Elastic collisions

• Newton's law of restitution states that e, the coefficient of restitution, is equal to the speed of separation divided by the speed of approach, or v/u.
• e can only have a value between 0 and 1, where e = 0 is a completely inelastic collision and particles coalesce (stick together) on impact, and e = 1 is a perfectly elastic collision.
• To find the speed with which a particle rebounds from a fixed plane, multiply the approach speed by e.
• The conservation of linear momentum can be written as m1 u1 + m2 u2 = m1 v1 + m2 v2.
• The loss of kinetic energy is the kinetic energy before minus the kinetic energy after.
• When a smooth particle hits a smooth surface, the impulse acts perpendicular to the surface, through the centre of the sphere.
• When a smooth particle hits a smooth surface, the component of velocity parallel to the surface is unchanged.
• When a smooth particle hits a smooth surface, the component of velocity perpendicular to the surface is divided by e.
• When two particles collide, the impulse acts along the line of centres.
• When two particles collide, the components of velocities perpendicular to the line of centres are unchanged, but newtons law of restitution applies to the parallel components.
• The components of a vector a in the direction of another vector b is given by ( a . b/ |b^2| ) [b], where [b] is a vector.
• Where the wall is not a long an i or j axis, the scalar product of the wall and the vector of either the initial or final speed will be equal.
• Where the line of centres is not along the i or j axis, newtons law of restitution is adapted to become -e u . I = v . I, where u, v and I are vectors and . represents the scalar product.