Ladder leaning against a vertical wall.

  • Context: Undergrad 
  • Thread starter Thread starter Reid
  • Start date Start date
  • Tags Tags
    Vertical Wall
Click For Summary

Discussion Overview

The discussion revolves around a physics problem involving a ladder leaning against a vertical wall, specifically focusing on determining the time at which the ladder loses contact with the wall. The scope includes theoretical approaches, mathematical reasoning, and potential applications of mechanics principles.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant expresses difficulty in determining the time when the ladder loses contact with the wall.
  • Another suggests calculating the horizontal force against the wall, noting that contact is lost when this force reaches zero.
  • A different participant proposes using the Lagrangian approach to find the equations of motion, indicating that the horizontal momentum's extremum relates to the loss of contact.
  • Another participant seeks clarification on setting up the problem, mentioning a professor's use of energy methods and expressing interest in solving it using moments and forces instead.
  • A participant references a formula from a book regarding the angle at which the ladder loses contact, indicating uncertainty about the details and a desire to verify the information.

Areas of Agreement / Disagreement

Participants present multiple approaches to the problem, with no consensus on the best method or the specifics of the solution. The discussion remains unresolved, with differing opinions on how to tackle the problem.

Contextual Notes

Participants mention various methods (Lagrangian mechanics, energy methods, moments and forces) without agreeing on the most effective approach. There are also references to assumptions about the ladder's motion and the conditions under which contact is lost, which remain unexamined.

Reid
Messages
33
Reaction score
0
I have encountered some problems with this exercise:

A ladder is leaning against a wall, it will slide due to its weight down the wall and along the floor.

I am supposed to determine the time at which the ladder looses contact with the wall, but how? :S
 
Physics news on Phys.org
Calculate the horizontal force against the wall as the ladder slides down. The ladder "loses contact" with the wall when that horizontal force is 0.
 
Easier said than done. I suppose what one could do is first find the Lagrangian assuming the ladder end touches the wall, solve the equations of motion, find the horizontal component of the momentum. The force will be zero when the horizontal momentum is an extremum (maximum). Such a maximum should exist - if we consider the case where the ladder cannot leave the wall the horizontal component of the momentum starts out as zero, and winds up as zero, but is non-zero in between.
 
How could you set this up, though? I had a similar problem in my mechanics class this week and I really want to figure it out. The prof said he used energy to solve it (we'll find out how in 2 days) but there has to be a way to solve it with moments and forces, right? I want to figure it out.

The book says the angle at which the ladder loses contact is [tex]sin^{-1}(sin(2/3\theta_{0}))[/tex], where [tex]\theta_{0}[/tex] is the initial angle between the ladder and the ground (I think, I left my book in my car, I'll double check later). Working backward has been so far fruitless.
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
3K
Replies
6
Views
3K
  • · Replies 6 ·
Replies
6
Views
8K
  • · Replies 40 ·
2
Replies
40
Views
7K
  • · Replies 14 ·
Replies
14
Views
2K
  • · Replies 5 ·
Replies
5
Views
5K
Replies
8
Views
2K
  • · Replies 11 ·
Replies
11
Views
4K
  • · Replies 10 ·
Replies
10
Views
4K
  • · Replies 11 ·
Replies
11
Views
2K