Question

Bomb of mass 30 kg at rest explodes into two pieces of masses 18 kg and 12 kg. the velocity of 18 kg piece is 6 ms–1. calculate the kinetic energy of the other piece.

Answer 1

Hey there!

According to law of conservation of momentum,

(mv) initial = (mv)final

Here, (mv) initial = 0 as the object is in rest.

∴ 0 = m1v1 + m2v2
where, m1 = 18kg
m2 = 12kg
v1 = 6 m/s
v2 = ?

0 = 18 × 6 + 12 × v2

0 = 108 + 12 × v2

12 × v2 = -108
v2 = -108/12

= -9 m/s

KE = 1/2mv ² 

= 1/2 × 12 × (-9) ² 
= 486 J

Thanks

Answer 2

→ Formula,

»m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

› m = 40kg

› u = 72km/hr =20m/s

» m₁= 15kg

›v₁ = 0

» m₂ = 40-15= 25kg

→we need to find v₂

» Therefore,

› 40×20 = 15×0+25×v₂

› 800 = 25v₂

» v₂ = 32

∴ The speed of the other will be 32m/s