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 $15.0 \mathrm{m}$ behind the front wheel, and the plane's center of gravity is $12.6 \mathrm{m}$ 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

Static Equilibrium

Static equilibrium refers to a state where an object is at rest and the sum of all forces and the sum of all torques acting on it are zero. This principle is essential for solving problems where an object, such as an airplane, is not accelerating, ensuring that upward forces balance downward forces and that moments about any pivot point cancel out.

Torque and Lever Arm

Torque is the rotational effect of a force, calculated by multiplying the force by the perpendicular distance from the line of action of the force to the pivot point (lever arm). Understanding torque is crucial in problems involving balance, as it allows one to set up equations that ensure the sum of the moments (torques) about any chosen pivot is zero.

Center of Gravity

The center of gravity is the point where the total weight of the object is considered to act. In balance and equilibrium problems, knowing the location of the center of gravity is important for determining how weight is distributed over different supports or wheels.

Normal Force Distribution

Normal force distribution involves determining how the weight of an object is supported by different contact points with the ground. In the context of static equilibrium, normal forces act upward at points of contact and must not only sum to the total weight but also provide the correct moments to balance the object.

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