A uniform 5.0m long ladder leans against a friction-less wall making an angle of 22 degrees with the floor. The ladder has a mass of 42kg and a 67kg painter stands 3.5m up the ladder.
A) Find the minimum coefficient of friction between the floor and the ladder.
Painter: 9.8kg/N * 67kg = 656.6N
Ladder: 9.8kg/N * 42kg = 411.6N
The Attempt at a Solution
[(3.5m)(cos 22)(656.6N)] + [(2.5m)(cos 22)(411.6N)] = Ff = 3085N
[(3.5m)(sin 22)(656.6N)] + [(2.5m)(sin 22)(411.6N)] = Fn = 1246N
mu = 3085N/1246N = 2.476
The above attempt was basically a cry of desperation because I am very confused by this problem. My class has done some vectors and kinematics last year but I am new to this so this is still quite confusing to me.
I'd just like to know how to go about doing this correctly. I don't want someone to give me the direct answer but to guide in the correct direction towards getting the answer would be great. Thanks in advance.
Also, I'm going to assume right now that the above "FBD" that I've drawn is set up wrong in at least some way. Just saying that the diagram is my interpretation of the question and that the diagram isn't actually given in the question.