# Static Equilibrium problem

• member 392791
In summary, the conversation revolved around a problem involving equilibrium, forces, and torques. The participants discussed the role of the height, h, in the problem and how it could be related to the forces and torques present. They also talked about the difference between a rigid-body problem and a non-rigid body problem, and how to resolve forces into their components. Ultimately, they arrived at a solution that took into account the string and its tension acting on both sides of the middle pulley.

#### member 392791

So with this problem, I have been thinking about it. Since it is in equilibrium, I know the sum of forces and torques will be equal to zero. However, I'm not sure how the height, h, fits into this. I know the weights have a force and are a distance away from that fulcrum, d and 2d, so I could see those as torques, and the 800 N one at 2d should counteract the 200 N one at d, but I just don't see how h fits into this, which is what we aim to find.

#### Attachments

• problem.pdf
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Woopydalan said:
So with this problem, I have been thinking about it. Since it is in equilibrium, I know the sum of forces and torques will be equal to zero. However, I'm not sure how the height, h, fits into this. I know the weights have a force and are a distance away from that fulcrum, d and 2d, so I could see those as torques, and the 800 N one at 2d should counteract the 200 N one at d, but I just don't see how h fits into this, which is what we aim to find.

I am not sure but try considering h as the height of rightmost pulley.

This is not a rigid-body problem. The masses are connected to a string, and the tension of the string counteracts with the weights. Draw the free body diagram for both weights.
ehild

can you explain to me the difference between a ''rigid-body problem'' and a non-rigid body problem? Also, with my free body diagram, I see the tensions are to counteract the weights, but I have no other equations. How does d come into play with the problem in order to get closer to solving for h?

Do you understand how to resolve a force into its components? For instance, the weight W puts a tension on the rope holding up load P? What are the components of the tension in the rope?

Woopydalan said:
can you explain to me the difference between a ''rigid-body problem'' and a non-rigid body problem? Also, with my free body diagram, I see the tensions are to counteract the weights, but I have no other equations. How does d come into play with the problem in order to get closer to solving for h?

The string and the two weights do not make a rigid body, that keeps shape during motion.
The forces of the string have both horizontal and vertical components. For equilibrium, both components of the net force have to cancel at each weight. The components depend on the angle the string makes with the horizontal. How does that angle depend on h and d?
You can take the tension equal everywhere along the string. That gives two equations for the unknown tension and h.

ehild

Here is my attempt

#### Attachments

• 2.54 attempt.pdf
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Your solution is not correct. The tension acts along the string at the point where it is attached to the object. The tension is the same along the whole string, at both sides of the pulley. If there are two strings, both exert force. ehild

When you say two strings, are you referring to the string attached to the 200 N crate? it looks like there is only 1 string throughout the whole drawing unless you consider that one. If it is a separate string, is its tension separate from the one connecting the two pulleys?

Woopydalan said:
When you say two strings, are you referring to the string attached to the 200 N crate? it looks like there is only 1 string throughout the whole drawing unless you consider that one. If it is a separate string, is its tension separate from the one connecting the two pulleys?

You are right, it is the same string at both sides of the middle pulley, but two pieces, and the same tension in both. Both pieces act on the pulley and balance the force of the vertical string attached to the 200 N crate.
The tension in the vertical string balances the weight of 200 N. ehild

Ok, so here is my 2nd attempt.

#### Attachments

• 2.54 attempt 2.pdf
186.3 KB · Views: 166
Again, you ignored that there are two forces from the string balancing the vertical force of 200 N.

ehild

Ok, now I think I understand what you wrote. I think this one is a good one, I finally considered the string on both sides of the middle pulley

#### Attachments

• 2.54 attempt 3.pdf
189.8 KB · Views: 200
It looks correct now.

ehild

1 person
Thanks for the help!

You are welcome.

ehild

## 1. What is static equilibrium?

Static equilibrium is a state in which all of the forces acting on an object are balanced and the object remains at rest or at a constant velocity.

## 2. How is static equilibrium different from dynamic equilibrium?

Static equilibrium is a state in which all forces and torques acting on an object are balanced, while dynamic equilibrium is a state in which an object is moving at a constant velocity with all forces and torques balanced.

## 3. How do you determine if an object is in static equilibrium?

An object is in static equilibrium if the vector sum of all the forces acting on it is equal to zero and the sum of all the torques acting on it is also equal to zero.

## 4. What are some real-world examples of static equilibrium?

Some examples of static equilibrium include a book resting on a table, a tower standing upright, and a person standing still on the ground.

## 5. What are the steps to solving a static equilibrium problem?

The steps to solving a static equilibrium problem are:

• Draw a free-body diagram of the object
• Identify all the forces acting on the object and their directions
• Sum up all the forces in the x and y directions
• Set the sum of forces equal to zero and solve for any unknown forces
• Sum up all the torques acting on the object
• Set the sum of torques equal to zero and solve for any unknown torques
• Check if the object is in static equilibrium by comparing the calculated forces and torques to the known values