To solve this problem, we can use the work-energy principle, which states that the net work done on an object is equal to its change in kinetic energy. In this case, the net work done on the plane is the force exerted by the cables multiplied by the distance over which the force acts, and the change in kinetic energy is equal to the initial kinetic energy (due to the plane's motion) minus the final kinetic energy (when it comes to a stop). We can set these two expressions equal to each other and solve for the force:
Force x distance = (1/2) x mass x (final velocity)^2 - (1/2) x mass x (initial velocity)^2
where mass = 236 kN / 9.81 m/s^2 = 24.06 metric tons
Plugging in the given values, we get:
Force x 84.0 m = (1/2) x 24.06 t x (0 m/s)^2 - (1/2) x 24.06 t x (66.8 m/s)^2
Simplifying and solving for the force, we get:
Force = - 572.7 kN
The negative sign indicates that the force exerted on the plane is opposite to its direction of motion. Therefore, we can conclude that the arresting cables exert a force of 572.7 kN in the opposite direction to the plane's motion to bring it to a stop.