Collisions (OCR A Level Physics)

Revision Note

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Katie M

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Katie M

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Collisions in One & Two Dimensions

One-dimensional Problems

  • Momentum (p) is equal to: p = m × v
  • One-dimensional momentum problems are when collisions are taken place in just the x (horizontal) or just the y (vertical) direction
  • Using the conservation 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

Two-dimensional Momentum Problems

  • Since momentum is a vector, in 2D it can be split up into its x and y components
  • Two-dimensional momentum problems are when collisions are taken place in both the x (horizontal) and the y (vertical) direction
  • Using the conversation of linear momentum as well as resolving vectors, it is possible to calculate changes in momentum
  • This is shown in the example below:

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 at P.

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

Elastic & Inelastic Collisions

  • In both collisions and explosions, momentum is always conserved
  • However, kinetic energy might not always be
  • A collision (or explosion) is either:
    • Elastic – if the kinetic energy is conserved
    • Inelastic – if the kinetic energy is not conserved

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

Elastic & Inelastic Collisions, downloadable AS & A Level Physics revision notes

Elastic collisions are where two objects move in opposite directions. Inelastic collisions are where two objects stick together

  • An explosion is commonly to do with recoil
    • For example, a gun recoiling after shooting a bullet or an unstable nucleus emitting an alpha particle and a daughter nucleus

  • To find out whether a collision is elastic or inelastic, compare the kinetic energy before and after the collision
  • The equation for kinetic energy is:

Kinetic energy equation, downloadable AS & A Level Physics revision notes

Worked example

Trolley A of mass 0.80 kg collides head-on with stationary trolley B at speed 3.0 m s–1. Trolley B has twice the mass of trolley A.The trolleys stick together and travel at a velocity of 1.0 m s–1.Determine whether this is an elastic or inelastic collision.

Collisions Worked Example Answer (1), downloadable AS & A Level Physics revision notesCollisions Worked Example Answer (2), downloadable AS & A Level Physics revision notes

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.

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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.