A fully loaded airliner has a mass of 361,000 kg and is coming in for a landing at a speed of 70.0 m/s. At touchdown, all braking systems are used and the plane comes to rest in 1575 m. What is the magnitude of the braking force?
To calculate the magnitude of the braking force, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, we need to find the acceleration caused by the braking force first.
To find the acceleration, we can use the kinematic equation:
v^2 = u^2 + 2as
Where:
v = final velocity = 0 m/s (since the plane comes to a rest)
u = initial velocity = 70.0 m/s
a = acceleration
s = displacement = 1575 m
Rearranging the equation to solve for acceleration, we have:
a = (v^2 - u^2) / (2s)
a = (0^2 - 70.0^2) / (2 * 1575)
a = (-4900) / (3150)
a ≈ -1.56 m/s^2
The negative sign indicates that the acceleration is in the opposite direction of the initial velocity, representing deceleration or braking force.
Now that we have the acceleration, we can calculate the magnitude of the braking force using Newton's second law:
F = ma
F = (361,000 kg) * (-1.56 m/s^2)
F ≈ -563,160 N
The magnitude of the braking force is approximately 563,160 N. Note that the negative sign indicates that the force is applied in the opposite direction of motion.