| BETA : Cyclic : Centripetal Force 05 : Balanced Forces Kinetic Energy For Vertical Circular Motion : Beta Physics Homework Game
Description : Balanced forces and kinetic energy for vertical circular motion.
Discussion : At the balance velocity, the centripetal force and gravity force are equal when the mass is at the top of the circle. At this point the kinetic energy is at a minimum and the potential energy is at a maximum. At the bottom of the circle the kinetic energy at at a maximum and the potential energy is at a minimum. See Figure Vertical Circular Motion At the balance condition at the top of the cycle:
vt = √(r * g)
kt = m / 2 * vt2
rearranging
r = v2 / g
vt = √(2 * kt / m)
At the bottom of the circle:
kb = kt + 2 * m * g * r
vb = √(2 * kb / m)
where
vt = velocity at top of circle
vb = velocity at bottom of circle
kt = kinetic energy at top of circle
kb = kinetic energy at bottom of circle
r = radius
m = mass
g = gravity acceleration
Gravity is given here as a constant : g = 9.81 m/s2.
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