Originally posted by joe shmoI have to say that I didn't actually read al of your post with that much attention but this bit I'm quoting isn't necessarily true.
and dF/dA = -mg*sinA = 0; A=0
which minimizes the force function i just derived.
but i should expect the force to be maximized when her velocity is maximized at A =0
Originally posted by AThousandYoungIf this is serious question, she eccentially straightened the S hook on the bottom causing the chain to come free of the crossbar.
I'm really curious what bending an S hook is such that it sends her into the air...
(yes I know this is about playgrounds and the little metal S that attaches the seat to the chain)
What you exclaimed above is consistent with the equation, so I guess it comes down to poor logical interpretation of the model.This time I'll actually read your post.
and why did i say it?
F=(m/R)*v^2
m/R is constant, so the force would be largest in its valid range, when velocity is largest in its domain? Thats how I interpret it, why thats apparently incorrect i'm not sure?
subbing this in to the energy equation and solving for v^2
v^2 = 2gR(cosA -1)
Originally posted by adam warlockAs for the "RsinA"...For some reason I just dont see that simplification.
This time I'll actually read your post.
"-mgh = (1/2)mv^2"
What this equation expresses is that you're considering the point of highest height (hence with zero velocity) and the point of 0 height (hence with maximum speed ).
Your next equation: h = R - R*cosA tells me that your A angle is measured starting from the axis that represents maximum your post but I want to be sure I really understood the scenario you're describing.
Originally posted by joe shmo
So where do we go from here, I also am having trouble wrapping my head around how/why my starting equation pigeon holes the height to be a maximum
and that negative had was not because of g (wether right or wrong) it came from
final PE minus Intital PE, final is 0, and final KE - Initial KE, this side inital =0
I also am having trouble wrapping my head around how/why my starting equation pigeon holes the height to be a maximum
and that negative had was not because of g (wether right or wrong) it came from
final PE minus Intital PE, final is 0, and final KE - Initial KE, this side inital =0
Originally posted by adam warlock"1/2mv^2+mgh=1/2mu^2+mgz where v and u represent velocities and h and z represent heights. If you write -mgh = (1/2)mv^2 you're dropping terms from the full equation and the meaning of dropping those two terms is that you're saying the left hand side of your equation has zero velocity (thus maximum height) and the right side of your equation has zero height (thus maximum velocity)."I also am having trouble wrapping my head around how/why my starting equation pigeon holes the height to be a maximum
Because by conservation of energy we know that:
1/2mv^2+mgh=1/2mu^2+mgz where v and u represent velocities and h and z represent heights. If you write -mgh = (1/2)mv^2 you're dropping terms from the full equation and ...[text shortened]... tion states is that v^2<0 and this can't be since v is a real number.
Sorry for the delay.
Originally posted by joe shmoThis is why whenever you're solving a problem in Physics you should always precisely state your assumptions and conditions. And at the end you should also check if the final expression makes sense or not...
and about the "g" I did realize that it must be negative to make sense, however as you can see rather than redflagging the result for further analysis( which may have led me to my inconsitency) I blew it off...something I won't take lighty anymore.