Does a Pendulum Stop Swinging in a Falling Lift?

[Glenn G]

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.

 

[lekh2003]

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.

 

[anorlunda]

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.

Clever question. I like it. I think @lekh2003 gave the right answer.

One of those schoolchildrern should ask the ISS astronauts if a pendulum clock would work in orbit.

 

[sophiecentaur]

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.

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]

So it would continue to move sideways and vertically relative to the lift cage if the pivot point started to accelerate downwards at g.

Ahh, thanks for the correction.

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.

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]

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.

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.