How far can the person climb up the ladder before it starts sliding?

[ClearWhey]

Homework Statement

A person climbs a ladder like in the picture, how far can he climb up before the ladder starts sliding?

Relevant Equations

Ladder length 4m
Person weight 60kg
Ladder weight 10kg
Ladders coeficient of friction on both contact points 0,35

Look on picture two for my equations, I’m pretty sure my first three equations are correct as it’s the same on the answer paper I got. Answer paper only shows the three equations and correct answer so I have no idea how they got to it.

When I put the equations togheter And solve out ”h” i get like 1,5m something which is wrong. The answer is 2,34m. Can someone please look into this, did I simplify the equations wrong? Or is it something else. Have tried myself for like 2-3 hours and this is my last resort. Thanks in advance!

 

[TSny]

I found a sign error here:

I suggest that you start by using equations 2 through 4 to find $N_B$ and $F_B$. Evaluatue these numerically and then substitute into equation 1 to find $h$.

 

[ClearWhey]

I found a sign error here:
View attachment 269629

I suggest that you start by using equations 2 through 4 to find $N_B$ and $F_B$. Evaluatue these numerically and then substitute into equation 1 to find $h$.

Changed that sign to + and now I got the correct answer! Thanks you so much.

I could only solve it with my method by placing in the equation for FB and NB into my last equation. But you wrote something about substituting into the first equation, how? Would it be easier to solve this kind of problem with another method?

 

[haruspex]

I could only solve it with my method by placing in the equation for FB and NB into my last equation. But you wrote something about substituting into the first equation, how? Would it be easier to solve this kind of problem with another method?

It is generally easier to start with the simplest equations that allow you to eliminate some unknowns. The most complicated equation doesn't use F_A or N_A, so eliminate those first.
$F_A=N_B$
$N_A=N_B/\mu$
$F_B=N_B\mu$
$F_B+N_A=N_B\mu+N_B/\mu=M_m+M_s$
$N_B=\frac{\mu(M_m+M_s)}{1+\mu^2}$
$F_B=\frac{\mu^2(M_m+M_s)}{1+\mu^2}$
Etc.

 

[ClearWhey]

It is generally easier to start with the simplest equations that allow you to eliminate some unknowns. The most complicated equation doesn't use F_A or N_A, so eliminate those first.
$F_A=N_B$
$N_A=N_B/\mu$
$F_B=N_B\mu$
$F_B+N_A=N_B\mu+N_B/\mu=M_m+M_s$
$N_B=\frac{\mu(M_m+M_s)}{1+\mu^2}$
$F_B=\frac{\mu^2(M_m+M_s)}{1+\mu^2}$
Etc.

Thanks for clarifying this, now this question seems a lot easier. By the way do you know if there is anyway you can mark this thread as complete or solved? Or do you just leave it be when the homework is solved?

And again thanks to you and TSny for helping me!

 

[haruspex]

if there is anyway you can mark this thread as complete or solved?

(@berkeman)
There had been requests for such a feature for quite a while, and finally it was implemented. Shortly afterwards, there was a major upgrade to the whole system and the feature disappeared.
Various other retrograde changes happened at the same time: subscript and superscript, except via Latex, was lost (now reinstated under the "..." pull down). But the most annoying is that clicking on Quote to some text in post #1 results in the whole of the Homework Statement and Relevant Equations sections being quoted as well as the selected text. Since I often want to quote several parts of post #1 and respond to them individually, I then have to go laboriously through deleting pages of duplication.

 

[etotheipi]

But the most annoying is that clicking on Quote to some text in post #1 results in the whole of the Homework Statement and Relevant Equations sections being quoted as well as the selected text. Since I often want to quote several parts of post #1 and respond to them individually, I then have to go laboriously through deleting pages of duplication.

I found that if you highlight the text you want to quote, a little pop-up comes up with 'quote' and 'reply' options. If you hit 'reply', then it'll only copy that part into your text box, and not the whole post. One caveat is that it doesn't work for LateX. Do you have that feature too?

 

[haruspex]

I found that if you highlight the text you want to quote, a little pop-up comes up with 'quote' and 'reply' options. If you hit 'reply', then it'll only copy that part into your text box, and not the whole post. One caveat is that it doesn't work for LateX. Do you have that feature too?

I just tried that and it did the same as Quote, just immediately instead of needing to click Insert Quotes.
Another behaviour I forgot to mention is that if you highlight a part of Homework Statement and Relevant Equations then you can do a Copy but there is no quote /reply option.
None of these have ever worked with Latex. There used to be another option, something about Mathjax?, which revealed the latex source in a popup and you could copy that. Reply of the whole post copies the latex ok, and I often do that just to get the latex, then delete all the rest.