AshPhys

Explosions and crash-landings

AshPhys · Revision cheat sheet
AS Level9702 AS Ch.6Chapter 6: MomentumLesson 6.4Sections 6.4

Goal: Use zero total momentum to find recoil velocities, and explain where momentum goes in a crash-landing.

velocity

01The big picture

An object at rest has zero momentum. When it explodes or pushes apart, the pieces still have zero total momentum: they fly apart with equal and opposite momenta. Kinetic energy is created from chemical or elastic potential energy, so it is not conserved.

When a falling object lands and stops, its momentum is not lost: it is passed to the Earth. The Earth’s mass is so large that its change in velocity is far too small to notice.

Recoil [paraphrase]
The backward motion of one part when another is pushed or fired forwards.
Fig. 1 · Pushing apart from rest
Pushing apart from restBefore: a large block and a small block touch, at rest. After: the large block moves left slowly (short arrow) and the small block moves right quickly (long arrow).before: at rest, p = 0afterMMVvm
Equal and opposite momenta: the small mass moves fast, the large mass slowly.

02Key equations

From rest
0=m1v1+m2v20 = m_1v_1 + m_2v_2
Recoil velocity
v2=−m1v1m2v_2 = -\frac{m_1v_1}{m_2}
Symbols and units
  • mmmass of each partkg\mathrm{kg}
  • vvvelocity of each part afterm s−1\mathrm{m\,s^{-1}}

03Sample problems with solutions

Sample 1 · Rifle recoil
A 4.0 kg rifle fires a 0.010 kg bullet at 400 m s⁻¹. Calculate the recoil velocity of the rifle and the total kinetic energy released.

  1. Total momentum stays zero:

    v2=−0.010×4004.0=−1.0 m s−1v_2 = -\frac{0.010 \times 400}{4.0} = -1.0\ \mathrm{m\,s^{-1}}

  2. Kinetic energy of both parts:

    Ek=12(0.010)(400)2+12(4.0)(1.0)2=800+2.0=802 JE_\mathrm{k} = \tfrac{1}{2}(0.010)(400)^{2} + \tfrac{1}{2}(4.0)(1.0)^{2} = 800 + 2.0 = 802\ \mathrm{J}
Answer: 1.0 m s⁻¹ backwards; 802 J (8.0 × 10² J)
Unit check: kg m s−1kg=m s−1 ✓\frac{\mathrm{kg\,m\,s^{-1}}}{\mathrm{kg}} = \mathrm{m\,s^{-1}}\ \checkmark

04Practice problems

  1. P1
    An object at rest explodes into pieces. What is their total momentum?
    Final answerZero
    Answer: Zero
  2. P2
    Skaters of 60 kg and 40 kg push apart from rest. The 40 kg skater moves at 3.0 m s⁻¹. Find the other’s velocity.
    Final answer2.0 m s⁻¹ the opposite way
    Answer: 2.0 m s⁻¹ the opposite way
  3. P3
    A 2.0 kg object at rest splits into 0.50 kg at 12 m s⁻¹ and the rest. Find the speed of the rest.
    Final answer4.0 m s⁻¹ the opposite way
    Answer: 4.0 m s⁻¹ the opposite way
  4. P4
    A 0.50 kg ball hits the ground at 6.0 m s⁻¹ and stops. What happens to its 3.0 kg m s⁻¹ of momentum?
    Final answerIt goes to the Earth
    Answer: It goes to the Earth

05Other useful information

Common mistakes

  • ✗ Wrong: Kinetic energy is conserved in an explosion.

    ✓ Right: It increases; it comes from stored energy.

Exam tips

  • The heavier part always moves off more slowly: equal momenta, unequal masses.

What the syllabus asks

  • 9702 topic 3: apply conservation of momentum, including changes in kinetic energy. Coursebook 6.4.

Explore: Practice questions for this lesson