What was the amount of energy released in the 9/11 terrorist attacks? I read somewhere on the internet that the amount of energy released by the terrorist attacks on the twin towers on 9/11 should have been of the order of 100 tons of TNT. This number surprised me, because this would be equivalent to the 0.1 kT test explosion preliminary to the Trinity test.
So I tried to estimate the kinetic energy of a plane with weight 100 tons and a speed of 200 m/s:
$$
E_{kin} = \frac{1}{2}m v^2 = 1/2 * (200)^2 * 100*10^3 = 2 * 10^9 J
$$
A ton of TNT roughly releases $4*10^9 J$, so the kinetic energy by the impact of one plane can only account for an equivalent of 0.5 tons of TNT, two planes would then be about 1 ton of TNT.
So the impact of the planes alone cannot account for the estimate of 100 tons of TNT.
But what about the energy of the exploding fuel and the potential energy released by the collapse of the twin towers? Can someone give a estimate for these energies? Could these add up to 100 tons of TNT in total? 
 A: Estimating is always a fun aspect of physics - so let's do some, without looking up any values.
What is the kinetic energy of a plane? We need to know the mass of a plane and its speed. I am going to use seriously rounded numbers - let's see how close we get.
We "know" a full size car is about 1000 kg, and can carry 5 passengers of 100 kg. That means a car has about 3:1 ratio of total mass to cargo.
Planes are built to be light - so let's assume a plane has a 2:1 ratio. This implies that a plane that can carry 200 people will have a mass around 40,000 kg (loaded, before fuel). If fuel is a significant factor in the cost of a plane ticket, and one way ticket is USD300, then the plane spends about USD30,000 to fill up. Let's assume USD1 / liter, or 30,000 liter. That adds another 25,000 kg or so - and presumably the structure of the plane needs to be strong enough to carry that. So let's put the full mass of the plane at 100,000 kg.
Flying the 3500 miles across the US in 6 hours implies a cruising speed around 800 km/h or 200 m/s, for a kinetic energy of $\frac12 m v^2 = 0.5 \cdot 10^5 \cdot 20,000 = 2\cdot 10^{9} J$.
How much energy would the fuel contain? I imagine that if the engines of a plane failed, it would have to glide home at a glide angle of about 5 degrees with reduced speed - a 1 in 10 glide angle means the drag force is 1/10th of the weight, and if we multiply that by the 3000 miles (5000 km) distance that the plane was supposed to fly (IIRC it was going from Boston to LA so it had a lot of fuel) we end up with $E = 5\cdot 10^6 \cdot 4\cdot 10^4 = 2\cdot 10^{11}J$ . Now the engine won't convert all the energy in the fuel into useful kinetic energy for the plane, and the drag is higher at high speeds. So let's estimate the energy in the tank at $10^{12} J$ - a factor 5x for efficiency and higher drag seems reasonable (given that drag goes with velocity squared). Even without this scaling, this is clearly much more than the kinetic energy in the plane - as it has to be given that a plane can't glide across the continent, it needs fuel to keep going.
How does that compare to the energy in TNT? Well - TNT like other explosives "carries its own oxygen" so the energy density is probably lower than for kerosene. Let's assume (since you need two oxygen for one carbon, but one oxygen for two hydrogen) that TNT has about half the energy density of kerosene. 
We had earlier estimated 25,000 kg of fuel; two planes = 50,000 kg, times two = 100,000 kg of TNT or 0.1 kTon. Which is the number you got...
A: Assuming kerosene is C8H18, has 25 chemical bonds, each of which releases 1eV when burned, gives an energy in fuel of 20 MJ/kg.
The weight of a plane shortly after take off is significantly fuel. If I'd guessed I would have said 20 tonnes per plane; (Floris' comment suggests more like 30).
This gives 400 GJ per plane, equivalent to 100 tons of TNT per plane (assuming the 4MJ/kg for TNT given in the question).
A: Based on the answers here is my summary:
Kinetic energy of one plane:
$$
E_{kin} = 2 * 10^9 J = 0.5 \text{ tons of TNT}
$$
Chemical energy of the plane fuel (very close to the amazing estimation of Floris):
$$
E_{chem} = 38000 L * 35 * 10^6 J/L = 1.33*10^{12} J = 330 \text{ tons of TNT} 
$$
Potential energy of one collapsing tower:
$$
E_{pot} = 300000*10^3 kg * 10 m/s^2 * (1/2)*400 m = 6*10^{11} J = 150 \text{ tons of TNT}
$$
For the potential energy we use the formula $E_{pot}=mgh$. The factor of $1/2$ comes from the fact, that the symmetry of the tower allows us to assume that the center of mass was right at the middle at a height of 200m.  
The calculations are based on the following estimates:


*

*speed of plane: 200 m/s

*mass of plane: 100 tons

*mass of fuel: 10000 US Gallons = 38000 L (see https://en.wikipedia.org/wiki/American_Airlines_Flight_11)

*energy density of jet fuel: 35 MJ/L (see https://en.wikipedia.org/wiki/Jet_fuel)

*mass of one tower: 300000 tons (see http://www.journalof911studies.com/letters/wtc_mass_and_energy.pdf)

*height of tower: 400 m 

*gravitational acceleration: 10 m/s^2

*ton of TNT: 4.184 * 10^9 J (https://en.wikipedia.org/wiki/TNT_equivalent)


The estimates here are consistent with the results given for example at https://www.uwgb.edu/dutchs/pseudosc/911NutPhysics1.HTM . 
