Equilibrium Force: Solving for Centre of Mass | Homework Statement

In summary, the conversation discusses the concept of static equilibrium and the conditions for it to be achieved. The topic is related to the center of mass and how it affects the distribution of weight when carrying objects. The relevant equations for static equilibrium are mentioned, as well as the factors that determine which person will have to carry more weight in a given scenario. The conversation also touches on the concept of rotation and how it is affected by the distribution of forces.
  • #1
CH Lee
2
0

Homework Statement



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Homework Equations

The Attempt at a Solution


I'm not sure about which topic it is asked. I think it's something about the centre of mass . Because the statement " The pole and the box do not change form" . The answer is
(1 + tan Θ)/(1 - tan Θ)
 
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  • #2
What are (all!) the relevant equations for static equilibrium ?

Who do you think will have to carry more in the right picture ? B or A ? Why ?

The "don't change form" remark is to reassure you the center of gravity stays in the same place in the box/pole combo.
 
  • #3
BvU said:
What are (all!) the relevant equations for static equilibrium ?

Who do you think will have to carry more in the right picture ? B or A ? Why ?

The "don't change form" remark is to reassure you the center of gravity stays in the same place in the box/pole combo.

A will carry more, I think it's because he's in higher position.
And is there any special formula for static equilibrium ? I just draw a triangle and use the formula F=ma.
 
  • #4
Hehe, you never had to carry something heavy down the stairs, I suppose ?

The conditions for equilibrium I hinted at in post #1 are in the first place ##\Sigma \vec F = 0## So that with your formula a = 0 ##\Rightarrow## v = constant. v = 0 remains v = 0. No translation.

But that's not enough. You also want no rotation, in other words: ##\Sigma \vec \tau = 0##.
And now the positions where the forces act come in the expressions.
 
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  • #5
CH Lee said:
A will carry more, I think it's because he's in higher position.
And is there any special formula for static equilibrium ? I just draw a triangle and use the formula F=ma.

F = ma comes into question when acceleration comes into question. Here, a = 0 and v = 0. All forces balance each other out. FA and FB act vertically upward. In which direction do you think 'W' acts?
 
  • #6
The forces are vertical. That is a constraint on the answer given by the question statement. In an actual case of carrying a couch down a ramp the people doing the carrying probably would not arrange their hand-holds that way, but the problem requires it.

The pole is not rotating while it is being carried.
 

FAQ: Equilibrium Force: Solving for Centre of Mass | Homework Statement

What is equilibrium force?

Equilibrium force is the force that is required to keep an object in a state of balance or equilibrium. This means that all forces acting on the object are balanced and there is no net force causing it to accelerate in any direction.

How do you solve for the center of mass?

To solve for the center of mass, you need to calculate the weighted average of the mass distribution of an object. This can be done by dividing the total mass of the object by the sum of the individual masses multiplied by their respective distances from a chosen reference point. This will give you the coordinates of the center of mass.

What is the importance of finding the center of mass?

Finding the center of mass is important because it allows us to understand the overall motion and stability of an object. It is also crucial in determining the balance and distribution of weight in an object, which is essential in designing structures and machines.

Can the center of mass be outside of an object?

Yes, the center of mass can be outside of an object. This can happen when the object has an irregular shape or when the mass is distributed unevenly. In such cases, the center of mass may be located in empty space or even outside the boundaries of the object.

How is the center of mass affected by external forces?

The center of mass is affected by external forces only when the object is not in a state of equilibrium. When external forces act on an object, the center of mass will shift in the direction of the net force. However, if the external forces are balanced, the center of mass will not be affected and will remain at the same coordinates.

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