A large passenger ship weighs 75,000 tonnes and has a cruising speed of 45 km/h. The engines burn diesel fuel (approximately the same energy content as crude oil) with an efficiency of 20%. The drive system has an average efficiency of 55% for converting mechanical energy into propulsion for the ship. Calculate the volume of fuel needed to accelerate the ship from rest to cruising speed.

Question

Quizplus · Accepted Answer

The Answer is At rest the kinetic energy is zero. At 45 km/h

[ ( 45000 \mathrm {~m} / \mathrm { h } ) / 3600 \mathrm {~s} / \mathrm { h } ) = 12.5 \mathrm {~m} / \mathrm { s } ]

the kinetic energy will be

E = ( 1 / 2 ) m v ^ { 2 } = ( 0.5 ) imes \left( 7.5 imes 10 ^ { 7 } \mathrm {~kg} ight) ( 12.5 \mathrm {~m} / \mathrm { s } ) ^ { 2 } = 5.85 imes 10 ^ { 9 } \mathrm {~J}

The energy content of the fuel is

3.85 imes 10 ^ { 7 } \mathrm {~J} / \mathrm { L }

. The Energy available for propulsion is

( 0.2 ) imes ( 0.55 ) imes \left( 3.85 imes 10 ^ { 7 } \mathrm {~J} / \mathrm { L } ight) = 4.235 imes 10 ^ { 6 } \mathrm {~J} / \mathrm { L }

. The fuel needed to provide the kinetic energy of the ship is

\left( 5.85 imes 10 ^ { 9 } \mathrm {~J} ight) / \left( 4.235 imes 10 ^ { 6 } \mathrm {~J} / \mathrm { L } ight) = 1.38 imes 10 ^ { 3 } \mathrm {~L}

A Large Passenger Ship Weighs 75,000 Tonnes and Has a Cruising