Question

Bomb of mass 16 kg at rest explodes into two pieces of masses of 4 kg and 12 kg.

The velocity of the 12 kg mass is 4 m/s. The kinetic energy of the 4 kg mass is​

Answer 1

Answer:

$\bigstar{\bold{Kinetic\:Energy=288\:J}}$

Explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• Total mass of the bomb (M) = 16 kg
• Velocity of the bomb (V) = 0 m/s
• Mass of first piece (m₁) = 4 kg
• Mass of second piece (m₂) = 12 kg
• Velocity of second piece(v₂) = 4 m/s

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• The kinetic energy of the first piece

$\Large{\underline{\underline{\bf{Solution:}}}}$

→ First we have to find the velocity (v₁) of the first piece.

→ By conservation of momentum we know that momentum before explosion + momentum after explosion = 0

 M V + m₁ v₁ + m₂ v₂ = 0

→ Substituting the datas we get,

  16 × 0 + 4 v₁ + 12 × 4= 0

  0 + 4v₁ + 48 = 0

  4v₁ = -48

     v₁ = -48/4

     v₁ = -12 m/s

→ Taking only the magnitude v₁ = 12 m/s

→ Hence velocity of the first piece is 12 m/s

→ Now we need to find the kinetic energy of the first piece.

→ Kinetic energy is given by the formula,

  K.E = 1/2 m₁ (v₁)²

→ Substituting the datas,

  K.E = 1/2 × 4 × 12 × 12

  K.E = 576/2

  K.E = 288 J

→ Hence kinetic energy posessed by the body is 288 J

$\boxed{\bold{Kinetic\:Energy=288\:J}}$

$\Large{\underline{\underline{\bf{Notes:}}}}$

→ Kinetic energy is defined as the energy posessed by a body due to virtue of its motion.

→ It is given by thhe formula,

  K.E = 1/2 × m × v²