Question About Conservation of Momentum

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Discussion Overview

The discussion centers around the conservation of momentum in the context of a swinging pendulum. Participants explore the implications of momentum loss as the pendulum comes to a stop, considering external forces and interactions with the environment.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant notes that the pendulum has momentum due to its mass and velocity, but questions where the momentum goes as it loses amplitude.
  • Another participant asserts that the pendulum is not an isolated system, and therefore its momentum is not conserved.
  • A follow-up inquiry seeks to identify which external masses gain the momentum lost by the pendulum.
  • It is suggested that the Earth absorbs the momentum, although the change in its velocity is negligible.
  • Participants discuss the mechanisms of momentum transfer, including friction at the fulcrum and air resistance affecting the pendulum's motion.
  • One participant emphasizes that every force exerted by the Earth on the pendulum results in an equal and opposite force, leading to momentum transfer.
  • Another point raised is that the pendulum loses momentum not just as it stops, but continuously during its oscillations.

Areas of Agreement / Disagreement

Participants generally agree that the pendulum is not a closed system and that momentum is transferred to the Earth. However, the specifics of how this transfer occurs and the implications of momentum loss remain points of discussion.

Contextual Notes

There are discussions about the roles of friction and air resistance, but the exact quantitative effects and the definitions of the system boundaries are not fully resolved.

Who May Find This Useful

This discussion may be of interest to those studying mechanics, particularly in understanding momentum conservation and the effects of external forces on dynamic systems.

Master Wayne
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This has been bugging me for a while. Imagine a pendulum swinging. Since it has mass and velocity, it has momentum. After a while, though, it will swing with less and less amplitude until it has stopped. Where did the momentum go? Thanks a lot for your help!
 
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A pendulum is not an isolated system. Its momentum is not conserved.
 
DaleSpam said:
A pendulum is not an isolated system. Its momentum is not conserved.

I understand. So where did the momentum go? Which masses have now the velocity? Outside of the pendulum, that is.
 
Master Wayne said:
I understand. So where did the momentum go? Which masses have now the velocity? Outside of the pendulum, that is.
The earth. The resulting change in the Earth's velocity is incredibly small, but that is where the momentum went.
 
DaleSpam said:
The earth. The resulting change in the Earth's velocity is incredibly small, but that is where the momentum went.

That's quite interesting. But how does that transfer of momentum happen in terms of the forces involved?
 
The reason the pendulum is NOT a 'closed system' is that you have friction both at the fulcrum and with the air. As the pendulum moves to the right, say, the friction between it and the support applies a force to the left on the support. If the support is rigidly attached to, say, a table which in turn is attached to a floor which ... is attached to the earth, that force is transmitted to the earth. The air resistance, on the other hand, reduces the momentum of the pendulum by transmitting momentum to individual molecules in the air.
 
Master Wayne said:
That's quite interesting. But how does that transfer of momentum happen in terms of the forces involved?
Every force that the Earth exerts on the pendulum has an equal and opposite force that the pendulum exerts on the earth. Therefore, whatever momentum the pendulum loses is gained by the earth. This is a basic feature of Newtonian mechanics.

PS in case it is not clear, I am including the air and the support structure as part of the earth, not just dirt and rocks etc.
 
Last edited:
And, of course, it's not just as the oscillations die down that the pendulum loses its momentum. Every half-swing the pendulum loses its momentum, and in the next half cycle it acquires (and then loses) momentum in the opposite direction.
 
I believe I understand this now. Thanks a lot for your help!
 

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