Chapter 7, Problem 23P

A 100 kg desk rests on a horizontal plane with a coefficient of friction of $\mu =0.4$. It is pulled with a force of $F=800\text{N}$ at an angle of $\theta =45°$ as shown in Fig. P7.23. The normal force $N_f$ and acceleration a in ${\text{m/s}}^{\text{2}}$ satisfy the following system of equations:

$565.6-0.4N_f=100a$ $(7.128)$ $N_f+565.5=9.81\times 100$. $(7.129)$ Where forces F and N are in kN.

1. Find $N_f$ and $a$
2. using the substitution method.
3. Write the system of equations $(7.128)$ and $(7.129)$
4. in the matrix form $Ax=b$, where $x=\left[\begin{array}{c}{N}_f\\ a\end{array}\right]$. In the other words, find matrices A and b.

(c) Find $N_f$ and $a$ using the matrix algebra method. Perform all computations by hand and show all steps.

(d) Find $N_f$ and $a$ using the Cramer’s rule.