Find the missing energy value given a set of data (Hypothetical question)

[l2aizou]

Hypothetical question:

Let's say there's a granite cube with a volume of 60 cubic centimeters. A cannon ball is shot at it, reducing it to rubble, and the kinetic energy of the ball was 10,000 joules.

We use the same ball with the same kinetic energy output on a stronger unknown substance with a cubic volume of 300 cubic centimeters, but this time we only manage to destroy 50 cubic centimeters.

Is there a way to figure out the energy required to completely destroy the unknown cube, both in total and the rest of the remaining volume?

 

[mfb]

I don't see a scenario where you could reduce a small part to rubble while keeping the rest unharmed.
In general that problem is not well-defined, because the size of the rubble that is produced will have a strong impact on the energy you need for that, and similar dependencies.

 

[l2aizou]

What if it were possible though? Would it be as simple as creating a ratio between the volumes, which would also be the energy difference?

I don't need a specific answer, just a general sense of direction.

 

[mfb]

What if it were possible though?

Then it depends on the details of the process.

You can assume that the energy needed is proportional to the volume, but it is unclear how good that assumption is. Real life is usually more complicated than physics homework questions.

 

[l2aizou]

Then it depends on the details of the process.

You can assume that the energy needed is proportional to the volume, but it is unclear how good that assumption is. Real life is usually more complicated than physics homework questions.

So how would this work? Division of the volumes or something?

 

[mfb]

Simple proportionality. 6 times the volume might need 6 times the energy.
That is probably a very unrealistic model, however.

 

[l2aizou]

But if you destroy more volume with granite using the energy required, and less volume of an unknown, stronger substance, doesn't that mean the volume isn't the concern?

 

[mfb]

What do you mean by "isn't the concern"?

 

[l2aizou]

So, if I can obliterate the volume a weaker substance, but only marginally damage another substance, meaning it is stronger but still capable of causing damage, how would I find out how much energy it would take to destroy the equivalent volume of the first substance for the second substance in simple terms?

 

[CWatters]

Let's say you run a waste processing plant...

If you feed something like mixed waste plastic into a massive machine that cuts it into small bits then over long periods the energy required will almost certainly depend on the volume of material processed.

However over short periods it's very unlikely to be linearly dependent on volume. If the volume of material processed is very small then overheads might dominate the energy cost so for example processing two small plastic cups might not consume twice as much as one cup. If overheads vary you might even find it takes less energy to process two cups than it does one.

In the field of aerodynamics things don't scale well due to the viscosity of the air. Small planes don't behave like larger ones of the same shape. Scale factors (like Reynolds Number) are employed to try and account for the difference.

Going back to your question... I think you will either have to assume it's proportional to mass or volume, or carry out you own experiments.

 

[jbriggs444]

how would I find out how much energy it would take to destroy the equivalent volume of the first substance for the second substance in simple terms?

You cannot. As has been stated already, it is not simple. At best, "it depends".