The discussion revolves around the behavior of a pendulum in a lift that is accelerating downward at gravitational acceleration (g) after the cable breaks. Participants explore whether the pendulum would stop swinging and remain in its current position relative to the lift.
Participants express differing views on the conditions under which the pendulum would stop swinging or remain stationary. No consensus is reached, as multiple competing perspectives are presented throughout the discussion.
The discussion includes assumptions about the pendulum's initial conditions and the effects of acceleration on its motion, which remain unresolved. The dependence on specific angles and kinetic energy states is also highlighted but not fully clarified.
Glenn G said:Assume a pendulum was swinging in a lift. If the cable breaks and the lift starts to accelerate down at g would the pendulum stop swinging and freeze in its current position?
Merry Xmas.
G.
The bob was originally following a circular path. It would (in general) have a vertical and horizontal component to its velocity. and tension in the string So it would continue to move sideways and vertically relative to the lift cage if the pivot point started to accelerate downwards at g. There would / could still be some tension in the string (details depending on the part of the cycle of the pendulum. The only situation in which the bob would carry on down in the same position relative to the lift cage would be if the cable broke when the pendulum was horizontal, at which point there would be no tension and the acceleration of the bob would just be g. Only then it would appear "frozen".lekh2003 said:Yes it would, assuming the lift is accelerating exactly at g. The only thing keeping the pendulum moving was the acceleration downward relative to its surroundings. If its surroundings are accelerating downwards, then the pendulum should stay still.
Ahh, thanks for the correction.sophiecentaur said:So it would continue to move sideways and vertically relative to the lift cage if the pivot point started to accelerate downwards at g.
That isn't correct though. The pendulum could have zero kinetic energy when it is at any angle. It doesn't have to be completely horizontal. It will not move when it has zero kinetic energy.sophiecentaur said:The only situation in which the bob would carry on down in the same position relative to the lift cage would be if the cable broke when the pendulum was horizontal, at which point there would be no tension and the acceleration of the bob would just be g.
Oh yes, I think you're right there. Any situation where the bob is stationary wrt the lift frame (extremity of its swing), the tension would disappear etc. etc.lekh2003 said:That isn't correct though. The pendulum could have zero kinetic energy when it is at any angle. It doesn't have to be completely horizontal.