Chapter 8, Problem 75A

To determine

The position of the center of mass of the car.

Answer to Problem 75A

  $1.6\text{m}$ from the front tires

Explanation of Solution

Given:

  $53$ percent of the car’s weight is on the front tires while $47$ percent of the car’s weight is on the rear tires.

The length of the wheel base is, $l=2.46\text{m}$

Formula used:

The torque is given by,

  $\tau =Fr\sin \theta$

Where, F is the applied force, r is the distance of the point of application of force from the axis of rotation, and $\theta$ is the angle between F and r .

Calculation:

Let the weight of the car be $W$ , then the weight on the front tires be,

  $F_f=0.53W$

And, the weight on the rear tires be,

  $F_r=0.47W$

Let the center of mass of the car be at a distance of $x$ from the front tires, then its distance from the rear tires will be,

  $r_r=2.46-x$

Now, the torque on the car due to the weights on the front and the rear tires is balanced about the center of the mass, thus

  $\begin{array}{c}{\tau }_f={\tau }_r\\ F_f{r}_f\sin 90°=F_r{r}_r\sin 90°\end{array}$

Using given and assumed values in above,

  $\begin{array}{c}\left(0.53W\right)x=\left(0.47W\right)\left(2.46-x\right)\\ x\approx 1.6\text{m}\end{array}$

Conclusion:

Thus, the center of mass of the car will lie at a distance of $1.6\text{m}$ from the front tires.