Chapter 12, Problem 12.1CYU

Check Your Understanding Solve Example 12.1 by choosing the pivot at the location of the rear axle.

To determine

The distance of the center of mass of car by assuming the pivot at the location of the rear axle.

Answer to Problem 12.1CYU

The distance of the center of mass of car by assuming the pivot at the location of the rear axle is $1.3\text{m}$.

Explanation of Solution

Given:

The car wheelbase, $D$ is $2.5\text{m}$.

The weight on the front wheel, $F_F$ is $0.52w$.

The weight on the rear wheel, $E_R$ is $0.48w$.

Formula used:

The force acting along vertical direction is given by,

$\begin{array}{c}{\displaystyle \sum F_y}=0\\ F_F+F_R-w=0\\ F_F+F_R=w\end{array}$   ..... (I)

The moment about point $O$ is given by,

$\begin{array}{c}{\displaystyle \sum M_O}=0\\ -\left(2.5-x\right)F_F+x\left(F_R\right)=0\end{array}$   ..... (II)

Calculation:

The following figure shows the free body diagram of the given diagram.

Figure-(1)

The moment about O is calculated as,

$\begin{array}{c}-\left(2.5-x\right)F_F+x\left(F_R\right)=0\\ x\left(0.48w\right)=\left(2.5-x\right)0.52w\\ \left(0.48w\right)x=1.3w-\left(0.52w\right)x\\ \left(1w\right)x=1.3w\end{array}$

Solve further,

$x=1.3\text{m}$

Conclusion:

The distance of the center of mass of car by assuming the pivot at the location of the rear axle is $1.3\text{m}$.