I get the theory:
Fc = Ft + Fg
Uniform circular motion, in the vertical plane.
Fc = net force = centripetal force
Ft = force of tension in the string
Fg = force of gravity
so at the top, with vector addition:
Ft = Fc- Fg
And if we define 'up' as positive, then should the equation look like
-Ft = -(mv^2/r) - (-mg)
because all these forces point down (to the centre)
or just
Ft = -(mv^2/r) - (-mg)
because Ft should COME OUT negative after the arithmetic?
Sometimes, in some questions, the answer key has Ft positive. Why? Does that mean the system is impossible (ie/ velocity is not sufficient) or just that the answer keys are wrong? My sense is that IF Ft comes out positive, that would imply that the string pushes outward, which is not what physics tells us. All the forces are directed toward the centre of the circle (at the top of the circle). Period.
Should we just define "to the centre" as positive and then this won't be a problem? Help!?
Fc = Ft + Fg
Uniform circular motion, in the vertical plane.
Fc = net force = centripetal force
Ft = force of tension in the string
Fg = force of gravity
so at the top, with vector addition:
Ft = Fc- Fg
And if we define 'up' as positive, then should the equation look like
-Ft = -(mv^2/r) - (-mg)
because all these forces point down (to the centre)
or just
Ft = -(mv^2/r) - (-mg)
because Ft should COME OUT negative after the arithmetic?
Sometimes, in some questions, the answer key has Ft positive. Why? Does that mean the system is impossible (ie/ velocity is not sufficient) or just that the answer keys are wrong? My sense is that IF Ft comes out positive, that would imply that the string pushes outward, which is not what physics tells us. All the forces are directed toward the centre of the circle (at the top of the circle). Period.
Should we just define "to the centre" as positive and then this won't be a problem? Help!?
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