Answer :
Answer:
Each kilogram of the cannonball has a total energy of 52396.454 joules.
Explanation:
From Principle of Energy Conservation we understand that energy cannot be destroyed nor created, but transformed. In this case non-conservative forces can be neglected, so that total energy of the cannonball ([tex]E[/tex]) is the sum of gravitational potential ([tex]U_{g}[/tex]) and translational kinetic energies ([tex]K[/tex]), all measured in joules. That is:
[tex]E = U_{g}+K[/tex] (Eq. 1)
By applying definitions of gravitational potential and translational kinetic energies, we proceed to expand the expression:
[tex]E = m\cdot g \cdot y + \frac{1}{2} \cdot m \cdot v^{2}[/tex] (Eq. 2)
Where:
[tex]m[/tex] - Mass of the cannonball, measured in kilograms.
[tex]g[/tex] - Gravitational acceleration, measured in meters per square second.
[tex]y[/tex] - Height of the cannonball above ground level, measured in meters.
[tex]v[/tex] - Speed of the cannonball, measured in meters per second.
As we do not know the mass of the cannonball, we must calculated the unit total energy ([tex]e[/tex]), measured in joules per kilogram, whose formula is found by dividing (Eq. 1) by the mass of the cannonball. Then:
[tex]e = g\cdot y + \frac{1}{2}\cdot v^{2}[/tex]
If we know that [tex]g = 9.807\,\frac{m}{s^{2}}[/tex], [tex]y =122\,m[/tex] and [tex]v = 320\,\frac{m}{s}[/tex], the unit total energy of the cannonball is:
[tex]e = \left(9.807\,\frac{m}{s^{2}}\right)\cdot (122\,m)+\frac{1}{2}\cdot \left(320\,\frac{m}{s} \right)^{2}[/tex]
[tex]e = 52396.454\,\frac{J}{kg}[/tex]
Each kilogram of the cannonball has a total energy of 52396.454 joules.