1. ## Question 7

I hope this is an easy one

A thin semi-infinite rod is made of high explosive. The detonation speed is v
(that is the speed at which the detonation propagates down the rod is v)
The speed of the detonation products through space is u<v.

Describe the shape of the shape of the explosion in time and space. That is
what is the time evolution of the region occupied by the explosion products.

RonL

2. Originally Posted by CaptainBlack
I hope this is an easy one

A thin semi-infinite rod is made of high explosive. The detonation speed is v
(that is the speed at which the detonation propagates down the rod is v)
The speed of the detonation products through space is u<v.

Describe the shape of the shape of the explosion in time and space. That is
what is the time evolution of the region occupied by the explosion products.

RonL
Is there any specific direction in which detonation produvts would travel?

Keep Smiling
Malay

3. Originally Posted by malaygoel
Is there any specific direction in which detonation produvts would travel?

Keep Smiling
Malay
Unlike in SF movies the products from a small amount of explosive will expand
in a shperical shell.

RonL

4. Originally Posted by CaptainBlack
Unlike in SF movies the products from a small amount of explosive will expand
in a shperical shell.

RonL
what would we the centre of the spherical shell?

Keep Smiling
Malay

The point of detonation of the small quantity of explosive.

RonL

5. Would it be a solid cone that increases in base radius at the speed of the explosion products and hiegth at the speed of the explosion's movment up the rod? At the base of the cone, there is a semisphere whose radius increases with the explosion products' speed as well.
The cone angle is 90u / v˚, since slope can be found by rise (u) over run (v) and be compared to the angle of the x- and y-axes (the y-axis is the cone's hypotenuse). It will always be less than 90˚, since the speed of the explosion particles is less than that of the explosion itself.

Move the green point to see the explosion

The speed of the detonation products through space is set by the distance from S to U (which you can change)

7. Originally Posted by Quick
[Move the green point to see the explosion

The speed of the detonation products through space is set by the distance from S to U (which you can change)
And what is the angle involved?

RonL

8. Originally Posted by CaptainBlack
And what is the angle involved?

RonL
What angle?

9. Originally Posted by Quick
What angle?
The angle the "cone" makes when projected against a flat surface. ie. what is the angle the top of the cone makes?

-Dan

10. ## Solution

First ask what happens when a single, tiny particle explodes. It will explode in all directions, giving a spherical explosion. The radius of the sphere containing the explosion products will expand at speed u.

Now fir the semi-infinite rod, consider it to be made up chain of particles of the explosive. Each particle generates a spherical explosion that spreads through space with speed u. However, the particles do not all explode at the same time. The explosion propagates down the rod with speed v. The result is a series of spheres, the largest growing from the end of the rod and having radius ut, and as you proceed down the rod to later explosions, successively smaller spheres, until you arrive at the point where the explosion is just occurring. The successively shrinking spheres add up, as shown in the attached figure, to a cone of altitude vt with a hemispherical cap of radius ut fitted perfectly on to the base of the cone.

RonL

11. A truly great illustration. That's pedagogy.
It reminds me of a sound barrier from a plane going in over the speed of sound.
And a really nice illustration from Quick as well.

12. Originally Posted by TriKri
And a really nice illustration from Quick as well.
I agree. Too bad MathGuru is considering dropping the program from the forum

To get that diagram, type in: