Review Conceptual Example 7 as background material for this...

Review Conceptual Example 7 as background material for this problem. A jet transport has a weight of $1.00 \times 10^{6} \mathrm{N}$ and is at rest on the runway. The two rear wheels are 15.0 m behind the front wheel, and the plane’s center of gravity is 12.6 m behind the front wheel. Determine the normal force exerted by the ground on (a) the front wheel and on (b) each of the two rear wheels.

Key Concepts

Normal Force Distribution

Normal forces are the support forces exerted perpendicular to the surface on which an object rests. In multi-support systems, like a vehicle with multiple wheels, the distribution of normal force among the supports can be determined by analyzing the static equilibrium conditions, ensuring that the sum of the individual normal forces equals the total weight.

Center of Gravity

The center of gravity is the point at which the total weight of an object is considered to act. In analyzing balance problems, it is important to know the position of the center of gravity relative to the supports so that one can accurately calculate the contributions of the weight to the torque about any pivot point.

Static Equilibrium

This concept refers to a state where an object is at rest or moving at a constant velocity, so that the sum of all forces and the sum of all torques (moments) acting on it are zero. In problems like these, static equilibrium is used to set up equations based on force balance and moment balance, ensuring that the net translational and rotational effects are null.

Torque and Moment Arms

Torque is the rotational effect produced by a force acting at a distance from a pivot point, calculated as the product of the force and its lever arm (the perpendicular distance from the line of action of the force to the pivot). Moment arms are crucial for determining how forces distributed at different points contribute to the overall balance of an object in equilibrium.

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