Question

the 95,000-kg jet airliner is being stopped by brake action only. the engines are at idle and producing negligible thrust, and the velocity of the aircraft is too slow to produce measurable aerodynamic lift or drag. only the main landing gear is equipped with brakes, and the coefficient of friction between the tires and runway is 0.6. if under these conditions the brakes are applied hard enough that the main wheels are on the verge of slipping, determine the vertical force on the nose wheel strut.

Answer 1

The vertical force on the nose wheel strut can be calculated using the maximum frictional force, which is the product of the coefficient of friction and the normal force on the main wheels. Subtracting this force from the airliner's total weight will give the vertical force on the nose wheel.

Step-by-step explanation:

To calculate the vertical force on the nose wheel strut of a 95,000-kg jet airliner, we must understand that the maximum possible braking force is provided by the friction force of the main wheels, which is the product of the normal force and the coefficient of friction (μ). Since the engines are at idle and there's no measurable aerodynamic lift or drag and the wheels are on the verge of slipping, we know that the frictional force is at its maximum, which is μ times the normal force on the main wheels. This maximum frictional force equals the maximum braking force.

The normal force on the main wheels is the total weight of the airliner minus the vertical force on the nose wheel. The total weight (W) of the airliner is the product of its mass (m) and acceleration due to gravity (g), which is W = m * g. The coefficient of friction (μ) is 0.6. Therefore, if Fmax is the maximum friction force, Fmax = μ * (W - Fnose), where Fnose is the vertical force on the nose wheel. Rearranging, we get Fnose = W - Fmax/μ. By substituting the given values and solving for Fnose, we can find the vertical force on the nose wheel strut.