Static equilibrium marbles problem

In summary: So the torque at point C is .5*(.01m)*(sin(30))=6.9Nm.In summary, the force at points A,B, and C are equal and the torque at point C is 6.9Nm.
  • #1
krko
4
0
Hey all, new member here

Homework Statement


Two uniform 75g marbles 2cm in diameter are stacked on top of each other in a container that is 3cm wide
the top marble touches right side of the container, the bottom touches the left side.
Point A is the bottom marble left contact point with the container, point B is the bottom marble touch the bottom of the container, point c is the top marble's contact point with the container

Attempt at a figure:
l top marble, point Cl
lmarble contact pointl
lpoint A, bottom marble l
l_____point B________l
What is the force the container exerts at point A,B, and C?
What force does each marble exert on each other?

Homework Equations


Basically since its static equilibrium, , all force and torques add up to zero. Also the equation for Torque, T=sin(phi)*lever arm

The Attempt at a Solution



force at B is easy to get since that's just the normal force equal to the combined weight of the two marbles.
At A and C, its obvious that they're equal. I can also get the torque due to the top marble on the bottome marble: weight*(.01m)*(sin(30)) after that I don't know what else to do.
 
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  • #2
Welcome to PF!

Hey, krko ! Welcome to PF! :smile:
krko said:
… I can also get the torque due to the top marble on the bottome marble: weight*(.01m)*(sin(30)) after that I don't know what else to do.

Is this frictionless?

You're taking moments about the point of contact between the marbles … why? :confused:

If you take moments (torques) about a point, you must do it for all the forces … that's why we usually choose a point about which some of the forces have zero moment.

Try again, taking moments about a different point. :smile:
 
  • #3
Okay, i uploaded an image of the problem. The torque I'm talking about is the torque caused by the top marble about point the center of the bottom marble. Although looking back i think I found my mistake, that I neglected the effect of the force of the container on point C on the bottom marble.
 

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Related to Static equilibrium marbles problem

1. What is the concept of static equilibrium in the context of the marbles problem?

Static equilibrium refers to a state in which an object is at rest and all forces acting on it are balanced. In the marbles problem, it means that the marbles are not moving and the forces acting on them are equal and opposite, resulting in a stable system.

2. How many marbles are typically used in a static equilibrium marbles problem?

The number of marbles used in a static equilibrium marbles problem can vary, but it is usually between 3 to 5 marbles. This allows for a more complex and challenging problem, while still maintaining a stable equilibrium.

3. What factors affect the equilibrium in the marbles problem?

The equilibrium in the marbles problem is affected by the weight, size, and placement of the marbles as well as the surface they are resting on. Other factors such as air resistance and friction may also play a role in the equilibrium.

4. How can the static equilibrium of the marbles problem be determined?

To determine the static equilibrium of the marbles problem, we must consider the forces acting on the marbles and ensure that they are balanced. This can be done by drawing a free body diagram and using the principles of Newton's laws of motion to analyze the forces.

5. What real-life applications use the concept of static equilibrium marbles problem?

The concept of static equilibrium marbles problem can be applied in various situations, such as in architecture and engineering, where structures must be designed to maintain a stable equilibrium. It is also used in physics experiments to demonstrate the principles of forces and equilibrium.

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