Approximate a Boeing 777 aircraft as a system with a fixed mass of 200,000 kg. T

Question

Approximate a Boeing 777 aircraft as a system with a fixed mass of 200,000 kg. The plane initially cruises at 270 m/s at an altitude of 10,000 meters. The plane descends to land in Denver, Colorado at an altitude of 1600 meters. During the gliding descent the spoilers on the plane create drag to reduce the energy of the aircraft. The final kinetic energy of the plane upon landing is 10% of the cruise kinetic energy. External heat transfer, propulsion power and fuel usage during descent are all negligible. Given: g = 9.8 m/s2

, 1 kJ = 10^3J , 1 GJ = 10^9J

Find the change in potential energy of the plane, PE_2-PE_1=_______(GJ)

Find the work done against friction during the descent, W_2=________(GJ)

If drag were zero, what would the speed of the plane be as it approached Denver, V=________(m/s)

Explanation / Answer

we have change in PE=mg(h2-h1)

= -200000*9.8*(10,000-1600)

= - 16.464 GJ

work done aginst friction= change in enrgy

= change in PE+ change in KE

= 16.464*10^9+0.1*0.5*m*V^2

=17.193 GJ

then change in KE= loss in PE

or KF= Ki+16.464*10^9

so Vf=487.4 m/s

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