Write a matlab script to solve the seven simultaneous equations and print output

Question

Write a matlab script to solve the seven simultaneous equations and print output with proper units. Assume static friction is negligible. We have the following constraints W= 50; L = 12ft; g=32.2; theta= 35*pi/180; U_k = 0.2 (coefficient of kinetic friction)

we have these equations and you dont need the rest of the question to solve.... i just really have no idea how to set it up!!!! :

N_a - f_b = (W/g)*a_cmx       (1)

N_b +f_a - W = (W/g) * a_cmy    (2)

-(N_a + f_b)(L/2)cos(theta) + (N_b - f_a)(L/2)(sin(theta)) = (1/12)*(W*L^2)/(g) *alpha    (3)

U_k*N_a = f_a (4)

U_k*N_b = f_b    (5)

a_cmx = (alpha)(L/2)cos(theta)   (6)

a_cmy = (-)(alpha)(L/2)sin(theta)   (7)

The seven unknowns are:

N_a, N_b, f_a, f_b, a_cmx,a_cmy, alpha

Explanation / Answer

w=50;
L=12;
g=32.2;
theta=35*pi/180;
u_k=0.2;
syms n_a n_b f_a f_b a_cmx a_cmy alpha

[n_a n_b f_a f_b a_cmx a_cmy alpha]=solve(n_a-f_b-w/g*a_cmx,n_b+f_a-w-w/g*a_cmy,-(n_a+f_b)*(L/2)*cos(theta)+(n_b-f_a)*(L/2)*sin(theta)-w*L^2/(g*12)*alpha, u_k*n_a-f_a,u_k*n_b-f_b,a_cmx-alpha*(L/2)*cos(theta),a_cmy+alpha*(L/2)*sin(theta));

n_a=double(n_a);

n_b=double(n_b);

f_a=double(f_a);

f_b=double(f_b);

a_cmx=double(a_cmx);

a_cmy=double(a_cmy);

alpha=double(alpha);

fprintf('%n_a= 0.2f unit of n_a n_b= %0.2f unit of n_b f_a= %0.2f unit of f_a f_b= %0.2f unit of f_b a_cmx=%0.2f unit of a_cmx a_cmy=%0.2f unit of a_cmy alpha=%0.2f unit of alpha ',n_a,n_b,f_a,f_b,a_cmx,a_cmy,alpha)

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