Normal and Friction Force of Leaning Ladder against a Corner

[lizzyb]

How do we set up the normal and friction force at the place where the ladder (the red line) touches the corner?

http://img56.imageshack.us/img56/6655/prob08021sketch01.gif

Worked Done So Far

I used a normal force the headed off to the top left at 45 degrees and a perpendicular friction force but came up with the wrong answer.

 

[tiny-tim]

Hi lizzyb!

Show us your full calculations, and then we can see what went wrong, and we'll know how to help.

 

[lizzyb]

We're to find the smallest mu_s given that the ladder is 6.5 m, m = 10 kg, and mu_s is at each surface.

http://img408.imageshack.us/img408/4034/0821diagram1.png

Work completed thus Far

http://img255.imageshack.us/img255/5127/08210001.th.jpg http://img44.imageshack.us/img44/3205/08210002.th.jpg http://img44.imageshack.us/img44/9206/08210003.th.jpg http://img337.imageshack.us/img337/4198/08210004.th.jpg http://img41.imageshack.us/img41/6672/08210005j.th.jpg http://img188.imageshack.us/img188/6554/08210006.th.jpg

In an effort to solve it, I went on and on and finally came up with an incorrect answer.

 

[tiny-tim]

ah!

the normal force means normal to the ladder!

Try again! ​

 

[lizzyb]

oops there is a glaring error in the calculation of the distance between the ladder's center of gravity along the x-axis - it should be 1.25.

 

[lizzyb]

should the normal force at the bottom be slanted 15 degrees or should it, too, be at 67.38 degrees? I tried it with the bottom being 15 degrees and came slightly off but I had to use a computer program to come up with the answer - there's a lot of computations.

http://img408.imageshack.us/img408/5466/082120001.jpg

 

[lizzyb]

I came up with the right answer using 15 degrees on the bottom (there was an error in one of my equations). I used maxima to solve the simultaneous equations. Thanks for you help.