Question

Confirm the value given for the kinetic energy of an aircraft carrier in Table 7.1. You will need to look up the definition of a nautical mile (1 knot = 1 nautical mile/h).

Short answer

The kinetic energy of the aircraft is \(1.1 \times {10^{10}}{\rm{J}}\).

Step-by-step solution

Definition of Concept

Kinetic energy: The energy stored in the body by the virtue of its motion is called kinetic energy. When a body is in motion, the energy associated with is in form of kinetic energy. According to the work-energy theorem, the work done on the body results in a change in the kinetic energy of the body.

The expression of the kinetic energy is,

\(KE = \frac{1}{2}m{v^2}\)

Here, \(m\) denotes the body's mass and \(v\) denotes its velocity.

Find the kinetic energy of the aircraft

The kinetic energy of aircraft is given as,

\(K{E_a} = \frac{1}{2}{m_a}v_a^2\)

Here,\({m_a}\)is the mass of the aircraft\(\left( {{m_a} = 90000{\rm{ ton}}} \right)\)and\({v_a}\)is the velocity of the aircraft\(\left( {{v_a} = 30{\rm{ knot}}} \right)\).

Putting all known values,

\(\begin{aligned}K{E_a} = \frac{1}{2} \times \left( {90000{\rm{ ton}}} \right) \times {\left( {30{\rm{ knot}}} \right)^2}\\ = \frac{1}{2} \times \left( {90000{\rm{ ton}}} \right) \times \left( {\frac{{1000{\rm{ kg}}}}{{1{\rm{ ton}}}}} \right) \times {\left( {\left( {30{\rm{ knot}}} \right) \times \left( {\frac{{0.514{\rm{ m}}/{\rm{s}}}}{{1{\rm{ knot}}}}} \right)} \right)^2}\\ \approx 1.1 \times {10^{10}}{\rm{ J}}\end{aligned}\)

Therefore, the required kinetic energy of the aircraft is \(1.1 \times {10^{10}}{\rm{J}}\).