are expressed in centimeters and that the variation of the angle is 2 radians per seconds in anti-clockwise, find the speed at which the point Q is moving when θ = π/2


    c) What do we need to calculate if we want to find for which angle θ point P is moving the fastest.



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  2. #2
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    law of cosines ...

    L^2 = a^2 + x^2 - 2ax\cos{\theta}

    \frac{d}{dt}(L^2 = a^2 + x^2 - 2ax\cos{\theta})

    0 = 2x \frac{dx}{dt} + 2ax\sin{\theta}\frac{d\theta}{dt} - 2a\cos{\theta}\frac{dx}{dt}

    when \theta = \frac{\pi}{2} , x = \sqrt{L^2 - a^2}

    0 = 2\sqrt{L^2 - a^2} \frac{dx}{dt} + 4a\sqrt{L^2 - a^2}

    \frac{dx}{dt} = -2a units/sec

    for part (c), point P will move at a constant speed if \frac{d\theta}{dt} is constant ... does the problem say that it is variable?
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  3. #3
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    Talking

    Nope not specified at at all. Every part of the problem is there. For part (c) I'll manage to solve it on my own or I,l ask a classmate for specifications... Thank so much for the solution. I didn't actually think it to be that simple... I guess I wasn't thinking about the law of cosines.
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