CritABCD
A.2 · 15 · A.2 Forces and momentum · explosions, conservation of momentum, energy considerations

Explosions and recoil

Bodies pushed apart from rest: the momenta cancel, the lighter body moves faster, and the kinetic energy comes from stored energy.

SL+HLHarder22 minFree
Hook

A rifle kicks back when it fires. A firework bursts into pieces that fly in every direction. Before the bang the total momentum is zero. What must it be afterwards?

A collision played backwards
1 / 5

Momentum in an explosion

Simulation

Zero splits into plus and minus

The idea: Watch the zero break into two equal and opposite momenta, and the light piece pay with speed what the heavy piece pays with mass.

Definition

Explosion: a process in which a body (or a system) breaks apart or bodies are pushed apart, driven by stored energy (chemical, elastic, nuclear). The forces between the parts are internal.

If no resultant external force acts, the total momentum is the same before and after. For a system that starts at rest the total is zero, so the parts’ momenta add up to zero. In one dimension: m₁v₁ + m₂v₂ = 0, so m₁v₁ = −m₂v₂.

m1v1 + m2v2 = 0 (from rest)
  • equal and opposite momenta
  • the lighter body moves faster: v1 / v2 = −m2 / m1
Check 1 of 5

Two trolleys of masses 2.0 kg and 3.0 kg are pushed apart from rest by a spring. The 2.0 kg trolley moves at 3.0 m s⁻¹. The 3.0 kg trolley moves at…

Check 2 of 5

In an explosion of a stationary object, the total momentum afterwards is…

Check 3 of 5

After the explosion in question 1, the total kinetic energy is…

Check 4 of 5

A 60 kg skater at rest throws a 3.0 kg ball forwards at 10 m s⁻¹ (relative to the ice). The skater’s recoil speed is…

Check 5 of 5

Which statement about kinetic energy is correct?

Apply

A stationary shell explodes into two fragments of very different masses. Compare their speeds and their kinetic energies, and explain where the energy came from.

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Remember earlier lessons
From lesson A.2 · 5

Momentum is conserved when…

From lesson A.2 · 6

In an inelastic collision the kinetic energy…

Summary card

Key points

  • • In an explosion the total momentum is conserved (zero if the system starts at rest).
  • • m₁v₁ = −m₂v₂: the lighter body moves faster.
  • • Kinetic energy increases: stored energy is released. Total energy is conserved.
  • • Elastic: KE conserved; inelastic: KE decreases; explosion: KE increases.

Formulas

  • m1v1 + m2v2 = 0
  • KE = p² / 2m

Key terms

Recoil
:
the backwards motion of a body that expels something forwards

Common errors

  • • Forgetting the sign of the recoil velocity
  • • Assuming the KE is shared equally
  • • Saying energy is not conserved
Checks solved: 0 of 5
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