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4.2.3Linear Momentum

Momentum in Collisions — AP PHYSICS 1 Revision Notes & Topical Questions

5 min read 9 parts Lesson 10 of 13 1 quiz

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Lesson summary

4.2.3 Momentum in Collisions — AP PHYSICS 1 notes: Use conservation of momentum to analyse one- and two-dimensional collisions, including objects that stick together.Collision = an event in which two or more moving objects come together and exert forces on each other.Assumptions …

  • Sign convention
  • Plausibility
  • Components
  • x equation
  • y equation
  • Qualitative result

Part 1 of 7Collisions as isolated systems

Collisions as isolated systems
Collision
Collision an event in which two or more moving objects come together and exert forces on each other.
Assumptions
  • Assumptions internal forces are much larger than the net external force and the time interval is very short.
Momentum
  • Momentum total momentum just before equals just after: m1v1i + m2v2i = m1v1f + m2v2f.
Scope
  • Scope applies to every collision, whether kinetic energy is conserved or not.

Part 2 of 7Perfectly inelastic collisions

Condition
  • Condition the objects stick and move with a common velocity vf.
Equation
  • Equation vf = (m1v1i + m2v2i)/(m1 + m2), a weighted average of the initial velocities.
Energy
  • Energy the greatest loss of kinetic energy consistent with momentum conservation.
Examples
  • Examples clay hitting a block, coupling railway cars, a bullet embedding in wood.

Part 3 of 7One-dimensional collisions of separate objects

1
Identify the objects in the system and check no net external force acts.
2
Write expressions for the momentum of each object before and after.
3
Write the total momentum before and after.
4
Apply conservation of momentum and solve (e.g. mAv0A = −mAvA + mBvB).
Unknowns
  • Unknowns two final velocities need extra information.
    • (one final velocity or an elastic condition)
Sign convention
  • Sign convention choose a positive direction and use signed velocities.
Plausibility
  • Plausibility objects cannot pass through each other, so the trailing object cannot end up faster than the one ahead.

Part 4 of 7Collisions in two dimensions

Components
  • Components momentum is conserved separately in x and y.
x equation
  • x equation mAv0A = mAvAcosθA + mBvBcosθB.
y equation
  • 0 = mAvAsinθA − mBvBsinθB.
Qualitative result
  • Qualitative result if one particle moves up after the collision, the other moves down to cancel the vertical component.
Perfectly inelastic, car east and truck north
  • Perfectly inelastic, car east and truck north find px and py separately, then θ = tan−1(py/px).
Course level
  • AP Physics 1 treats 2D collisions qualitatively and semiquantitatively.

Part 5 of 7Energy and impulse in collisions

Kinetic energy change
  • ΔK = Kf − Ki gives energy transferred to thermal energy, sound and deformation.
Impulse on each object
  • Impulse on each object its own change in momentum; the two are equal and opposite.
Average force
  • Average force impulse divided by contact time.

Part 6 of 7Ballistic pendulum

1
Collision stage: use momentum conservation because the time is very short and tension is vertical.
2
Swing stage: use energy conservation because only gravity and the non-working tension act.
3
Never apply energy conservation across the embedding; mechanical energy is lost there.
4
Link the stages to get the projectile's speed from the swing height.

Part 7 of 7More from the specification

  • Explosion
    • Interaction pushing parts of a system apart.

Key terms

TermMeaning
CollisionShort interaction with large internal forces.
Perfectly inelasticCollision in which the objects stick together.
Ballistic pendulumBlock that a projectile embeds in and which then swings up.
Common velocityVelocity shared by objects that stick.
Impulse on each objectEqual and opposite, from Newton's third law.

Avoid these mistakes

1
Assuming kinetic energy is conserved in every collision.
2
Using speeds without signs in head-on collisions.
3
Forgetting that the final mass is the sum when objects stick.
4
Using momentum conservation over a long time when friction acts.
5
Believing the heavier object exerts a larger force — the forces are equal and opposite.

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