Chapter 7, Problem 25P

The weight of a vehicle is supported by reaction forces at its front and rear wheels as shown in Fig. P7.25. The reaction forces R₁ and R₂ satisfy the following system of equations:

$R_1+R_2-mg=0$ $(7.132)$ $l_1{R}_1-l_2{R}_{2}mak=0$. $(7.133)$

1. Write the system of equations $(7.132)$ and $(7.133)$
2. if $l_1=2\text{m}$, $l_2=1.5\text{m}$, $k=1.5\text{m}$, $g=9.81{\text{m/s}}^2$, $m=1000kg$ and $a=5m/s^2$.
3. For the system of equations found in part (a), find $R_1$ and $R_2$
4. using the substitution method.
5. Write the system of equations in the matrix form $Ax=b$, where $x=\left[\begin{array}{c}{R}_1\\ R_2\end{array}\right]$.

In the other words, find matrices A and b.

(d) Find $R_1$ and $R_2$ using the matrix algebra method.

(e) Find $R_1$ and $R_2$ using the Cramer’s rule.