How Does Energy Transfer Differ Between Two Airplane Crash Scenarios?

[tasp77]

Thought experiment (hopefully we don't need to crash a plane to figure this out);

Let's say we lift a commercial airliner up to 40,000 feet with a large balloon and then drop the airplane. It will hit the ground sometime later somewhere short of the speed of sound (600 mph or so, depending on it's orientation on the way down, I posit it will nose dive perpendicularly for maximum velocity).

Now let's take another plane, this one flying at 600 mph at 40,000 feet, and suddenly, the pilot shoves the stick forward, and dives the plane straight into the ground.

In the second case, the plane doesn't accelerate to 1200 mph on the way down as we might have thought at first take. The plane will reach the ground much faster in the second case and gravity has less time to further accelerate the plane. So it will hit the ground somewhat faster than in the first case, but will not be traveling twice as fast at the moment of impact.

Is there an 'energy deficit' in the second case? The plane has moved through Earth's gravity field the same distance, but in a faster time. Is there additional energy manifested in the system somewhere that I have not noted? Like the wreckage will be warmer in the second case?

Do the 'books balance' energy wise in both crashes?

 

[russ_watters]

Aerodynamic drag.

...because of it, a plane with no engines won't go anywhere close to 600mph.

 

[Antiphon]

If you consider the potential energy if the situation you will see the gravitational contribution must be the same. You would explain the higher kinetic energy and shorter time of flight in the second case as being powered by the jet fuel.

 

[AlephZero]

Forget about the planes and think about dropping a ball in a vacuum, so there is no air resistance.

In the first case, you drop the ball from height h and the velocity when it hits the ground is $v = \sqrt{2 g h}$

In the second case, you drop the ball from height h with an intial downwards velocity of $\sqrt{2 g h}$. The initial kinetic energy of the ball is $(1/2)mv^2 = mgh$.

When it hits the ground its KE has increased to $2mgh$.

So its final velocity will be given by $(1/2)mv^2 = 2mgh$ or $v = 2\sqrt{gh}$. In other words it will hit the ground about 1.414 times faster, not twice as fast.

 

[pmacias]

I appreciate your thought experiment and your curiosity about the energy budget of an airplane crash. In both scenarios, the airplane is experiencing a transfer of energy as it falls towards the ground. In the first case, the energy is primarily gravitational potential energy being converted into kinetic energy as the plane accelerates towards the ground. In the second case, the energy is primarily kinetic energy being converted into destructive energy as the plane impacts the ground.

In terms of your question about an "energy deficit" in the second case, it is important to note that the energy budget of the plane and its impact on the ground will depend on a variety of factors, including the angle of impact, the materials of the plane and the ground, and other variables. In both cases, there will be some energy lost due to factors such as air resistance and friction, but the majority of the energy will still be transferred to the ground.

As for the wreckage being warmer in the second case, it is possible that there may be some additional energy manifested in the form of heat due to the higher speed of impact. However, this would likely be minimal compared to the overall energy involved in the crash.

In terms of balancing the energy books, it is important to consider that energy cannot be created or destroyed, only transferred or transformed. In both scenarios, the energy of the plane is being transferred to the ground in some form, whether it be kinetic energy or destructive energy. Therefore, the energy budget would balance in both cases.

Overall, your thought experiment raises interesting questions about the energy involved in an airplane crash and how it is transferred and manifested in different scenarios. Further research and analysis would be needed to fully understand the energy budget of such a crash.