A LevelPhysicsCIERevision Notes3. Dynamics3.3 Linear Momentum & its ConservationElastic & Inelastic Collisions

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Elastic & Inelastic Collisions (CIE A Level Physics)

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Elastic collisions

  • When two objects collide, they may spring apart retaining all of the kinetic energy of the system
  • This would be a perfect elastic collision
  • In an elastic collision, all of the kinetic energy is conserved

  • Recall the kinetic energy equation:

E subscript k space equals space 1 half m v squared

  • Where:
    • Ek = kinetic energy in joules (J)
    • m = mass in kilograms (kg)
    • v = velocity in metres per second (m s-1)

  • Kinetic energy depends on the speed of an object
  • In a perfectly elastic collision (such as a head-on collision):

the relative speed of approach = the relative speed of separation

Worked example

Two similar spheres, each of mass m and velocity v are travelling towards each other.

The spheres have a head-on collision. What is the total kinetic energy after the impact?

WE - Elastic collision question image, downloadable AS & A Level Physics revision notes

Answer:

Step 1: Equate the kinetic energy before and after the collision

  • In an elastic collision, the kinetic energy of the system is conserved

E subscript k space b e f o r e end subscript space equals space E subscript k space a f t e r end subscript

Step 2: Write an expression for the kinetic energy before the collision

E subscript k space b e f o r e end subscript space equals space 1 half m v squared space plus space 1 half m v squared space

E subscript k space b e f o r e end subscript space equals space m v squared space equals space E subscript k space a f t e r end subscript

  • Therefore, the correct answer is C

Examiner Tip

Despite velocity being a vector, kinetic energy is a scalar quantity and therefore will never include a minus sign.

This is because in the kinetic energy formula, mass is scalar and the v2 will always give a positive value whether its a negative or positive velocity.

Inelastic collisions

  • Whilst the momentum of a system is always conserved in interactions between objects, kinetic energy is not always conserved
  • An inelastic collision is one where kinetic energy is not conserved

  • The kinetic energy is transferred to other energy stores
  • Inelastic collisions occur when two objects collide and they crumple and deform
  • All of the kinetic energy of the system may be transferred away from the system and the objects will come to a halt 
  • Or some of the kinetic energy of the system may be transferred away and the objects will move as one body at a slower speed than the original objects
  • A perfectly inelastic collision is when two objects stick together after collision

Worked example

Two trolleys X and Y are of equal mass. Trolley X moves towards trolley Y which is initially stationary.

After the collision, the trolleys join and move together.

Prove that this collision is inelastic.

Answer:

Step 1: Write an expression for the kinetic energy of the system before the collision

E subscript k space b e f o r e end subscript space equals space 1 half m subscript x v subscript x squared space plus space 0

  • Object Y is stationary before the collision, so its kinetic energy is zero

Step 2: Write an expression for the kinetic energy of the system after the collision

E subscript k space a f t e r end subscript space equals space 1 half open parentheses m subscript x space plus space m subscript y close parentheses v subscript x plus y end subscript squared

  • Both trolleys are of equal mass, therefore mx + my = 2m

E subscript k space a f t e r end subscript space equals space 1 half open parentheses 2 m close parentheses v subscript x plus y end subscript squared

Step 3: Compare the expressions and determine if they are equal

1 half m subscript x v subscript x squared space not equal to 1 half open parentheses 2 m close parentheses v subscript x plus y end subscript squared

E subscript k space b e f o r e end subscript space not equal to space E subscript k space a f t e r end subscript

  • The kinetic energy before the collision is not equal to the kinetic energy after the collision
  • Therefore, the collision is inelastic

Examiner Tip

Although kinetic energy may not always being conserved, remember momentum will always be conserved.

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    Leander

    Author: Leander

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    Leander graduated with First-class honours in Science and Education from Sheffield Hallam University. She won the prestigious Lord Robert Winston Solomon Lipson Prize in recognition of her dedication to science and teaching excellence. After teaching and tutoring both science and maths students, Leander now brings this passion for helping young people reach their potential to her work at SME.