Momentum (Non)Conservation in Pendulums

[justadream]

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So TBR says that momentum is not conserved in pendulums (since gravity acts as an external force).

If that is so, then why is momentum conserved in the "newton's cradle" situation (again, this is according to TBR)?

 

[orangetea]

Because in Newton's cradle the balls are experiencing elastic collisions(conservation of momentum and energy). Imagine if Newton's cradle consisted of only two balls.
When the first ball is lifted it transfers all of it's momentum to the second ball. Since the balls are the same mass the second ball's velocity is the same as the initial ball moving towards it. So the there is not net change in the momentum of the system.


Where as for a single pendulum there is an external force acting on the Pendulum (gravity) which means that while energy is conserved momentum is not since conservation of momentum is only true when there are no external forces acting on the object. Hope that makes sense.

 

[sillyjoe]

Because in Newton's cradle the balls are experiencing elastic collisions(conservation of momentum and energy). Imagine if Newton's cradle consisted of only two balls.
When the first ball is lifted it transfers all of it's momentum to the second ball. Since the balls are the same mass the second ball's velocity is the same as the initial ball moving towards it. So the there is not net change in the momentum of the system.


Where as for a single pendulum there is an external force acting on the Pendulum (gravity) which means that while energy is conserved momentum is not since conservation of momentum is only true when there are no external forces acting on the object. Hope that makes sense.

In a real system is Newton's cradle an elastic collision? And how is gravity not acting on Newton's cradle?

 

[orangetea]

In a real system does the conservation of momentum really occur in Newton's cradle?

I mean you ideally need a closed system which is like impossible but if you make sure the masses are the same and the balls are the same length it should be pretty accurate. I've also heard the more balls there are the less accurate it is. It's fun toy though!

 

[sillyjoe]

I mean you ideally need a closed system which is like impossible but if you make sure the masses are the same and the balls are the same length it should be pretty accurate. I've also heard the more balls there are the less accurate it is. It's fun toy though!

How is gravity not an external force in Newton's cradle as compared to a pendulum?

 

[sillyjoe]

How is gravity not an external force in Newton's cradle as compared to a pendulum?

Forget it. I found an answer from @BerkReviewTeach from a few years back:

For pendulum systems, you need to first consider whether energy is being lost (work is being done by friction). If energy is being lost then total energy is not conserved (and the bob doesn't reach as high of a maximum height on successive swings and it doesn't reach as great a maximum speed on successive swings). If there is no friction and the max height stays constant, then total energy is conserved.

Momentum of the pendulum is not conserved, because it is constantly changing during the flight of the pendulum. As you noted, gravity is acting on it. Dingyibvs brings up the fact that you need to pay attention to what exactly is included in the system you are considering. If it's just the pendulum, as your qurestion implies, then momentum is not conserved. But if it includes the earth, then as one gains momentum, the other counters it (recoils if you will), and momentum is conserved.

As far as the MCAT is concerned, it will likely be straight forward as described above, but do your due diligence and make sure it's just the pendulum bob they are asking about and whether friction is affecting its swing.

 

[orangetea]

Also Kevin Wei is a boss at explaining this.



best 3:12 min of my life.

 

[sillyjoe]

Thanks @orangetea !

 

[justadream]

@sillyjoe

Thanks for the dig-up. So are you implying that the system being considered for Newton's cradle is different from that of just a normal pendulum (is this the reason why momentum is considered to be "conserved" in the former but not the latter?)