Question

The rear wheels of a truck support 57.0 % of the weight of the truck, while the front wheels support 43.0 % of the weight. The center of gravity of the truck is 1.68 m in front of the rear wheels.


What is the wheelbase of the truck (the distance between the front and rear wheels)? Express your answer with the appropriate units.

Answer 1

To solve the problem it is necessary to apply the concepts related to torque, as well as the concepts where the Force is defined as a function of mass and acceleration, which in this case is gravity.

Considering the system in equilibrium, we perform sum of moments in the rear wheel (R2)

$\sum M = 0$

$F_g*1.68-R_1*d = 0$

$mg*1.68-R_1*d = 0$

Another of the parameters given in the problem is that the front wheel supports 43% of the weight, that is

$R1=0.43F_g$

$R1=0.43mg$

Replacing, we have to

$mg*1.68 -R_1*d = 0$

$mg*1.68 -0.43mg*d = 0$

$mg*1.68 =0.43mg*d$

$1.68 = 0.43*d$

$d =3.9m$

Therefore the wheelbase of the truck is 3.9m between the front and the rear.