An object initially at rest explodes in two fragments of masses 5 kg and 7.5 kg that move in diametrically opposite directions. If the speed of the first fragment is 8.1 m/s, find the internal energy of the explosion.

Given that,

The object is initially at rest. I. e Initial velocities u = 0m/s

The object explodes into two fragment

Let the first fragment mass be Ma = 5kg

Let the second fragment mass be Mb = 7.5kg

The objects move in opposite direction

The speed or the first fragment is Va = 8.1m/s

Internal energy of the explosion.

From the conservation of momentum

Momentum before collision = momentum after collision

Momentum P = mv

Momentum is a vector quantity, so since the fragment moves in opposite direction, let assume that Ma moves in positive direction and Mb moves in negative direction

Then,

(Ma+Mb) •u = Ma•-Va + Mb•Vb

0 = - 5 * 8.1 + 7.5Vb

0 = - 40.5 + 7.5Vb

7.5Vb = 40.5

Vb = 40.5/7.5

Vb = 5.4m/s

Now using conservation of energy

Total kinetic energy of the fragment is equal to energy of explosion

K. E = ½Ma•Va² + ½Mb•Vb²

K. E = ½ * 5 * 8.1² + ½ * 7.5 * 5.4²

K. E = 164.025 + 109.35

K. E = 273.375 J