Bannana Monkey System Homework: Explaining Movement of Centre of Mass

[ritwik06]

Homework Statement

The monkey wishes to get the bananas. It starts climbing up with an accleration 'a'.

Consider the situation using Newton's Laws of motion:
FBD for monkey:
T-mg=ma
For bananas:
T-mg=ma'

Its but obvious that a'=a. That is both the monkey and the bananas go up by the same acceleration.

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Now consider this situation:

The monkey pulley and bananas are in one system. The external forces acting on the system is just the gravitaional force by the Earth which is 2mg(other components assumed to be massless) vertically downwards. And the tension in the string segment btween the rigid support and the pulley.

How will we explain the movement of centre of mass?

 

[Dick]

If I'm guessing your picture correctly, then the support, pulley and the Earth are in the same system as the monkey and bananas. The center of mass of the entire system doesn't move.

 

[tiny-tim]

If I'm guessing your picture correctly, then the support, pulley and the Earth are in the same system as the monkey and bananas. The center of mass of the entire system doesn't move.

Hi Dick!

But the centre of mass of the system minus the Earth can move relative to the earth.

(btw, I'm guessing that the picture has a lady monkey up another tree, and the first monkey is throwing the bananas to her as soon as he gets them! )

 

[ritwik06]

If I'm guessing your picture correctly, then the support, pulley and the Earth are in the same system as the monkey and bananas. The center of mass of the entire system doesn't move.

No: The pulley, monkey string and bananas are assumed one system by me.
http://img135.imageshack.us/img135/1105/fbdcb6.th.jpg

 

[ritwik06]

Hi Dick!

But the centre of mass of the system minus the Earth can move relative to the earth.

(btw, I'm guessing that the picture has a lady monkey up another tree, and the first monkey is throwing the bananas to her as soon as he gets them! )

I support Tim, its exactly what I presume, everything except the earth.




But I wonder where's that lady monkey

 

[Dick]

The pulley and support are free falling? Or is something holding them up?

 

[Doc Al]

Don't forget the string that supports the pulley.

 

[ritwik06]

The pulley and support are free falling? Or is something holding them up?

They are not free falling.

 

[ritwik06]

Don't forget the string that supports the pulley.

If you read my first post carefully: I have mentioned tension in this segment of string as the external force.

 

[Doc Al]

If you read my first post carefully: I have mentioned tension in this segment of string as the external force.

You're right. So, what's the problem? If the monkey is to actually climb the rope, he must exert a tension greater than his weight. So there's a net upward force on the system.

 

[Dick]

If you read my first post carefully: I have mentioned tension in this segment of string as the external force.

A system with an 'external force' operating on it is not isolated. It's center of mass can move. Why should that be a problem? Can you state exactly what principle you are questioning?

 

[ritwik06]

I just wanted to get that Tension out without using Newton's Laws. Is it possible? Th centre of mass will have an accleration 'a' upwards. Right? But you know this only if you have the value of tension in the upper string.

 

[tiny-tim]

The external forces acting on the system is just the gravitaional force by the Earth which is 2mg(other components assumed to be massless) vertically downwards. …

How will we explain the movement of centre of mass?

Hi ritwik06!

Consider the forces on the string that goes round the pulley …

The mass of the monkey equals the mass of the bananas in this case … so why should the centre of mass move?

 

[Doc Al]

I just wanted to get that Tension out without using Newton's Laws. Is it possible? Th centre of mass will have an accleration 'a' upwards. Right? But you know this only if you have the value of tension in the upper string.

You know that the tension in the upper string equals the sum of the tensions in the lower string. That explains where the external force comes form. But you already knew the acceleration of the masses from the tension in the lower string.

What's your beef with Newton?

 

[Doc Al]

The mass of the monkey equals the mass of the bananas in this case … so why should the centre of mass move?

You are one crazy monkey, tiny-tim!

 

[tiny-tim]

more bananas, less beef!

I just wanted to get that Tension out without using Newton's Laws.

Why? Newton is your frend!

What's your beef with Newton?

"Nature and Nature's Laws lay hid in Night
God said, Let Newton be! and all was Light."​