Apparent weight problem (kinematics + conservation of Energy + Newton's laws)

[malawi_glenn]

Yeah, and at point 2 it would be:

$F_N \mathbf{\hat j} -mg \mathbf{\hat j} = \dfrac{v^2}{R} \mathbf{\hat j}$

I still feel as though we are manually intervening a bit?

One should probably write F_N2, v₂ and F_N3, v₃ to assert we are not dealing with the same F_N and v at all points.

 

[Orodruin]

@erobz there is a curse... if you mess with Newton, he will summon a giant apple from the sky which will fall upon thy head

Luckily Einstein’s theory showed that free falling objects have zero proper acceleration and he was saved as he adopted a local inertial feame where there was no ”up” for the apple to fall from.

 

[simphys]

Yeah, and at point 2 it would be:

$F_N \mathbf{\hat j} -mg \mathbf{\hat j} = \dfrac{v^2}{R} \mathbf{\hat j}$

I still feel as though we are manually intervening a bit?

Erobz do you know about the tangential and normal components aka n-t axes(for curvilinear motion)
it states that the positive normal axis (perpendicular to the tangential axis) is always towards the concave inside and thus towards center of curvature where in this case this center of curvature is constant as the motion itself is a circle.

 

[simphys]

Nobody is messing with Newton’s laws. It is just that you chose your positive direction to be away from the center instead of towards the center. The centripetal force has magnitude $mv^2/r$ and points to the center of the circular motion.

as orodruin actually indicated.

 

[Orodruin]

I wasn't making accusations, I just realized that I was making that adjustment to get a solution, without knowing the justification.

That was not the point or the important part of my post. The important point came after.

 

[erobz]

Erobz do you know about the tangential and normal components aka n-t axes(for curvilinear motion)
it states that the positive normal axis (perpendicular to the tangential axis) is always towards the concave inside and thus towards center of curvature where in this case this center of curvature is constant as the motion itself is a circle.

I may have known that 15 years ago..."If you don't use it, you lose it" is a real thing.

 

[erobz]

That was not the point or the important part of my post. The important point came after.

Yeah, it just bothered me that it seems like you have to have some knowledge of the center of rotation to properly solve the equation.

 

[simphys]

I may have known that 15 years ago..."If you don't use it, you lose it" is a real thing.

A quick check up and you're good to go if you would ever need it

 

[erobz]

Luckily Einstein’s theory showed that free falling objects have zero proper acceleration and he was saved as he adopted a local inertial feame where there was no ”up” for the apple to fall from.

The funny part of this (for me) was laughing at how hard I had to think...to not get it!

 

[simphys]

The funny part of this (for me) was laughing at how hard I had to think...to not get it!

Hahaha it happens sometimes. At least you get it now, I hope at least
xD

 

[simphys]

I mean if not it's whatever really.. you didn't these 15 years anyways lol

 

[erobz]

I mean if not it's whatever really.. you didn't these 15 years anyways lol

Yeah...you'd be surprised by what you can get away with, without knowing.