How Does Equilibrium Apply in the Classic Ladder Problem?

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In summary, the problem involves a 10ft ladder weighing 30lbs and a 180lb man standing 5ft up the ladder at a 60 degree angle against a wall. The equations used are equilibrium and torque to find the force of the wall and the forces of friction and normal. This problem is already being discussed in another thread.
  • #1
gamegene9060
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Homework Statement


http://i.imgur.com/5iA1G4i.jpg
A ladder that is 10ft long, weighs 30lbs, and has a 180 lb man standing 5ft up it, resting at 60 degrees on a wall

Homework Equations


equilibrium, and torque

The Attempt at a Solution


180lbs cos60° * 2.5ft + 30lbs cos60° * 10ft = Fwall sin60° * 10ft (all trig functions used to find component of force that is perpendicular to the ladder)
and when I solve for Fwall i get ≈43.3lbs

then I would simply set the force of friction (or as he has in his problem, the person standing at the bottom of the ladder on a frictionless floor, god know how that works, lol) to that as they are the only horizontal forces, then the normal force from the ground would be the two weights added together. So Ffriction is also 43.3lbs and Fnormal is 210lbs.
 
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  • #2
What is the problem??
 
  • #3
Let's start all over...

The self-weight of a uniform ladder acts through the ladder's midpoint.

The question says the man is half way up the ladder, your working implies he is one quarter of the way up the ladder. Which shall we use?

What are you solving for? I'm guessing the reaction at the floor?
 
  • #5


I would like to highlight the importance of understanding the assumptions made in this classic ladder problem. Firstly, the problem assumes that the ladder is in equilibrium, meaning that the forces acting on it are balanced. This is a key assumption and it is important to verify that the forces are actually balanced in real-life situations.

Secondly, the problem assumes that the ladder is a rigid body, meaning that it does not deform under the applied forces. This may not always be the case, especially for longer ladders or those made of flexible materials.

Thirdly, the problem assumes that the surface the ladder is resting on is frictionless. As mentioned in the solution attempt, this may not be realistic and the presence of friction would affect the forces and equilibrium calculations.

Lastly, it is important to consider the weight distribution of the man on the ladder. In this problem, the man is assumed to be standing at a fixed height of 5ft. In reality, the man's weight may shift as he moves or adjusts his position on the ladder, which would affect the forces acting on the ladder.

As a scientist, it is important to critically evaluate all assumptions made in a problem and consider their potential impact on the solution. Additionally, it is important to always check the validity of the solution by considering real-world factors and conducting experiments if necessary.
 

FAQ: How Does Equilibrium Apply in the Classic Ladder Problem?

1. What is the Classic Ladder Problem?

The Classic Ladder Problem is a mathematical puzzle that involves using a ladder to reach a high window or platform. The goal is to determine the minimum length of the ladder required to reach the desired height, considering the angle of the ladder and the distance from the base of the wall to the window or platform.

2. How is the Classic Ladder Problem solved?

The Classic Ladder Problem can be solved using trigonometry. By using the Pythagorean theorem and trigonometric ratios, the length of the ladder can be calculated. The formula for solving the problem is: ladder length = height / sine of the angle.

3. What are the key factors to consider in the Classic Ladder Problem?

The key factors to consider in the Classic Ladder Problem are the height of the window or platform, the distance from the base of the wall to the window or platform, and the angle of the ladder. These factors determine the length of the ladder needed to reach the desired height.

4. Are there any real-life applications of the Classic Ladder Problem?

Yes, the Classic Ladder Problem has real-life applications in fields such as construction, engineering, and architecture. It is also commonly used in high school math problems to teach trigonometry and geometry concepts.

5. Is the Classic Ladder Problem limited to just one type of ladder?

No, the Classic Ladder Problem can be solved for any type of ladder, as long as the ladder is straight and resting against a vertical surface. The length of the ladder may vary depending on its material, weight, and other factors, but the basic principles for solving the problem remain the same.

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