Brainstorm some characteristics of a crater that
could change depending on the energy of the impact?
Whakatika
Crater depth
Crater width
Amount/volume of debris ejected
Distance that debris is ejected
Conservation of Energy
Typically to increase the energy of an impact in a simulation we
increase the height that it is dropped from, thereby giving it more
gravitational potential energy to be converted to kinetic energy
(increasing its impact velocity).
\[\begin{aligned}
E_{p} &= E_{k} \newline
m \times g \times h &= \frac{1}{2}m \times v^{2} &&
\text{Mass cancels out} \newline
g \times h &= \frac{1}{2} \times v^{2} &&
\text{Re-arrange for v} \newline
2 \times g \times h &= v^{2} \newline
\sqrt{2 \times g \times h} &= v
\end{aligned}\]
Theoretical vs
Real-World
\[\begin{aligned}
v = \sqrt{2 \times g \times h}
\end{aligned}\]Source
This gives the theoretical impact velocity
of a rock dropped within Earth’s gravitational field.
Pātai: What assumption are we
making here?
Whakatika: That energy is
conserved
Pātai: What happens to some of
that energy?
Whakatika: That some energy is
lost to the atmosphere as light/heat/sound.
Whakakapi/Conclusion: Real-world
velocity is less than the theoretical maximum velocity.
Pātai
\[\begin{aligned}
v &= \sqrt{2 \times g \times h} \newline
E_{k} &= \frac{1}{2} \times m \times v^{2}
\end{aligned}\]
Calculate the impact speed of an object dropped
from \(1m\)
Calculate the impact speed of an object dropped
from \(2m\)
Calculate the impact speed of an object dropped
from \(5m\)
Calculate the impact kinetic energy of a \(10kg\) object travelling at \(3000ms^{-1}\)
Calculate the impact kinetic energy of a \(750kg\) object travelling at \(5000ms^{-1}\)
