Static Equilibrium: Why Does Changing Pulley Position Affect Relative Angles?

• Kevin de Oliveira
In summary, a 3 pulley system statically balanced with determined relative angles will not have a change in angles when one pulley is moved due to the forces remaining fixed. However, in a 4 pulley system, the angles will change because the forces may not be able to remain fixed when one pulley is moved. This is because the central ring is free to move in the 3 pulley case, but not necessarily in the 4 pulley case. A specific example was given to illustrate this concept.
Kevin de Oliveira
I have a 3 pulley system statically balanced hanging weights at a determined relative angle (we are taking into account friction). If I change the position of one pulley, angles will remain the same. However, if I have a 4 pulley system, at the same conditions, changing one's position will affect the relatives angles between them all.

I would like to know why that happen. Why, with 3 pulleys, changing one's position will not affect their relatives angles and not with 4 pulleys?

Kevin de Oliveira said:
I have a 3 pulley system statically balanced hanging weights at a determined relative angle (we are taking into account friction). If I change the position of one pulley, angles will remain the same. However, if I have a 4 pulley system, at the same conditions, changing one's position will affect the relatives angles between them all.

I would like to know why that happen. Why, with 3 pulleys, changing one's position will not affect their relatives angles and not with 4 pulleys?
Can you please present a specific example?

Here an example attached.
Just a correction, instead of 3 it's 2 and 4 it's 3.
In that example, there are only 2 pulleys. If I apply the same conditions in 3 pulleys, angles will change.

Attachments

• situation_1.pdf
156.1 KB · Views: 209
Sorry. I still don't get what you are asking.

I think I understand what he's asking...

Forget about the position of the pulleys for the moment. What matters is the magnitude and direction/angles of the forces acting on the central ring (see solution 1). Since it's a statics problem the vertical and horizontal components must sum to zero. The forces are fixed so in general (but not always) there will only be one solution for the angles.

In the two pulley case: If one pulley is moved the ring is also free to move horizontally and vertically so the forces acting on it stay at the angles required for the static solution.

In the three (or more) pulley case it's not always possible for the ring to move to maintain the required angles. However it _is_ possible to move a pulley in such a way that it preserves the angles.

Last edited:
For example in this set up the top pulley can be moved from position A to position B without changing any of the angles. If it's moved in any other direction the angles change and a new static solution will have to be found..

And just to add, I suppose that it's because there is one force applied on each side. In another word, if I apply an odd quantity of forces on the horizontal axis, the angles will no longer be the same. not sure if this physically makes sense

As I see it.. In the three pulley case you are asking us to prove that the angles change if you change the angles.

Yes

1. What is static equilibrium?

Static equilibrium is a state in which an object is at rest and all the forces acting on it are balanced. This means that the object is not accelerating and is in a stable position.

2. How does changing the position of a pulley affect relative angles in a system?

Changing the position of a pulley can affect the relative angles in a system by changing the direction and magnitude of forces acting on the system. This can lead to a change in the equilibrium of the system, causing the object to move or remain at rest in a different position.

3. Why is it important to understand the concept of static equilibrium?

Understanding static equilibrium is important for engineers and scientists to design and analyze structures and systems. It helps to determine the stability and safety of objects and structures, and to predict how they will behave under different forces.

4. Can the position of a pulley affect the stability of a structure?

Yes, the position of a pulley can affect the stability of a structure. If the pulley is not positioned correctly, it can cause an imbalance of forces and lead to instability, potentially causing the structure to collapse.

5. How can we calculate the relative angles in a system affected by changing a pulley's position?

The relative angles in a system can be calculated using trigonometric functions such as sine, cosine, and tangent. By measuring the lengths of the sides and angles in the system, we can use these functions to determine the new angles after changing the position of the pulley.

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