Centre of Mass: Hammer, Ruler, Balance

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Discussion Overview

The discussion revolves around the concept of center of mass as it relates to a hammer, ruler, and balance system. Participants explore definitions, stability, and the implications of center of mass in this context, including its application to a mobile structure.

Discussion Character

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

Main Points Raised

  • Some participants seek to define the center of mass in the context of the hammer and ruler setup, suggesting it is the weighted average location of mass.
  • There is a proposal that the center of mass of the hammer is near the hammer head, which may influence the center of mass of the entire mobile.
  • Participants question whether the center of mass must be vertically aligned with the table or if it can be below it, leading to discussions about stability.
  • One participant asserts that the center of mass being below the pivot point contributes to the stability of the system.
  • There is a discussion about the implications of the center of mass being located in empty space, as illustrated by the example of a donut.
  • Participants explore the concept of the pivot point and its relationship to the center of mass, noting that the pivot can move and affect stability.
  • Questions arise about the nature of restoring forces and how they relate to the equilibrium position of the hammer.
  • Concerns are raised about the conditions under which the mobile might collapse if the center of mass is no longer under the pivot point.
  • One participant describes a scenario where adding weight to one side of the ruler could lead to instability and potential tipping.

Areas of Agreement / Disagreement

Participants express various viewpoints on the definitions and implications of center of mass and stability, indicating that multiple competing views remain. The discussion does not reach a consensus on several key points, including the exact nature of the pivot point and the conditions for stability.

Contextual Notes

Participants highlight limitations in understanding the relationship between center of mass and pivot points, as well as the implications of mass distribution in relation to stability. There are unresolved questions regarding the mathematical treatment of these concepts.

Who May Find This Useful

This discussion may be of interest to those studying physics, particularly in the areas of mechanics and stability, as well as educators and students exploring concepts of center of mass and equilibrium.

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http://resources.scienceworld.ca/pdf/forces/Balance_Hammer.jpg

How do I explain this in terms of centre of mass?

And what's the definition of centre of mass in this context?
 
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tanyh123 said:
How do I explain this in terms of centre of mass?
Where's the center of mass of the hammer?

And what's the definition of centre of mass in this context?
The same as it is in any context. Think of it as the (weighted) average location of the mass.
 
Doc Al said:
Where's the center of mass of the hammer?

The centre of mass of the hammer is near the hammer head, so the centre of mass of the whole mobile should be found there as well?

Does the centre of mass of the mobile have to be vertically aligned with the table and a part of the ruler which is resting on the table or does it have to be under the table only?


Doc Al said:
The same as it is in any context. Think of it as the (weighted) average location of the mass.

But the centre of gravity of a donut is found around the centre of the donut, which is actually empty space. How do I explain that then?
 
The center of mass is below the pivot point therefore the system is inherently stable.
 
CWatters said:
The center of mass is below the pivot point therefore the system is inherently stable.

Can you explain to me why does positioning the centre of mass of the mobile below the pivot point, which I'm assuming is the edge of the table, makes the mobile stable and balanced?
 
tanyh123 said:
The centre of mass of the hammer is near the hammer head, so the centre of mass of the whole mobile should be found there as well?
Right.

Does the centre of mass of the mobile have to be vertically aligned with the table and a part of the ruler which is resting on the table or does it have to be under the table only?
The center of mass must be under the part of the ruler resting on the table.

But the centre of gravity of a donut is found around the centre of the donut, which is actually empty space. How do I explain that then?
Explain what? The center of mass does not have to be located where there is any mass. Think of it as a mathematical point that is useful for describing the behavior of a system, not as a part of a body.
 
Which is the pivot point, the part of the ruler resting on the table of the table itself?
 
The center of mass is EXACTLY below the pivot point (eg like a stationary pendulum).

The question is where is the pivot point? In the example photo it can move. It can be anywhere between the edge of the table or the right hand end of the ruler. This actually helps increase stability...

If the hammer is disturbed by pushing/swinging it slightly to the left the pivot point will probably move to the right hand end of the ruler. This increases the restoring force on the hammer.

If the hammer is disturbed by pushing it slightly to the right the pivot point will probably move to the left eg the edge of the table. This also increases the restoring force on the hammer.
 
CWatters said:
The center of mass is EXACTLY below the pivot point (eg like a stationary pendulum).

The question is where is the pivot point? In the example photo it can move. It can be anywhere between the edge of the table or the right hand end of the ruler. This actually helps increase stability...

If the hammer is disturbed by pushing/swinging it slightly to the left the pivot point will probably move to the right hand end of the ruler. This increases the restoring force on the hammer.

If the hammer is disturbed by pushing it slightly to the right the pivot point will probably move to the left eg the edge of the table. This also increases the restoring force on the hammer.

What do you mean by restoring force? And if the hammer is disturbed to an extent where the centre of mass is no longer under the pivot point, the mobile will collapse, won't it?
 
  • #10
tanyh123 said:
What do you mean by restoring force?
If you displace the hammer from its equilibrium position, its weight will create a torque that tends to bring it back to equilibrium. Imagine you had a ball on the end of a string, hanging down from your hand. If you move the ball aside, it will naturally tend to swing back. Same idea.
And if the hammer is disturbed to an extent where the centre of mass is no longer under the pivot point, the mobile will collapse, won't it?
No. When released from that point, it will tend to return to its equilibrium position.
 
  • #11
What is required for it to fall?
 
  • #12
tanyh123 said:
What is required for it to fall?

If you add weight to the left hand side of the rule the center of mass will move to the left. Keep adding weight and the rule will take up an angle to the horizontal (down on the left). The pivot point will move to the edge of the table and eventually the rule might reach an angle steep enough for the rule to slip off the edge of the table. That's if the head of the hammer doesn't hit the underside of the table first.
 

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