Impact and Detonation Calculations

[quatang]

Can someone help me to calculate the approximate impact on the Earth (as in a mining explosion), of 1 ton of dynamite.
And also the equivalent impact of say a 1 ton rock dropped from 10 meters.

Trying to estimate this for writing purposes, I very roughly got:

Impact of 1 ton of dynamite, Work = approx 1/2 megawatt.
Equivalent dropping a 1 ton rock 10 meters, approx 2/3 megawatt. Probably way off.

I didn't work very long at this and as I'll likely not be confident of getting the answer right, I thought I'd ask some people who would know how to do these calculations.

Appreciate any feedback.

 

[haruspex]

Work = approx 1/2 megawatt.

dropping a 1 ton rock 10 meters, approx 2/3 megawatt

Watts and Megawatts measure power, not energy (work).

 

[CWatters]

+1

Energy is measured in Joules.

The potential energy stored In a rock at height h is given by PE =mgh where m is the mass in kg, h the height in meters and g the acceleration due to gravity 9.8m/s/s.

You can look up the energy density of dynamite on Wikipedia.

 

[anorlunda]

@quatang ,

Look at my signature. Memorize that and you'll never make that mistake again.

Power is to Energy as Speed is to Distance​

As @CWatters says, energy is pressured in joules. Electric power: 1 watt = 1 joule per second, 1 megawatt = 1 megajoule per second.

 

[quatang]

Thanks guys. To clarify my question, what I am after is, what mass of rock I would need to drop from say 20 meters, that would send an equivalent seismic wave into the ground to match a 1 ton dynamite blast.

Hope that's clearer. The physics units are pretty complex for a novice, so I'll avoid using them.

I only need a rough idea that is realistic.
Thanks for any help...

 

[ZapperZ]

Thanks guys. To clarify my question, what I am after is, what mass of rock I would need to drop from say 20 meters, that would send an equivalent seismic wave into the ground to match a 1 ton dynamite blast.

Hope that's clearer. The physics units are pretty complex for a novice, so I'll avoid using them.

I only need a rough idea that is realistic.
Thanks for any help...

First of all, you cannot avoid using "physics units", because if you do, you'll be comparing apples to oranges.

Secondly, this link gives you the energy equivalent of 1 ton of TNT:

https://hypertextbook.com/facts/2002/AlexRoslyakov.shtml

Knowing this, will you be able to calculate the kinetic energy of impact of a rock of mass "m" from 20 meters up?

Zz.

 

[quatang]

Thanks guys. I think that's solved it.
I found that
A 10,000 kg rock, with 10 m drop, is about 1 MJ, which is about 0.28 kWh
And, 1 ton dynamite/tnt is approx 4.184 gigajoules = 1162 kWh

So there is no real possibility to create an impact on the ground by dropping a large boulder, equivalent to 1 ton of dynamite.

I estimate a ~40 kiloton boulder would need to be dropped. So this theme is out and back to the drawing board.

I'll check back tomorrow in case anyone can add anything to the above. Again thanks very for your comments.

 

[CWatters]

Unfortunately gravity is surprisingly weak (although I find it's stronger early on Sunday mornings).

I ran some rough numbers for a meteorite impact. Googling suggests a meteorite of around 5000-9000kg might hit the ground at say 1km/s as it's slowed down a bit by the atmosphere. The equation for the kinetic energy is 0.5mv^2 so we can work out how big a meteor you would need..

KE = 0.5mv^2

m = 2KE/v^2
= 2*4.184*10^9/1,000^2
= 8,000kg