Equilibrium of Forces on the Table

[hancan]

Homework Statement

This is a simple research problem that I am dealing with. It would be better to explain it with a diagram. There are three weights attached to some strings and tied together in a knot. There is an obstacle on the table. What happens to the weights under the situation illustrated in the diagram. Assume that there is no friction.

Homework Equations

We can draw a FBD on the edge of the obstacle. There are forces by the weights and there is a reaction force by the obstacle.

The Attempt at a Solution

I think that because the weights on either side of the obstacle is equal to each other, and the gravity does not affect the forces, the weights will remain in equilibrium when the knot is at the edge of the obstacle. If we move the knot towards the hole of 2w, the knot will remain at the place where we move it. Because the forces will be equal to each other in opposite directions (2w = w + w). But if we move the knot towards the other two weights, the knot will come back to the edge of the obstacle since their combined weight will not be enough to keep the knot in its new location. Furthermore, in order to keep the knot at the edge, we may use a smaller weight than 2w on the left side of the obstacle, such as the combined x-axis forces of the other two weights. But we may see very tiny movements of the knot at the edge of the obstacle.
I guess I am just opening it for a discussion.

 

[anathema]

Hello! I would like to offer my perspective on this problem. Firstly, you are correct in your assumption that the weights will remain in equilibrium when the knot is at the edge of the obstacle. This is because the forces acting on the knot are balanced and there is no net force to cause it to move.

However, I would like to add that the position of the knot on the table will also affect the equilibrium of the weights. For example, if the knot is placed closer to the heavier weight, the knot will move towards that weight due to the stronger gravitational force. This is because the force of gravity is directly proportional to the mass of the object.

Additionally, the type of knot used and the tension in the strings can also impact the equilibrium of the weights. For example, a slip knot may loosen and cause the weights to fall, while a tight knot may keep the weights in place.

Overall, this is a fascinating problem to explore and there are many variables that can affect the outcome. I would suggest conducting some experiments to test your predictions and see how different factors can impact the equilibrium of the weights. Thank you for bringing this discussion to the forum!

 

[tomcue]

I would approach this problem by first identifying all the forces acting on the system, including the weights, the strings, and the reaction force from the obstacle. I would then use the principles of Newton's laws of motion and the concept of equilibrium to analyze the situation and predict the outcome.

In this case, it seems that the system is in a state of equilibrium, meaning that all the forces acting on it are balanced and there is no net force on the system. This is because the weights on either side of the obstacle are equal in magnitude and opposite in direction, canceling out each other's effects. Additionally, the absence of friction allows the system to remain in this state of equilibrium.

If we were to move the knot towards the hole of 2w, the knot would remain in its new location as the forces on either side of the obstacle would still be balanced. However, if we were to move the knot towards the other two weights, the knot would return to the edge of the obstacle as the combined weight of the other two weights would not be enough to keep the knot in its new location. This is a result of the principle of equilibrium, where for an object to remain at rest, the net force acting on it must be zero.

To further explore this problem and understand the exact movements of the knot, we could use mathematical equations such as the equations of motion and the concept of vectors to calculate the forces and displacements involved in the system. Overall, this is a simple yet interesting problem that can be further explored and analyzed using the principles of physics.