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A 1540-kg truck has a wheel base of 3.13 m (this is the distance between the front and rear axles). The center of mass of the truck is 1.09 m behind the front axle.a) What is the force exerted by the ground on each of the front wheels?b) What is the force exerted by the ground on each of the back wheels? Hint: Remember that the truck has four wheels.

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Lanuel

a. The force exerted by the ground on each of the front wheels is 4918.16 Newton.

b. The force exerted by the ground on each of the back wheels is 2627.84 Newton.

Given the following data:

  • Mass of truck = 1540 kg
  • Distance between the front and rear axles = 3.13 meters.
  • Center of mass of the truck = 1.09 meters.

a. To determine the force exerted by the ground on each of the front wheels:

First of all, we would take moment about the rear wheels.

[tex]F(3.13) - 1540(9.8) \times (3.13 - 1.09) = 0\\\\3.13F - 15092 \times 2.04 =0\\\\3.13F -30787.68=0\\\\F=\frac{30787.68}{3.13}[/tex]

Force, F = 9836.32 Newton

For each front wheel:

[tex]Force = \frac{9836.32}{2}[/tex]

Force = 4918.16 Newton.

b. To determine the force exerted by the ground on each of the back wheels:

We would determine the sum of the vertical forces acting on the wheels.

[tex]9836.32 + B - 1540(9.8) = 0\\\\9836.32 + B - 15092 = 0\\\\B=15092-9836.32[/tex]

B = 5255.68 Newton.

For each back wheel:

[tex]Force = \frac{5255.68}{2}[/tex]

Force = 2627.84 Newton.

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