Question

A car weighs 1800 kg. The distance between its front and back axles is 1.8 m. Its centre of gravity is 1.05 m behind the front axle. Determine the force exerted by the level ground on each front wheel and each back wheel.

Answer 1

Mass of car $m=1800kg$

Distance between front and back axles $d=1.8m$

Distance between center of gravity and front axle$=1.05m$

Let $R_b$ and $R_f$ be the forces exerted by the level ground on the back and front wheels respectively.

At translational equilibrium:

$R_f+R_b=mg=17640N.....\left(i\right)$

For rotational equilibrium, on taking the torque about the C.G., we have:

$R_f\left(1.05\right)=R_b(1.8-1.05)$

$⟹R_b=1.4R_f.......\left(ii\right)$

Solving $\left(i\right)$ and $\left(ii\right)$ gives

$R_f=7350N$

$R_b=10290N$

The force exerted on each front wheel =$7350/2=3675N$
The force exerted on each back wheel =$10290/2=5145N$