# How to determine a value of force for equilibrium

1. Jan 4, 2016

### Strontium90

1. The problem statement, all variables and given/known data
Hi, I was working on a homework problem and could not resolve it. The problem reads as follows:
A ladder that weighs 240N rests against a frictionless wall at an angle of 60 degrees from the ground. A 600-N man stands on the ladder three-fourths of the distance from the top. How much force does the top of the ladder exert on the wall?

2. Relevant equations
The equations used are:
Στ = τ + τ + etc!
τ = F ⋅ L

3. The attempt at a solution
1.) write out a simple free-body diagram with all of the know forces and information displayed. In particular, I illustrated the weights and the angle that was given by the problem. The main difficulty I had was the condition that " man stands on the ladder three-fourths of the distance from the top." Did that mean he was three-fourths along the way on the hypotenuse of the right triangle made by the ladder or along the wall? Another problem I had with this question was what was the relative length of the ladder. The problem did not specify what was the length of the ladder in question. I went with a length of one and used the trig values of the angle for the other sides. I was not able to come up with the answer in the book which was 440N.

2. Jan 4, 2016

### ehild

What about the friction at the ground?

3. Jan 4, 2016

### SteamKing

Staff Emeritus
In cases like these, where a particular quantity is unknown, like the length of the ladder, it is OK to use a variable in place of a number, so the length of the ladder would be L.

In all likelihood, in the final answer, the value of L will not be a factor, or it will cancel out of the calculations at some point.

If the man is standing 3/4 of the distance from the top of the ladder, this implies that he is also standing 1/4 of the distance from the bottom. If you make a sketch of the ladder leaning against the wall, and you draw a sketch of the ladder, you'll quickly see that if you divide the length of the ladder in half, for example, by similar triangles, a line projected parallel to the ground from that halfway point on the hypotenuse of the triangle also divides the height of the ladder along the wall in half as well. Ditto for the base of the triangle. See the figure below:
http://00.edu-cdn.com/files/static/wiley/9780471330981/angular-measurements-dimensions-degrees-3.gif [Broken]
This is also the general principle behind linear interpolation.

For more detailed help figuring out the answer to the ladder problem, you should post your work.

Last edited by a moderator: May 7, 2017