Workers have loaded a delivery truck in such a way that its center of gravity is only slightly forward of the rear axle, as shown in the drawing. The mass of the truck and its contents is 6675 kg. Find the magnitudes of the forces exerted by the ground on the following. (a) the front wheels
(b) the rear wheels of the truck
To find the magnitudes of the forces exerted by the ground on the front and rear wheels of the truck, we need to consider the forces acting on the truck.
Let's assume that the center of gravity of the truck is located at a distance 'd' from the rear axle and 'L-d' from the front axle, where 'L' is the distance between the front and rear axles.
The weight of the truck, W, acts vertically downward and can be considered to act through the center of gravity of the truck. Therefore, the weight of the truck can be split into two forces - one acting on the front wheels and the other on the rear wheels.
(a) To find the magnitude of the force exerted by the ground on the front wheels, we need to consider the torque balance around the rear axle. Since the center of gravity is slightly forward of the rear axle, there is a torque that needs to be balanced.
The torque about the rear axle can be calculated as follows:
τ = (Weight of the truck) x (Distance of the center of gravity from the rear axle)
τ = W x d
To balance this torque, the ground exerts an equal and opposite torque through the force exerted by the front wheels:
τ = (Force exerted by the ground on the front wheels) x (Distance between the front and rear axles)
τ = (Force exerted by the ground on the front wheels) x (L)
Since the torques are equal, we can equate the two expressions and solve for the force exerted by the ground on the front wheels:
W x d = (Force exerted by the ground on the front wheels) x L
Force exerted by the ground on the front wheels = (W x d) / L
(b) Similarly, to find the magnitude of the force exerted by the ground on the rear wheels, we can use the same torque balance but consider the torque about the front axle:
τ = (Weight of the truck) x (Distance of the center of gravity from the front axle)
τ = W x (L - d)
Equating this torque with the torque exerted by the ground through the force on the rear wheels:
τ = (Force exerted by the ground on the rear wheels) x (Distance between the front and rear axles)
τ = (Force exerted by the ground on the rear wheels) x L
Again, we can equate the two expressions and solve for the force exerted by the ground on the rear wheels:
W x (L - d) = (Force exerted by the ground on the rear wheels) x L
Force exerted by the ground on the rear wheels = (W x (L - d)) / L
By substituting the given values for the weight of the truck, mass of the truck and its contents, and the distances, you can calculate the magnitudes of the forces exerted by the ground on the front and rear wheels of the truck.