Date: Jul 27, 2013 5:40 AM
Author: Arafat
Subject: Matlab simultaneous problem

You are working for a ladder company and are studying a problem related to the dynamics of the ladder slipping.  Consider a uniform ladder of weight W that slips when it is leaned against a building.  Shown is the free body diagram and treating it as a planar dynamics problems one can write the equation of motion as follows (using Linear momentum balance OR Newton-Euler equations of motions) are given :
1. Na-Fb=(W*g)/a_cmx
2. Nb +Fa-w=W/g a_cmy
3.-(Na+Fb)(L*cos(x))/2+(Nb-Fa) *(L*sin(x))/2= (W*L^2*a)/12*g
below with the following Na,Fa,Nb,Fb,a_cmx,a_cmy,a are unknown
a. To solve for the seven unknowns, we need four more equations. These are obtained from the friction and constraints which are given below. Assume the following values and W=50 lb, L=12ft, g=32.2 ft/s2, x=35*?/180 radians, ?k=0.2; Write a matlab script to solve the seven equations simultaneously and print output with proper units. Assume the ladder is starting to slip and so we do not have to worry about the static friction.
4. Na=mew_k *Fa
5.Nb=mew_k*Fb
6.a_cmx= a* L/2 *cos(x)
7.a_cmy=- a* L/2 *sin(x)

PLease help me on this. I really need some help on this. I tried so long on this but could not solve it