18 Aug '10 03:161 edit

So my mother, who likes to swing alot, bent the S hook whilst swinging, thus sending her into the air. I just wanted to see what kind of force she applied to it, but somewhere I feel that my mathematics are inconsistent, can anyone help me find the flaw in my mathematics/logic/model?

I started with conservation of energy

-mgh = (1/2)mv^2

m= mass

g= acceleration due to gravity

v= linear velosity

h = height

so I start with her at rest at 0 P.E., and allow her to be lifted to a certain height whitch as a function of the angle subtended "A" and the radius "R" is as follows:

h = R - R*cosA

subbing this in to the energy equation and solving for v^2

v^2 = 2gR(cosA -1)

since there are two chains im assuming the force is split equally amongst them

such that

F = mv^2/(2R) = mg(cosA-1)

here by inspection i see the force is max at A = pi/2

but i should expect the force to be maximized when her velocity is maximized at A =0

and dF/dA = -mg*sinA = 0; A=0

which minimizes the force function i just derived. ๐

where am I being inconsistent in my analysis? I realize due to a lack of a diagram this may be a tricky to explain.

I started with conservation of energy

-mgh = (1/2)mv^2

m= mass

g= acceleration due to gravity

v= linear velosity

h = height

so I start with her at rest at 0 P.E., and allow her to be lifted to a certain height whitch as a function of the angle subtended "A" and the radius "R" is as follows:

h = R - R*cosA

subbing this in to the energy equation and solving for v^2

v^2 = 2gR(cosA -1)

since there are two chains im assuming the force is split equally amongst them

such that

F = mv^2/(2R) = mg(cosA-1)

here by inspection i see the force is max at A = pi/2

but i should expect the force to be maximized when her velocity is maximized at A =0

and dF/dA = -mg*sinA = 0; A=0

which minimizes the force function i just derived. ๐

where am I being inconsistent in my analysis? I realize due to a lack of a diagram this may be a tricky to explain.