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Impact with a wall

Impact with a wall. v 2 – v 1 = –e(u 2 – u 1 ). u 2 = v 2 = 0 . v = - eu. v. I. Oblique Impact When an object hits a wall obliquely then an IMPULSE acts perpendicular to the wall causing the momentum to change. There is no change in momentum parallel to the wall. Oblique Impact. I.

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Impact with a wall

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  1. Impact with a wall • v2 – v1 = –e(u2 – u1) u2 = v2 = 0 v = -eu v I

  2. Oblique Impact When an object hits a wall obliquely then an IMPULSE acts perpendicular to the wall causing the momentum to change. There is no change in momentum parallel to the wall

  3. Oblique Impact I

  4. Oblique Impact Case1 Object hits smooth wall e = 1

  5. Oblique Impact Case1 Object hits smooth wall e = 1 I

  6. Since e = 1 this just reverses the direction and leaves the speed unchanged. V//= –U// V  Angle of Incidence = Angle of Reflection V//  I line of centre U   U // Because the ball and the floor are perfectly smooth, there are no horizontal forces acting on the body, and there are no forces that can alter the momentum perpendicular to the line of centre(parallel to the wall).  • The momentum perpendicular to the line of centre must therefore be the same after impact as before,  mU= mV. i.e   U = V

  7. Oblique Impact Case2 Object hits smooth wall e < 1

  8. Oblique Impact Case2 Object hits smooth wall e < 1 I

  9. V  Angle of incidence is < Angle of reflection V// As e < 1, the ball rebounds with reduced speed parallel to the line of centre.  I line of centre V//= –eU//  U  U// Because the ball and the floor are perfectly smooth, there are no horizontal forces acting on the body, and there are no forces that can alter the momentum perpendicular to the line of centre(parallel to the wall).  . • The momentum perpendicular to the line of centre must therefore be the same after impact as before,  mU= mVi.eU= V

  10. Oblique Impact Between 2 Moving Balls

  11. Case 3 Oblique impact between 2 moving balls When 2 balls collide obliquely then the impulse acts along Causing a change of momentum along the line of centres the line of centres f b line of centre a q

  12. Case 3 Oblique impact between 2 moving balls f b line of centre a q

  13. v1 u1 v2 u2 Case 3 Oblique impact between 2 moving balls Turn the diagram so that the line of centres is the x axis f b line of centre a q

  14. Case 3 Oblique impact between 2 moving balls V1  V2  V1// V2 // f b line of centre U1  a q U1// U2  U2// Since the spheres are smooth, there is no change in the momentum components in the direction perpendicular to the line of centre as the impulse acts along the line of centres. • m1u1sin a = m1v1sinb and m2u2sinq = m2v2sinf • u1sin a = v1sinband u2sinq = v2sinf

  15. Case 3 Oblique impact between 2 moving balls V1  V2  V1// V2 // b f line of centre U1  a q U1// U2  U2// Parallel to the line of centres use conservation of momentum m1u1cosa– m2u2cosq = –m1v1cosb + m2v2cosf • and using the restitution equation v2 – v1 = –e(u2 – u1) • v2cosf – (– v1cosb) = –e(–u2cosq – u1cosa)

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