Thread: 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?

post number eleven, thank you very much!

Quoting post # 11:

Originally Posted by Darkprince

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.

Thank you very much for all your time

You're welcome. Have a good one!