Shifting of the center of mass of a system

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Homework Help Overview

The problem involves a cubical block of ice placed in a tray, examining how the center of mass of the system changes as the ice melts. Participants are exploring the implications of forces acting on the ice and tray system, particularly focusing on the normal force and weight balance during the melting process.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the assumption that the center of mass remains unchanged without net force and question the behavior of the normal force as the ice melts. There is an exploration of how the melting process affects the forces acting on the ice and the tray.

Discussion Status

The discussion is ongoing, with participants raising questions about the forces involved and the movement of melted water. Some guidance has been offered regarding the relationship between the forces and the motion of the melted ice, but no consensus has been reached on the implications for the center of mass shift.

Contextual Notes

Participants are grappling with the conceptual understanding of forces acting on the ice as it melts, particularly regarding the normal force and its changes throughout the process. The original poster's understanding of the problem setup and assumptions is also under scrutiny.

carlyn medona

Homework Statement



A cubical block of ice of mass m and edge L is placed in
a large tray of mass M. If the ice melts, how far does the
center of mass of the system "ice plus tray" come down ?

Homework Equations

The Attempt at a Solution


What I thought was that if no net force is acting on the system then position of center of mass should not change. But the answer in my text is mL/2(m+M). Can somebody explain me why is there a shift in center of mass.
 

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carlyn medona said:
no net force
You are making an unwarranted assumption about the normal force on the ice from the tray.
 
the normal force and weight is balanced right?
 
carlyn medona said:
the normal force and weight is balanced right?
For a mass that is not accelerating vertically that is true. But when the ice on the top melts, what happens?
 
haruspex said:
For a mass that is not accelerating vertically that is true. But when the ice on the top melts, what happens?

I will not interfere with OP's attempt to find the amount by which CM shifts .

But I guess OP is having difficulty analysing the forces on melting ice . Even I am having .

On the conceptual side , I find it quite interesting that the net downward force on the ice increases as ice melts .The weight of ice/water remain same which means the Normal force on melting ice decreases . Could you explain how ?

Wouldn't the normal force , before the ice starts melting and after ice has completely melted be same ?
 
conscience said:
I will not interfere with OP's attempt to find the amount by which CM shifts .

But I guess OP is having difficulty analysing the forces on melting ice . Even I am having .

On the conceptual side , I find it quite interesting that the net downward force on the ice increases as ice melts .The weight of ice/water remain same which means the Normal force on melting ice decreases . Could you explain how ?

Wouldn't the normal force , before the ice starts melting and after ice has completely melted be same ?
Try answering the question I posed. Consider a small piece of ice high up on one side of the block. What happens when it melts?
 
haruspex said:
Try answering the question I posed. Consider a small piece of ice high up on one side of the block. What happens when it melts?

Isn't the ice in the shape of a cubical block placed at the center of the tray ?
 
conscience said:
Isn't the ice in the shape of a cubical block placed at the center of the tray ?
Yes, but so? Does that stop your answering my question?
 
haruspex said:
What happens when it melts?

Water gets dispersed on the tray . CM of the system is lowered .

Sorry , if I am not understanding your question .
 
  • #10
conscience said:
Water gets dispersed on the tray . CM of the system is lowered .

Sorry , if I am not understanding your question .
How does the melted piece reach the tray?
 
  • #11
Okay so the melted water comes down because of net downward force, which implies normal force is less than weight. So what is the net force on the system?
 
  • #12
carlyn medona said:
Okay so the melted water comes down because of net downward force, which implies normal force is less than weight. So what is the net force on the system?
Consider the forces between the melted fragment and the solid block.
 
  • #13
So that means melted part is not in my system
 
  • #14
carlyn medona said:
So that means melted part is not in my system
A system is whatever you define it to be. But if you define it to to be the plate, the block, and any meltwater then parts of the system can move with respect to other parts. This means you may need to analyse smaller systems to understand the forces.
 
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  • #15
haruspex said:
How does the melted piece reach the tray?

I really don't know how to answer that question . Would you rephrase the question ?
 
  • #16
conscience said:
I really don't know how to answer that question . Would you rephrase the question ?
A fragment of the ice, high up on one side of the block, is stationary. Then it melts, and we know it ends up on the tray. By what process does it get from the top of the block to the bottom? It is a very simple question, with a very simple answer.
 
  • #17
I agree it is a simple question but I don't have an answer . Pardon for my dumbness . Could you explain the force analysis .
 
  • #18
conscience said:
I agree it is a simple question but I don't have an answer . Pardon for my dumbness . Could you explain the force analysis .
I wasn't looking for a force analysis at this stage, just "it runs down".
The point is that it goes from stationary to moving. What does that tell you, in general terms, about the forces on it?
 
  • #19
haruspex said:
I wasn't looking for a force analysis at this stage, just "it runs down".
The point is that it goes from stationary to moving. What does that tell you, in general terms, about the forces on it?

That there is a net downward force on the molten ice .
 
  • #20
conscience said:
That there is a net downward force on the molten ice .
Right. So what is the affect on the normal force between the tray and the block?
 

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