# Understanding forces on a balanced ladder

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• issacnewton
In summary, the conversation discusses the concept of equilibrium and how it applies to the balanced ladder on a wall. The explanation states that in an equilibrium situation, the net torque of the applied forces is zero and uses the example of picking a point on the page to illustrate this concept. The statement in question, "Consequently the frictional force F at A passes through O," is explained by the fact that for the net torque to be zero, the force F must act along an imaginary lever drawn from O to A. This implies that the direction of F is along the line AO. Ultimately, the conversation ends with a confirmation that the explanation makes sense.
issacnewton
Hello

I have a question about the explanation given for the attached image about the balanced ladder on a wall. At the end the sentence says that, "Consequently the frictional force F at A passes through O". I am not able to understand why this is so. Can anybody please shed light on this statement ?

Thanks

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In an equilibrium situation, the net torque (about any point) of the applied forces is zero. For example, we can pick a point P on the page off to left of the diagram and unconnected to anything by a physical lever. If we draw imaginary levers from P to the points A,G,and B and compute the net torques on those imaginary levers cause by the forces at A,G, and B, then the net torque will be zero.

If we look at the point O, the net torques about O should be zero. The torques about O exerted by the forces W and R are zero because those R acts directly along the imaginary lever drawn from O to point B and W acts directly along the imaginary lever drawn from O to G. For the sum of torques to be zero, the torque exerted about O by force F must also be zero. Hence F must act directly along an imaginary lever drawn from O to A. This implies the direction of F is along the line AO.

Thanks Stephen... makes sense

## 1. What is the definition of a balanced ladder?

A balanced ladder is a ladder that is equally supported on both sides and does not tip over due to the forces acting on it.

## 2. What are the forces acting on a balanced ladder?

The forces acting on a balanced ladder are the weight of the ladder, the weight of the person on the ladder, and the reaction forces from the ground and the wall (or other support) it is leaning against.

## 3. How do you calculate the forces on a balanced ladder?

The forces on a balanced ladder can be calculated using Newton's second law, which states that the sum of all forces acting on an object is equal to its mass multiplied by its acceleration. In this case, the ladder is not moving, so the forces are balanced and the sum is equal to zero.

## 4. What factors can affect the balance of a ladder?

The balance of a ladder can be affected by the weight and position of the person on the ladder, the angle at which the ladder is leaned against the support, and the surface and stability of the ground or support.

## 5. How can we ensure the safety of using a balanced ladder?

To ensure the safety of using a balanced ladder, it is important to properly position and secure the ladder, avoid overloading it, and use caution when climbing and working on the ladder. It is also important to regularly inspect the ladder for any defects or damage that may affect its balance and stability.

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