TBR Physics Pendulum and conservation of momentum

[silverice]

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For those who have BR, this is physics chapter 5 passage 1 question2. The question is basically asking in a oscillating pendulum whether or not kinetic energy and momentum are conserved. BR answer key said that it is not. I'm very confused. I thought KE is conserved. please see image for detailed question and answer key.

 

[milski]

I cannot even see the pictures that you've attached, so what I say might not be directly related to the question.

If there is no friction, KE is preserved in a sense that no energy is lost.As the pendulum swings KE is continuously converted to PE and back to KE. So KE will change but at any point PE+KE=const.

The question of momentum is slightly more complex, it depends on what you define as your system. If you consider only the pendulum and treat its stand as non-moving, the momentum is not preserved. That's fairly obvious, if you consider that the speed of the pendulum at its most deflected position is 0, making its moment 0.

With that said, that does not contradict the preservation of momentum, since you need to consider the whole system including whatever the pendulum is attached to to say that the momentum is preserved. That does not have much practical value, at least for the MCAT.

If I had to guess, they are trying to say that you cannot say that the KE or the momentum of the pendulum are the same at any point of its movement.

 

[silverice]

Hi I've reattach the images, it should be fine this time.
I think the system is just the pendulum but it is affected by gravity of course otherwise it wouldn't be swinging.
I get very confused in general when I approach to physics problems. What is my system, what conditions should I assume and what conditions should I not assume. Regarding to this question, how would I know they asking about conservation overall, or conservation at a given point.
View attachment photo.JPG

View attachment photo (1).JPG

 

[silverice]

I cannot even see the pictures that you've attached, so what I say might not be directly related to the question.

If there is no friction, KE is preserved in a sense that no energy is lost.As the pendulum swings KE is continuously converted to PE and back to KE. So KE will change but at any point PE+KE=const.

The question of momentum is slightly more complex, it depends on what you define as your system. If you consider only the pendulum and treat its stand as non-moving, the momentum is not preserved. That's fairly obvious, if you consider that the speed of the pendulum at its most deflected position is 0, making its moment 0.

With that said, that does not contradict the preservation of momentum, since you need to consider the whole system including whatever the pendulum is attached to to say that the momentum is preserved. That does not have much practical value, at least for the MCAT.

If I had to guess, they are trying to say that you cannot say that the KE or the momentum of the pendulum are the same at any point of its movement.

Thank you very much for your help.
I'm a little confused about the preservation of momentum concept. Momentum is conserved whenever the velocity hasn't changed?

 

[milski]

Thank you very much for your help.
I'm a little confused about the preservation of momentum concept. Momentum is conserved whenever the velocity hasn't changed?

Momentum is conversed in closed systems - when there are no external forces to the system. In the case of pendulum you have gravity acting on it. You have to include the Earth itself to be able to talk about preservation of momentum.

What that means is that the sum of all momentums in the system will stay constant. In the pendulum case, its momentum decreases to zero when it stops. The momentum of Earth at that moment has to increase to keep the sum constant.

 

[silverice]

Momentum is conversed in closed systems - when there are no external forces to the system. In the case of pendulum you have gravity acting on it. You have to include the Earth itself to be able to talk about preservation of momentum.

What that means is that the sum of all momentums in the system will stay constant. In the pendulum case, its momentum decreases to zero when it stops. The momentum of Earth at that moment has to increase to keep the sum constant.

when you mention the earth and sun you just made it a lot more intuitive.

 

[MedPR]

when you mention the earth and sun you just made it a lot more intuitive.

The earth and sun?

Momentum is not conserved because you can pick two points on the path of the pendulum and see that the velocities are different.

 

[milski]

The earth and sun?

Momentum is not conserved because you can pick two points on the path of the pendulum and see that the velocities are different.

Earth and sum is what he probably meant.

Momentum is not conserved because you have a force external to the system. Being able to pick the two point is just a demonstration of that, not a reason.

 

[MedPR]

Earth and sum is what he probably meant.

Momentum is not conserved because you have a force external to the system. Being able to pick the two point is just a demonstration of that, not a reason.

There aren't any external forces in elastic collisions? I can't think of any, but I just want to be sure 🙂

 

[milski]

There aren't any external forces in elastic collisions? I can't think of any, but I just want to be sure 🙂

Will answer, driving home...


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I am here: http://maps.google.com/maps?ll=47.650019,-122.322062

 

[milski]

There aren't any external forces in elastic collisions? I can't think of any, but I just want to be sure 🙂

No, there are no external forces in elastic collision, if you consider the two bodies colliding to be the system and there is no friction/air resistance, etc. In that case not only the momentum but the kinetic energy is preserved as well.

 

[silverice]

No, there are no external forces in elastic collision, if you consider the two bodies colliding to be the system and there is no friction/air resistance, etc. In that case not only the momentum but the kinetic energy is preserved as well.

Hi, I'm sorry for being so slow. But how do you determine whether momentum or kinetic energy is conserved?

 

[milski]

Hi, I'm sorry for being so slow. But how do you determine whether momentum or kinetic energy is conserved?

No problem, it can be confusing matter. The conservation of momentum comes from the law of conservation of momentum: "If the sum of the external forces on a system remains zero, the total momentum of the system remains constant". Lack of external forces is obviously a case of their total sum being zero.

The kinetic energy preservation comes from the definition of elastic collision: In an elastic collision, the kinetic energy of the system is the same before and after the collision. These generally don't happen in real life, at least not on macro level. Most collisions of real life objects are at least somewhat inelastic which means that you end up with less kinetic energy.

Note that the conservation of momentum does not depend on the type of collision.

 

[MedPR]

No problem, it can be confusing matter. The conservation of momentum comes from the law of conservation of momentum: "If the sum of the external forces on a system remains zero, the total momentum of the system remains constant". Lack of external forces is obviously a case of their total sum being zero.

The kinetic energy preservation comes from the definition of elastic collision: In an elastic collision, the kinetic energy of the system is the same before and after the collision. These generally don't happen in real life, at least not on macro level. Most collisions of real life objects are at least somewhat inelastic which means that you end up with less kinetic energy.

Note that the conservation of momentum does not depend on the type of collision.

I'd say this is as good an explanation as any. It's hard to give a really clear, yet general enough explanation to apply to different types of situations (pendulum, collisions, incline plane, pulleys, etc), if you don't have a good understanding of the underlying concepts of KE and mv.

When I started out I had absolutely 0 understanding of both, and "it's easier to do conservation of energy rather for almost any problem" was definitely not true for me. After doing lots of problems my way (trying to, anyway) I slowly began thinking about conservation of energy and now it makes sense. It's really discouraging at first because you might have absolutely no idea where to even begin. With experience, everything in physics begins to make sense.

 

[silverice]

No problem, it can be confusing matter. The conservation of momentum comes from the law of conservation of momentum: "If the sum of the external forces on a system remains zero, the total momentum of the system remains constant". Lack of external forces is obviously a case of their total sum being zero.

The kinetic energy preservation comes from the definition of elastic collision: In an elastic collision, the kinetic energy of the system is the same before and after the collision. These generally don't happen in real life, at least not on macro level. Most collisions of real life objects are at least somewhat inelastic which means that you end up with less kinetic energy.

Note that the conservation of momentum does not depend on the type of collision.

In the case of the pendulum, we can say momentum is not conserved because gravity is acting upon it.
We can look for hints from the system to see if momentum is conserved or not by picking two points of the oscillating path and see if the velocities are the same?

 

[milski]

In the case of the pendulum, we can say momentum is not conserved because gravity is acting upon it.
We can look for hints from the system to see if momentum is conserved or not by picking two points of the oscillating path and see if the velocities are the same?

Yes, that's the idea. Although you want to make sure that the momentum is the same, (m*v), not just the velocity. For constant mass what you're saying makes sense.

MedPR, what was your concern about elastic collisions? Or am I too tired to pick up a joke? 😴

 

[MedPR]

Yes, that's the idea. Although you want to make sure that the momentum is the same, (m*v), not just the velocity. For constant mass what you're saying makes sense.

MedPR, what was your concern about elastic collisions? Or am I too tired to pick up a joke? 😴

I just wanted to make sure that my understanding of elastic collisions and conservation of mv is accurate.

So conservation of mv = external forces sum to 0.

I have memorized that KE and mv are both conserved in elastic collisions. So, in elastic collisions are there:

A. no external forces?
B. external forces that sum to 0?

If B, what are the external forces?

 

[milski]

For practical purposes what you are saying is correct. Since collisions happen in a very short time interval a lot of times you can ignore the change of momentum that is coming from any external forces.

For example if you have a big ball which has bounced from the floor and is going up collide with another ball dropping on top of it, you can treat that as an elastic collision and calculate the new velocities of the balls as if that was a closed system and the moment was preserved.

In reality, there is a constant gravity force on both balls and during the collision the raising ball will lose a bit of momentum to Earth, the falling ball will lose a bit of momentum to it. For the short time period in which the collision happens both of these changes will be insignificant.

 

[chiddler]

What's the difference between angular momentum and momentum?

 

[milski]

What's the difference between angular momentum and momentum?

Same as the difference between rotational and linear motion. 😉 The former applies to rotations, the latter to linear motion.

 

[Meredith92]

( sorry for bumping up this thread) just to check- conservation of angular momentum also requires no external forces?

 

[milski]

( sorry for bumping up this thread) just to check- conservation of angular momentum also requires no external forces?

Good question - the answer is that it requires no external torque, which is not the same as no external force. You can have external non-zero net force and still preserve angular momentum. For example, a CD player on a car - as the car accelerates/decelerates on a straight line, it does experience external forces but the CD in the player maintains constant angular momentum.

In general
torque/angular velocity/angular acceleration/angular momentum
[translational] force/[translational] velocity/[translational] acceleration/[translational] momentum
are two independent things and you can move between the two only by going through torque/force exchange.

 

[Meredith92]

So in the example of the pendulum there's a net torque on the system? Is that also from gravity acting on the pendulum? Would the string holding the pendulum mass act as a lever arm?

And thanks for your help

 

[Meredith92]

( since the answer says angular momentum is not conserved)

 

[milski]

Exactly. At any point (different from the equilibrium point), you'll have a torque created by the gravity action on the pendulum.