# B Calculate Force in Newtons of a nuke on a given area

1. Dec 31, 2017

### Idont Know

Hi all, a 15 year old noob here. I want to calculate how much FORCE in NEWTONS would be delivered by a 100 kiloton nuke on an object of area around 2cm^2 from a distance of about 5 meters. This might sound like a stupid question, but all the answers about nukes are its POWER in joules, not FORCE. So any help? If some more data are required for meaningful answer, I can provide that.

2. Dec 31, 2017

### Staff: Mentor

We welcome curious 15 year old students.

The force on an object from an explosion obviously depends on the shape and orientation of the object. A flat square oriented flat side toward the center would experience different force than the same square oriented edge-on. We could calculate the force given the pressure of the explosion and the area of the object facing the center.

But in the case of a nuclear explosion, any object that close would be vaporized. It would no longer have any shape or size. Therefore the force would be impossible to define.

3. Dec 31, 2017

### Idont Know

Ok.. so what would be the minimum distance for a cube of volume 1cm^3 in a vacuum to be near such a nuke to NOT be vaporized and actually gain acceleration due to that? Much like that Project Orion, which planned to use nukes to propel a spacecraft to relativistic speeds?

4. Dec 31, 2017

### Staff: Mentor

Not dumb but difficult, and maybe just asking questions without studying the source first is not the best way to learn. Try reading this Wikipedia article https://en.wikipedia.org/wiki/Project_Orion_(nuclear_propulsion) before asking more questions.

Part of the idea of Orion was that part of the craft would be vaporized in each nuclear explosion, but not the whole thing. It would run out of bombs before the whole thing was vaporized. Also part of the idea was very specific shapes and sizes. The ideas can't be simplified to a cube.

5. Dec 31, 2017

### Drakkith

Staff Emeritus
There really isn't a single answer that we could give you. The force would depend on the properties of the medium the explosion is in (water, air, space), whether you want average force or maximum force, they type of weapon, and more. A nuclear explosion is a very complicated phenomenon and the details are not easy to mathematically predict.

6. Jan 2, 2018

### lekh2003

These are phenomenally difficult questions. You can't really blow up a nuclear bomb and expect it to accelerate objects. Project Orion works differently, it sets explosion outwards and propels itself normally like a regular rocket. What you are suggesting is the other way around. You are being hit by the rocket's nukes which accelerates you away. The problem is that this acceleration will most definitely vaporise you.

Another thing, forget relativistic speeds. Modern nukes are no way near that energy. Even if we could create an infinitely powerful bomb, it would just vaporise everything. Using nukes to go to relativistic speeds is straight from sci-fi. Modern tech and physics is much more down to Earth and non-violent.

7. Jan 2, 2018

### Khashishi

You mean energy. Power is measured in watts, not joules. Also, you asked for force, but what you probably want is impulse. Impulse is to force as energy is to power.

You can make some simple assumptions to get the approximate impulse from a nuke from the energy. You can assume that most of the energy is reflected by the hemispherical reflector. (If energy is instead absorbed by the reflector, this means you get roughly half the impulse, and the reflector will be quickly destroyed.)
You have the kinetic energy of the blast. The total energy is given by
$E^2 = m^2 c^4 + p^2 c^2$
and the kinetic energy of the blast is
$T = E - m c^2 = \sqrt{m^2 c^4 + p^2 c^2} - m c^2 = (\gamma-1) m c^2$
The particles that make up the blast probably have a distribution of energies, but for simplicity, I assume that they all have the same energy. Then the total magnitude of momentum of the blast particles is just
$p = \gamma m v$
which we can write in terms of T
$p = (\frac{T}{m c^2} + 1) m v$
We assume the blast is spherically symmetric. Only 1/6 of the blast is in the correct direction to contribute to moving the reflector, but the momentum transferred per particle is doubled because we assume an elastic collision and that the reflector is much more massive than the blast. So, the impulse is 1/3 the total momentum.
$I = p/3$

I honestly don't see the distinction you are raising here.

8. Jan 2, 2018

### lekh2003

OP was suggesting to use the blast power from the bomb to accelerate. Project Orion used nuclear energy as a kind of propulsion attached to the rocket. Project Orion wasn't a project where you set off a bomb under a rocket and hope it goes flying.

Last edited: Jan 2, 2018
9. Jan 2, 2018

### Staff: Mentor

You may be thinking of a different proposal for nuclear propulsion, or you're making a distinction that's not clear to me. Project Orion proposed propelling a spaceship with a series of nuclear explosions behind it.