Equilibrium of Two Rods: Finding the Point of Toppling

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In summary, the rod AB, which has a weight of 200 N and a length of 3 m, and the rod CD, which also has a weight of 200 N but a length of 2 m, are involved in a problem where a boy is moving from point A towards point B. The question is, at what distance from point A will the rod topple? The options are 0.4 m, 0.5 m, 0.6 m, 1 m, and 2 m. The solution involves considering the torque of the weight of DC around point E, and placing the pivot of rod DC at E. The boy's weight is 600 N and the correct answer is 0.5
  • #1
songoku
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Homework Statement


Weight of AB = CD = 200 N
Length of AB = 3 m
Length of CD = 2 m
A boy moves from point A toward B. At what distance from point A the rod will topple?
a. 0.4 m b. 0.5 m c. 0.6 m d. 1 m e. 2 m
untitled-6.jpg



Homework Equations


Newton's law
torque


The Attempt at a Solution


When rod AB topples, the normal force at B = normal force at C = 0 right?

Will there be normal force at point A? Where should I take the pivot?

Thanks
 
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  • #2
What is the boy's weight?
The rod AB topples only when DC does it. It happens when the torque of the weight of DC around E can not balance the torque arising from the other rod. In that case the support C does not exert force. Put the pivot of rod DC at E.

ehild
 
  • #3
ehild said:
What is the boy's weight?
The rod AB topples only when DC does it. It happens when the torque of the weight of DC around E can not balance the torque arising from the other rod. In that case the support C does not exert force. Put the pivot of rod DC at E.

ehild

Oh I'm sorry. The boy's weight is 600 N. Is 0.5 m the correct answer? Thanks
 
  • #4
songoku said:
Oh I'm sorry. The boy's weight is 600 N. Is 0.5 m the correct answer? Thanks

I got the same. :smile:

ehild
 
  • #5
ehild said:
I got the same. :smile:

ehild

Thanks for the help :)
 

What is the concept of equilibrium in relation to two rods?

Equilibrium in relation to two rods refers to a state where the two rods are balanced and not experiencing any net force or torque. This means that the two rods are at rest and are not moving or rotating.

How is equilibrium achieved in a system with two rods?

Equilibrium is achieved in a system with two rods when the forces acting on each rod are balanced. This means that the sum of all the forces acting on each rod must be equal to zero. Additionally, the sum of all the torques acting on each rod must also be equal to zero.

What factors affect the equilibrium of two rods?

The equilibrium of two rods can be affected by the length, mass, and position of the rods. The forces and torques applied to each rod can also impact the equilibrium. Additionally, the presence of external forces or friction can also affect the equilibrium.

What happens if the equilibrium of two rods is disturbed?

If the equilibrium of two rods is disturbed, the rods will no longer be balanced and will start to move or rotate. This can happen if the forces or torques acting on the rods are changed, or if external forces are introduced to the system.

How is the equilibrium of two rods useful in real-world applications?

The concept of equilibrium in relation to two rods is important in many real-world applications, such as construction, engineering, and physics. It helps engineers and scientists to design and analyze structures, machines, and systems to ensure they are stable and balanced. It also allows for the prediction and understanding of how forces and torques affect objects in equilibrium.

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