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Math Help - tension in rope angular momentum

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    tension in rope angular momentum

    A bucket of mass 2kg is attached to a rope of length 2 meters and is swinging in a vertical circle. The speed of the bucket at the lowest point is 10m/s.

    a) find the tension in the rope as a function of the angle.

    b) show that the tension in the rope reaches a maximum value when the bucket is at the lowest point.


    am not sure what equation to start of with? Any help appreciated.
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  2. #2
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    Re: tension in rope angular momentum

    as always in these sorts of problems you start by sketching a force diagram. There are two forces acting on the bucket. What are they?
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    Re: tension in rope angular momentum

    gravity, and tension?
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    Re: tension in rope angular momentum

    Quote Originally Posted by Tweety View Post
    gravity, and tension?
    well the tension is going to end up being the vector sum of two forces, one of which is gravity. What sort of force does circular motion get you?
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    Re: tension in rope angular momentum

    Without gravity, the centripetal force is F= ma where "a" is the acceleration toward the center of the circle. You can calculate that knowing the speed of the pail. Once you have found that force, add it to the force of gravity.
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    Re: tension in rope angular momentum

    Is this the equation that i need to use?  \omega = \frac{1}{r^{2}} r \times v ?
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    Re: tension in rope angular momentum

    Quote Originally Posted by Tweety View Post
    Is this the equation that i need to use?  \omega = \frac{1}{r^{2}} r \times v ?
    This equation comes from an equality of angular momentum in terms of the moment of inertia and the angular momentum for a point particle. It is not likely to solve your problem as the question has nothing to do with this.

    You seem to be looking for someone to give you the final answer. You've been around enough to know we don't simply do that. If nothing else your equation doesn't use the tension anywhere so that should tell you something. Go back and take a look at the other posts and see if you can follow the logic to get to the solution.

    -Dan
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    Re: tension in rope angular momentum

    Quote Originally Posted by topsquark View Post
    This equation comes from an equality of angular momentum in terms of the moment of inertia and the angular momentum for a point particle. It is not likely to solve your problem as the question has nothing to do with this.

    You seem to be looking for someone to give you the final answer. You've been around enough to know we don't simply do that. If nothing else your equation doesn't use the tension anywhere so that should tell you something. Go back and take a look at the other posts and see if you can follow the logic to get to the solution.

    -Dan

    No, am really not expecting anyone to give me the full answer! just a start up, cause i still am very lost with this question, and don't know where to start.
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    Re: tension in rope angular momentum

    Quote Originally Posted by Tweety View Post
    No, am really not expecting anyone to give me the full answer! just a start up, cause i still am very lost with this question, and don't know where to start.
    centripetal force is what you're after. It always points inwards towards the center of rotation and the opposite reaction, plus gravity, is what creates tension on the rope.

    the magnitude of the force is $\dfrac {m|v|^2} r$

    draw the force body diagram now that you know about this force.

    You might try drawing it w/o gravity to begin with, as if you were spinning a bucket deep in space.
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