1. Collisions
Chapter 4

2. Chapter Objectives
Use the impulse-momentum principle and the principle of conservation of linear momentum in vector form
Apply conservation of linear momentum and Newton’s Law of Restitution to solve problems involving direct impact
Model and solve problems involving successive impacts

3. You met these principles in M1 I = mv – mu m1u1 + m2u2 = m1v1 + m2v2
Use the impulse-momentum principle and the principle of conservation of linear momentum in vector form
You met these principles in M1
I = mv – mu
the impulse of a force is equal to the change in momentum produced
m1u1 + m2u2 = m1v1 + m2v2
the total momentum before impact equals the total momentum after impact

6. 4.1

9. Apply conservation of linear momentum and Newton’s Law of Restitution to solve problems involving direct impact
a direct impact is a collision between particles, of the same size, which are moving along the same straight line. The speeds of the particles after the impact depend on the materials they are made of.

10. DRAW DIAGRAMS FOR BEFORE AND AFTER
It is worth remembering that at this point one could not be certain of the direction of v1.

11. unlike this example please state Newton’s law

12. DRAW DIAGRAMS FOR BEFORE AND AFTER
SET UP THE TWO EQUATIONS ( NEWTON AND CONSERVATION)

14. Impact of a particle with a fixed surface. 4.3
It is assumed that the collisions occur normally (i.e. along a perpendicular line)
Newton’s Law becomes:
Speed of rebound = e
Speed of approach
As well as horizontal collisions with fixed surfaces one can also be asked to consider particles falling from a height and rebounding to a new height.

15. A small smooth ball falls from a height of 3m above a fixed smooth horizontal surface. It rebounds to a height 1.2m. Find the coefficient of restitution between the ball and the plane.
The first task is to calculate the time it takes to fall to the surface and the speed at the time of contact.

17. DRAW DIAGRAMS FOR BEFORE AND AFTER
SET UP THE TWO EQUATIONS ( NEWTON AND CONSERVATION)

20. Two small smooth spheres, A and B, of equal radius, have masses m and 5m respectively. The sphere A is moving with speed u on a smooth horizontal table when it collides directly with B, which is at rest on the table. As a result of the collision the direction of motion of A is reversed The coefficient of restitution between A and B is e.
a) Find the speed of A and B immediately after the collision
b) Find the range of possible values of e.

21. DRAW DIAGRAMS FOR BEFORE AND AFTER
SET UP THE TWO EQUATIONS ( NEWTON AND CONSERVATION)

25. 4.4 Multiple collisions and problems involving
three particles.
Once again these questions only require the same approach as before, you should be able to set up the first set of simultaneous equations and find the values for v1 and v2.
Lets look at some examples to see what goes on. .

27. DRAW DIAGRAMS FOR BEFORE AND AFTER
SET UP THE TWO EQUATIONS ( NEWTON AND CONSERVATION)

28. Conservation of momentum gives:

30. Considering B going on to strike C
DRAW DIAGRAMS FOR BEFORE AND AFTER
SET UP THE TWO EQUATIONS ( NEWTON AND CONSERVATION)

39. 4.5 change in energy due to an impact or the application of an impulse

40. DRAW DIAGRAMS FOR BEFORE AND AFTER
SET UP THE TWO EQUATIONS ( NEWTON AND CONSERVATION)

42. End