oblique-collisions-with-a-surface

Oblique collisions with a surface

What are oblique collisions (with a surface)?

• In a normal collision a particle collides with a surface at right angles

• In an oblique collision the angle at which the particle collides with the surface is not 90°

• In oblique collisions

  • there are two dimensions of motion of the particle to consider

  • the velocity of the particle will change and so its momentum will change

  • this is caused by an impulse from the surface to the particle

    • the impulse acts perpendicular to the surface

What modelling assumptions are used for oblique collisions?

• Problems are usually presented with a diagram in plan view (i.e. from above)

• Modelling assumptions

  • the surface the particle is moving across (‘the floor’) is horizontal

  • the surface the particle will collide with (‘the wall’) is flat and fixed

  • the ‘floor’ and ‘wall’ are smooth (no friction)

  • particles are usually smooth spheres

    • this is so that the impact of the collision can be considered as occurring at a single point in space

What equations are needed to solve oblique collision problems?

• In the diagram

  • m s^-1 is the velocity before impact, m s^-1 is the velocity after impact

  • ° is the angle of approach, ° is the angle of rebound

  • N is the impulse (which always acts perpendicular to the surface)

  • is the coefficient of restitution (between the particle and the surface)

• The component of velocity parallel to the surface remains unchanged

  • 

• The component of velocity perpendicular to the surface can be found by applying Newton’s Law of Restitution

  • 

  • Rearranging

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