A 13 kg asteroid is traveling with velocity 110 meters s when it breaks into 3 equal pieces one piece is left at rest and the second continues at the same velocity what was the energy of the explosion?

Answer 1

The total initial energy = the asteroid kienetic energy = 1/2 m v2 -----------> (1)

The total energy after disintegration = (first mass energy=0) + 1/2 (1/3 m) v2 + K.E. of the third piece + disintegration energy ------------> (2)

K.E. of the third piece = 1/2 (1/3 m)v'2

From conservation of energy, the two equations (1) and (2) are equal, then

1/2 m v2 =1/2 (1/3 m) v2 + 1/2 (1/3 m)v'2+ disintegration energy

Then, the disintegration energy = 1/2 m [v2 -1/3v2-1/3v'2] --------> (3)

* still need to find v'

using the conservation of momentum

mv= 0+1/3mv+1/3mv'

then v'= 3v- v= 2v

substitute in equation (3)

Then, the disintegration energy = 1/2 m [v2 -1/3v2-1/3 (2v)2 ] ?

Answer 2

To find the energy of the explosion, we can use the principle of conservation of momentum. Before the explosion, the total momentum is 13 kg * 110 m/s. After the explosion, two pieces are moving, each with 13/3 kg * 110 m/s momentum. The change in momentum due to the stationary piece is (13/3) kg * 110 m/s. Therefore, the energy of the explosion can be calculated as (13/3) kg * 110 m/s^2 * (110 m/s).