Question

A stationary of bomb of mass 5kg explodes into one part A of mass 2kg flying off with a velocity 50m/s and another part B flying off with a velocity in opposite direction find velocity and total kinetic energy produced

Answer 1

Before Exploding ...
Momentum of bomb = mv
= 5 × 0
= 0 kg.m/s

After Exploding...
Part A : momentum = mv1
= 2 × 50 = 100kg.m/s

Part 2 : mass, m = 5-2 = 3kg
velocity = v
momentum = mv2 = 3v kg.m/s

Total momenta of parts = mv1 + mv2
= 100+3v

According to the law of conservation of momentum..

Momentum of bomb = total momenta of parts
0 = 100 + 3v
v = -100/3 = -33.34 m/s ( since: it is in opposite direction that's why its velocity is negative)

Kinetic energy of Part A = 1/2mv²
= 1/2×2×50×50 = 2500Joule
Kinetic energy of Part B = 1/2mv²
= 1/2×3×(-33.34)²
= 1667.34 Joule

Total Kinetic energy produced = sum of Kinetic energy of A and B
= 2500 + 1667.34
= 4167.34 Joule