How Does Equilibrium Apply in the Classic Ladder Problem?

[gamegene9060]

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.

 

[nil1996]

What is the problem??

 

[NascentOxygen]

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?

 

[NascentOxygen]

I see you already have a thread going for this problem. https://www.physicsforums.com/showthread.php?t=719827

Nothing more needed on this one then.

 

[Nickie]

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.