Minimum Velocity for a Loop-the-loop Pendulum
Most recent answer: 10/05/2014
- Shawn (age 16)
India
Hi shawn,
Both answers are right! It depends on what sort of pendulum you are dealing with. If the pendulum is made with a weight at the end of a mass-less rod then you get v2 = 4gL This is easily obtained by equating the kinetic energy at the bottom, 1/2 mv2, to the potential energy at the top, 2mgL. However, if you suspend the mass on a flexible string then the string cannot support any compressive force and will crumple before it gets to the top due to the gravitational force. If you want to prevent this you need some extra velocity in order to have a centrifugal force counteracting that of gravity at the top. This is mv2/L = mg. Adding this needed extra energy will give you the other answer v2 = 5gL.
LeeH
(published on 10/05/2014)