An automobile with a mass of 1360 kg has 3.05 m between the front and rear axles. Its center of

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An automobile with a mass of 1360 kg has 3.05 m between the...

An automobile with a mass of 1360 $\mathrm{kg}$ has 3.05 $\mathrm{m}$ between the front and rear axles. Its center of gravity is located 1.78 $\mathrm{m}$ behind the front axle. With the automobile on level ground, determine the magnitude of the force from the ground on (a) each front wheel (assuming equal forces on the front wheels) and (b) each rear wheel (assuming equal forces on the rear wheels).

An automobile with a mass of 1360 $\mathrm{kg}$ has 3.05 $\mathrm{m}$ between the front and rear axles. Its center of gravity is located 1.78 $\mathrm{m}$ behind
the front axle. With the automobile on level ground, determine the
magnitude of the force from the ground on (a) each front wheel (assuming equal forces on the front wheels) and (b) each rear wheel (assuming equal forces on the rear wheels).

Key Concepts

Static Equilibrium

Static equilibrium refers to the condition in which an object is at rest or moving with constant velocity, meaning that all the forces and torques acting on it balance out. In problems like this, the net force in any direction and the net moment about any point must be zero, allowing us to set up equations that relate the various forces acting on the object.

Center of Gravity

The center of gravity is the point at which the entire weight of an object is considered to be concentrated. Its location is crucial in determining how the weight is distributed among the support points, such as the wheels of an automobile. The position of the center of gravity relative to the axles directly affects the magnitude of the normal forces acting on each wheel.

Torque (Moment) Balance

Torque, or moment, is the product of a force and the perpendicular distance from the line of action of the force to the pivot point. In weight distribution problems like this, balancing the moments (taking moments about a specific axle or point) allows for the calculation of unknown forces by ensuring that the clockwise and counterclockwise moments cancel each other out.

Free-Body Diagram

A free-body diagram is a graphical representation that isolates an object and illustrates all the external forces acting on it. In this context, drawing a free-body diagram of the automobile helps to visualize the weight acting at the center of gravity, the normal forces at each wheel, and any other external forces, which is essential for setting up the equilibrium equations needed to solve the problem.

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