# How Do Ladders Interact in a Frictionless Environment?

• matg360
In summary, the problem involves two hinged ladders, 4.00 m and 3.00 m in length, tied together by a horizontal rope 0.90 m above the floor. The ladders weigh 480 N and 360 N respectively, and their centers of gravity are at their respective centers. The floor is assumed to be frictionless. The problem asks to find the upward force at the bottom of each ladder, the tension in the rope, the magnitude of the force one ladder exerts on the other at point A, and the tension in the horizontal rope if an 800 N painter stands at point A. By using net torque, the correct answers are found to be 391 N and 449 N for
matg360

## Homework Statement

Two ladders, 4.00 m and 3.00 m long, are hinged at point A and tied together by a horizontal rope 0.90 m above the floor. The ladders weight 480 N and 360 N respectively, and the center of gravity of each is at its center. Assume that the floor is freshly waxed and frictionless.
• a) Find the upward force at the bottom of each ladder.
• b) Find the tension in the rope.
• c) Find the magnitude of the force one ladder exerts on the other at point A.
• d) If an 800 N painter stands at point A, find the tension in the horizontal rope.

Image: http://www.solutioninn.com/images/P-M-EE%20(98).PNG

## The Attempt at a Solution

For part a I attempted to do net torque, but I cannot figure how to account for all of them. The book says that the answer for part a is 391 for the left ladder (4m one) and 449 for the right ladder (3m one).

For part a I attempted to do net torque, but I cannot figure how to account for all of them.

How many do you think there are? Perhaps start by adding forces and dimensions to the diagram and posting that so we can see where you are going wrong. eg Which ones can't you account for?

Hint: I have an origin and three forces on my version.

## 1. What is the purpose of hinging two ladders at point A?

Hinging two ladders at point A allows for the creation of a stable triangular structure that can be used for various tasks, such as reaching high places or supporting heavy objects.

## 2. How does the angle of the hinged ladders affect their stability?

The angle at which the ladders are hinged at point A greatly affects their stability. A wider angle will create a more stable structure, while a narrower angle may result in a less stable structure.

## 3. Can two different length ladders be hinged at point A?

Yes, two different length ladders can be hinged at point A. However, it is important to ensure that the longer ladder is securely anchored to the ground to maintain stability.

## 5. Are there any safety precautions that should be taken when using hinged ladders?

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