## Thursday, September 23, 2021

### [lmsftfmq] sqrt tnt speed

teraton tnt = 51.3 ton * c^2 , using Einstein's E=mc^2 on the right hand side.

solve for tnt:

tnt = 5.1316205e-11 c^2

or, c^2/tnt is a dimensionless constant 1.9487022e+10 , the specific energy efficiency of a stoichiometric matter-antimatter bomb over TNT.

c = 139596 sqrt(tnt)

sqrt(tnt) = 2147.5732 m/s = 4803.9844 mph = 1.33444 mile / second = 7.16e-6 c = c/140000

one could express speed or velocity in units of millisquareroottnt :

100 km/h = 62 mph = 12.93 millisquareroottnt

an object of mass m = 1 ton traveling at speed v = 10 millisquareroottnt = 48 mph has Newtonian kinetic energy 0.5 * m * v^2 = 50 microtons tnt = 1.6 oz tnt.  (for comparison, KE/c^2 = 8.21e-11 oz.)  this seems a surprisingly small amount of TNT to accelerate a 1 ton frictionless object to 48 mph.

an object dropped from 77 feet (25 m) hits the ground at 48 mph.

a 1 ton 48 mph object colliding with (say) a wall does the same amount of damage as 1/5 a stick of dynamite (1 MJ/stick).  or, 1 stick equals 5 such collisions to the same spot.

You have: 50 micro ton tnt
You want: MJ
* 0.2092

gasoline (mass density 0.75 g/cm^3) has about 10 times higher energy density than TNT, but cars are not frictionless and typically weigh more than 1 ton.  if we assume these effects cancel out (giant handwave), a tankful (15 gallons) of gasoline can accelerate a car to 48 mph about 1000 times.

You have: 15 gal
You want: 50 micro ton / (0.75 g/cc)
* 938.858

more generally, if you have a specific energy (energy per unit mass), you can always take the square root to get a speed:

sqrt(gasoline) = 15000 mph

(TNT = 1e+6 kilocalorie/ton (exactly).  gasoline = 10.3e+6 kilocalorie/ton)