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First teaching 2020

Last exams 2024

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Conservation of Momentum (CIE AS Physics)

Revision Note

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Katie M

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Katie M

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The Principle of Conservation of Momentum

  • The principle of conservation of momentum is:
    • The total momentum of a system remains constant provided no external force acts on it

  • For example if two objects collide:

the total momentum before the collision = the total momentum after the collision

  • Remember momentum is a vector quantity. This allows oppositely-directed vectors to cancel out so the momentum of the system as a whole is zero
  • Momentum is always conserved over time

External and Internal Forces

  • External forces are forces that act on a structure from outside e.g. friction and weight
  • Internal forces are forces exchanged by the particles in the system e.g. tension in a string
  • Which forces are internal or external will depend on the system itself, as shown in the diagram below:

External and internal forces on a mass on a spring, downloadable AS & A Level Physics revision notes

Internal and external forces on a mass on a spring

  • You may also come across a system with no external forces being described as a ‘closed’ or ‘isolated’ system
  • These all still refer to a system that is not affected by external forces
  • For example, a swimmer diving from a boat:
    • The diver will move forward, and, to conserve momentum, the boat will move backwards

  • This is because the momentum beforehand was zero and no external forces are present to affect the motion of the diver or the boat

Collisions in One & Two Dimensions

One-dimensional momentum problems

  • Momentum (p) is equal to: p = m × v
  • Using the conversation of linear momentum, it is possible to calculate missing velocities and masses of components in the system. This is shown in the example below

Worked example

Trolley A of mass 0.80 kg collides head-on with stationary trolley B at a velocity of 3.0 ms-1.Trolley B has twice the mass of trolley A.The trolleys stick together. Using the conservation of momentum, calculate the common velocity of both trolleys after the collision. Determine whether this is an elastic or inelastic collision.

WE - 1D momentum conservation answer image (1), downloadable AS & A Level Physics revision notesWE - 1D momentum conservation answer image (2), downloadable AS & A Level Physics revision notes

  • To find out whether a collision is elastic or inelastic, compare the kinetic energy before and after the collision
    • If the kinetic energy is conserved, it is an elastic collision
    • If the kinetic energy is not conserved, it is an inelastic collision

  • Elastic collisions are commonly those where objects colliding do not stick together and then move in opposite directions
  • Inelastic collision are where objects collide and stick together after the collision

Two-dimensional momentum problems

  • Since momentum is a vector, in 2D it can be split up into its x and y components
  • Review revision notes 1.3 Scalars & Vectors on how to resolve vectors

Worked example

A ball is thrown at a vertical wall. The path of the ball is shown belowThe ball is thrown from S with an initial velocity of 15.0 m s-1 at 60.0° to the horizontal. The mass of the ball is 60 × 10-3 kg and rebounds at a velocity of 4.6 m s-1.Calculate the change in momentum of the ball if it rebounds off the wall.

Examiner Tip

If an object is stationary or at rest, it’s velocity equals 0, therefore, the momentum and kinetic energy are also equal to 0.When a collision occurs in which two objects are stuck together, treat the final object as a single object with a mass equal to the sum of the two individual objects.In 2D problems, make sure you’re confident resolving vectors. Here is a small trick to remember which component is cosine or sine of the angle for a vector R:Vector components, downloadable AS & A Level Physics revision notes

Resolving vectors with sine and cosine

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Katie M

Author: Katie M

Expertise: Physics

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.