Answer to Question #156098 in Physics for Arvin Shopon

Question

A passenger aircraft with a mass of 78,000 kg flies at a cruising altitude of 11,300 m at a speed of 864 km/h. How big is it

a) kinetic energy

b) potential energy in relation to the ground

c) mechanical energy?

Answer 1

a) We can find the kinetic energy from the formula:

$$KE=\dfrac{1}{2}mv^2,$$

$KE=\dfrac{1}{2}\cdot78000\ kg\cdot(864\ \dfrac{km}{h}\cdot\dfrac{1000\ m}{1\ km}\cdot\dfrac{3600\ s}{1\ h})^2=2.25\cdot10^9\ J.$

b) We can find the potential energy in relation to the ground from the formula:

$$PE=mgh,$$ $$PE=78000\ kg\cdot9.8\ \dfrac{m}{s^2}\cdot11300\ m=8.64\cdot10^9\ J.$$

c) By the definition of the mechanical energy, we have:

$$E=PE+KE,$$ $$E=8.64\cdot10^9\ J+2.25\cdot10^9\ J=1.09\cdot10^{10}\ J.$$

Answer:

a) $KE=2.25\cdot10^9\ J.$

b) $PE=8.64\cdot10^9\ J.$

c) $E=1.09\cdot10^{10}\ J.$