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Math Help - Potential question

  1. #16
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    Re: Potential question

    Yeah, the u_c is included. So you could make those half-open intervals. Which post in particular did you have in mind for me to review?
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  2. #17
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    Re: Potential question

    post number eleven, thank you very much!
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  3. #18
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    Re: Potential question

    Quoting post # 11:

    Quote Originally Posted by Darkprince View Post
    I am still confused to tell you the truth, let me write again how I would have written the solution to guide me over my way or if you can explain me again the way on your previous post with uc.

    Let u (vector) be the initial velocity and v=magnitude(u) i.e speed. Then total enerfy = 0.5*v^2-1/20
    Now if a) u>0, we need 0<=E<1/16,
    Correct.

    b) if u<0 we need E>=0 and if u=0 then E=-1/20 and our condition is not satisfied.
    Right. The particle will not escape the potential well.

    a) 0<=0.5*v^2-1/20<1/16 leads to the solution sqrt(10)/10 <= v < 3* sqrt(10)/20, since v is speed and is always positive! But since we need positive velocity for this case then sqrt(10)/10 <= u (velocity) < 3* sqrt(10)/20
    I buy that.

    b) 0.5*v^2-1/20>=0 leads to the solution v>= sqrt(10) / 10 but we need negative velocity so u<= -sqrt(10)/10

    Our final solution is u exists in [sqrt(10)/10, 3*sqrt(10)/20) or u<= -sqrt(10)/10
    Yep. Looks good to me.
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  4. #19
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    Re: Potential question

    Thank you very much for all your time
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  5. #20
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    Re: Potential question

    You're welcome. Have a good one!
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