What happens to a pendulum clock in a lift when the cable breaks?

[songoku]

Homework Statement

A pendulum clock is being operated in a lift. What will happen to the pendulum when the lift cable breaks?
a. oscillation will continue but the period will decrease
b. oscillation will stop
c. oscillation will continue but the period will increase
d. the pendulum will hit the ceiling of lift

Relevant Equations

T = 2π √(L/g)

I think the answer will be either (b) or (d).

If the pendulum is at its amplitude when the cable breaks, then the oscillation will stop since the pendulum is also not moving at that instant.

If the pendulum is at any points except amplitude, then it will hit the ceiling since it still has speed at this instant.

I guess the answer is (d) because the question does not specify that the pendulum is at its amplitude so I assume the pendulum is moving when the cable breaks.

Am I correct? Thanks

 

[haruspex]

Don't confuse "oscillation will stop" with "pendulum will stop rotating".

 

[songoku]

Don't confuse "oscillation will stop" with "pendulum will stop rotating".

By pendulum rotating you mean it moves in circular?

 

[haruspex]

By pendulum rotating you mean it moves in circular?

I mean moving relative to the lift. You seem to have interpreted "oscillation will stop" as "will be stationary relative to the lift".

 

[songoku]

I mean moving relative to the lift. You seem to have interpreted "oscillation will stop" as "will be stationary relative to the lift".

Yes that's how I interpreted it

Because I think when the pendulum is at its amplitude, the speed is zero so it is instantaneous at rest so when the cable breaks, the pendulum and lift will move downward with same initial velocity (zero) and same acceleration (gravity) so the pendulum will be stationary relative to lift. Am I wrong?

 

[haruspex]

Yes that's how I interpreted it

Then why did you rule out b?

 

[songoku]

Then why did you rule out b?

I think I get the hint.

If it is at its amplitude, the oscillation will stop and the pendulum is stationary with respect to the lift.

If it is not at its amplitude, it will move with respect to the lift and will hit the lift (either the left / right side or the ceiling) and the oscillation will also stop

So the answer should be (b) because in either case the oscillation will stop and we can not know for sure whether it will hit the ceiling.

Am I correct? Thanks

 

[jbriggs444]

If it is at its amplitude, the oscillation will stop and the pendulum is stationary with respect to the lift.

If it is not at its amplitude, it will move with respect to the lift and will hit the lift (either the left / right side or the ceiling) and the oscillation will also stop

So the answer should be (b) because in either case the oscillation will stop and we can not know for sure whether it will hit the ceiling.

You have the physics correct. The remaining difficulty is trying to guess the mind-set of the question setter. Do we trust that the question was carefully phrased so that exact word meanings matter? Or do we expect that the focus was on the physics with little care for "trivial" things like wording?

The fact that a collision with the walls was not mentioned as a possibility leads me to distrust the question setter. So I'd pick d.

 

[songoku]

You have the physics correct. The remaining difficulty is trying to guess the mind-set of the question setter. Do we trust that the question was carefully phrased so that exact word meanings matter? Or do we expect that the focus was on the physics with little care for "trivial" things like wording?

The fact that a collision with the walls was not mentioned as a possibility leads me to distrust the question setter. So I'd pick d.

Why do you think (b) is wrong? Or at least not as good as (d)?

 

[jbriggs444]

Why do you think (b) is wrong? Or at least not as good as (d)?

If we decide that the question setter is being sloppy then "oscillation stopping" can be read as "relative motion stopping". Since relative motion does not [usually] stop, that would make b wrong in the eyes of the question setter.

 

[haruspex]

If we decide that the question setter is being sloppy then "oscillation stopping" can be read as "relative motion stopping". Since relative motion does not [usually] stop, that would make b wrong in the eyes of the question setter.

I'm not sure.
Its relative motion would be to rotate at constant rate, which I would not count as oscillating in an everyday sense. Perhaps one can argue that is still technically an oscillation.
It does not say the pendulum swings from the ceiling of the lift, so no reason to suppose it can hit it; rather, it is described as a clock, which would imply e) it will hit the side of the clock!

 

[brotherbobby]

The question (using Einstein's PoE) is the same as the lift hanging in gravity-free space with the pendulum inside it.
(1) If the pendulum is at rest (having exactly reached its amplitude), then it remains at rest.
(2) If the pendulum was moving with a speed $v$, it undergoes a uniform circular motion with the speed, attached to the string. The centripetal force necessary for such a motion is provided by the tension in the string. Such a tension will pull on the lift at its point of suspension, which the lift has to make up for using its own rigid forces.

 

[songoku]

(2) If the pendulum was moving with a speed $v$, it undergoes a uniform circular motion with the speed, attached to the string. The centripetal force necessary for such a motion is provided by the tension in the string. Such a tension will pull on the lift at its point of suspension, which the lift has to make up for using its own rigid forces.

Won't the string become slack and the tension is zero? I though the motion of the pendulum will be more like projectile motion rather than circular motion

 

[haruspex]

Won't the string become slack and the tension is zero? I though the motion of the pendulum will be more like projectile motion rather than circular motion

Putting the lift into free fall just removes gravity. What is the motion of a mass attached to a fixed point by a taut string, in the absence of gravity, when given an initial tangential push?

 

[songoku]

Putting the lift into free fall just removes gravity. What is the motion of a mass attached to a fixed point by a taut string, in the absence of gravity, when given an initial tangential push?

I see. It will move in uniform circular motion until it hits something.

Thank you very much for the help haruspex, jbriggs444, brotherbobby