A 18000 kg plane flying at 70 m/s will be landing on an aircraft carrier and nee

Question

A 18000 kg plane flying at 70 m/s will be landing on an aircraft carrier and need to stop within 115 m. To help the airplane stop, it is caught by an elastic band. For this problem we will assume it is a cable and applies a constant force to help the plane come to rest. If the coefficient between the rubber tires and the aircraft carrier is 0.85, the carrier is stationary and the carrier is level, what is the force the cable needs to apply to stop the plane in time? ( please help exaplin how to do this)

Explanation / Answer

This is easier than your probably thinking. When the plane hits the deck it has a kinetic energy of:
KE = ½ • m • ² = ½ • (18000) • (74)² = 49284000 Kg • m² sec²
= 4.93 • 10^7 joules
and the work done to stop it (independent of how long it takes or how much distance it takes) is the same amount of energy in the opposite direction:
W = -4.93 • 10^7 joules

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