The energy added to the system due to the explosion in the observer's frame of reference will be given by: Eadd = 1/6 mv²
Law of conservation of linear momentum : -
The law of conservation of linear momentum asserts that the vector sum of a system of two colliding objects is constant and unaffected by their mutual interaction when no external forces are acting on the system.
The object's mass is m.
v is the object's velocity in relation to a stationary observer.
As a result, k= 1/2 mv2 will be used to calculate the object's initial kinetic energy in the observer's frame of reference.
The thing detonates.
Let m represent the mass of the piece with less mass.
Therefore, mh=3ml will provide the mass of the larger piece.
Following the explosion, the lighter piece moves at a speed of vl=0 and the less massive piece comes to a standstill.
Let vh=0 represent the speed of the larger piece following the explosion.
Applying the equation of conservation of linear momentum to the system's explosion and one-dimensional motion, we can now write:
Therefore, the energy added to the system due to the explosion in the observer's frame of reference will be given by:
E add = Kf-Ki
Eadd= 2/3 mv² - 1/2 mv²
Eadd = 1/6 mv²
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