1. Different kinds of collisions
Momentum
Collisions 1
Next Slide
Different kinds of collisions
Completely inelastic collision
Completely elastic collision
Partially elastic collision
Explosion
Examples
Photo

2. Experiments about collisions
Momentum
Collisions 2
Next Slide
Experiments about collisions
Use of friction-compensated inclined plane
Photo
Use of ticker-timer to study velocity
Diagram
Preparations of different kinds of collisions
Diagram
Parameters : collisions, mass, initial velocities
Results
Calculation

3. Conservation of momentum
Next Slide
Conservation of momentum
Definition of momentum :
Mass  velocity (mv) (vector! Why?)
Unit :
Conservation of total momentum in the experiment

4. Conservation of momentum
Next Slide
Conservation of momentum
Law of conservation of momentum
In a collision the total momentum of the objects before the collision is equal to the total momentum after the collision, provided that there is no external force acting on the colliding objects.
Examples and explanation of external forces
Diagram

5. Conservation of momentum
Next Slide
Conservation of momentum
Example (partially elastic collision)
Calculation
Example (elastic collision)
Calculation
Example (inelastic collision)
Calculation
Example (explosion)
Calculation
Daily examples
Diagram
Disappearing momentum examples
Diagram

6. Impulse and Newton’s second law
Momentum
Impulse 1
Next Slide
Impulse and Newton’s second law
Investigate a collision in details
Calculation
Time of contact
Average force and average acceleration during time of contact
Combine
Newton’s second law (new form) :

7. Impulse and Newton’s second law
Momentum
Impulse 2
Next Slide
Impulse and Newton’s second law
Definition of Impulse
Impulse = Force  time (Ft) (vector! Why?)
Impulse of a body
=change in momentum that body
Unit :
Applicable even when law of conservation of momentum fails

8. Impulse and Newton’s second law
Momentum
Impulse 3
Next Slide
Impulse and Newton’s second law
Example 1
Calculation
Example 2
Calculation
Daily examples
Photo
Discussion

9. Newton’s Third Law of Motion
Momentum
Newton’s Third Law 1
Next Slide
Newton’s Third Law of Motion
Revision of Newton’s third law of motion
Spotting the action and reaction pairs
Diagram

10. END of Momentum

11. Momentum Back to Collisions 1 Click Back to
Completely inelastic collision
Completely elastic collision
Partially elastic collision
Explosion

12. Momentum Back to Collisions 2 Click Back to
A friction-compensated inclined plane is prepared as shown. Two trolleys are placed on the inclined plane. Different kinds of collisions are performed by the trolleys.

13. Momentum Back to Collisions 2 Click Back to
Paper tapes which pass through a ticker timer are attached to the trolleys. Hence, we can study their motions in different kinds of collisions.
paper tapes
trolleys
friction-compensated inclined plane

14. Momentum Collisions 2 Next Slide
Arrangement for different kinds of collisions
Partially elastic collision
Inelastic collision
Attach spring to the trolley
Attach pin and cork to the trolleys S
Attach magnets to the trolleys N S
Attach magnets to the trolleys

15. Momentum Back to Collisions 2 Click Back to
Arrangement for different kinds of collisions
Explosion
A spring is compressed
by two trolleys
The spring would force the trolleys
to move in opposite directions

16. Momentum Back to Collisions 2 Click Back to
We consider the result in inelastic collision. The data obtained is shown in the following table.
The quantity, mass x velocity is called momentum.
The total momentum before collision is equal to the total momentum after collision.

17. Momentum Momentum 2 Next Slide
Consider the collision of two balls in space as shown
Before collision
In contact F
The only forces arise in this collision are the forces acting on each ball by another one.
We say that there are no external forces and the conservation of momentum holds.

18. Momentum Back to Momentum 2 Click Back to
Consider the collision of two sliding balls on a rough surface as shown.
Before collision
Rough surface
In contact F
friction
Apart from the forces acting on each ball by another one, we also have friction acting on the balls. We say we have external force (friction).
The conservation of momentum does not hold when we have external force.

19. Momentum Back to Momentum 3 Click Back to Before collision
Two identical balls (2 kg) are moving towards each other with the same speed 3 m s-1. After collision, one of the ball is bounced backwards with speed 1 m s-1. Find the velocity of the other ball.
Before collision
After collision
+ve
By conservation of momentum,
Velocity of the ball : 1 m s-1 (forward)

20. Momentum Back to Momentum 3 Click Back to Before collision
Two identical balls (2 kg) are moving towards each other with the same speed 3 m s-1. After collision, one of the ball is bounced backwards with speed3 m s-1. Find the velocity of the other ball.
Before collision
After collision
+ve
By conservation of momentum,
Velocity of the ball : 3 m s-1 (forward)

21. Momentum Back to Momentum 3 Click Back to After collision
Two identical balls (2 kg) are moving towards each other with the same speed 3 m s-1. After collision, the two balls stick together.
After collision
Before collision
+ve
By conservation of momentum,
Velocity of the ball : 0 m s-1

22. Momentum Back to Momentum 3 Click Back to
Two identical balls (2 kg) stick together and are at rest initially. Some explosive is placed at the conjunction between the two balls. After explosion, One ball moves forward with a velocity 4 m s-1. Find the velocity of the other ball.
Before explosion
After explosion
+ve v
By conservation of momentum,
Velocity of the ball : 4 m s-1(backward)

23. Momentum Collisions 1 Next Slide
Daily Examples: (Newton’s colliding balls)

24. Momentum Collisions 1 Next Slide
Daily Examples: (Newton’s colliding balls)

25. Momentum Back to Collisions 1 Click Back to
Daily Examples: (Rocket is accelerating in space.)
Daily Examples: (A cannon ball is fired from a cannon.)

26. Momentum Back to Collisions 1 Click Back to
When a car collides with a fixed wall on the ground, it seems that the momentum of the car disappears.
If we view the wall with the earth as a whole object, then the car actually collides with a very large object. Conservation of momentum still holds but the motion of the wall plus the earth is so small that it can hardly be observed.

27. Momentum Impulse 1 Next Slide
We consider the collision of two balls as shown in the following figure. A B
Before collision
They are in contact for time interval t (time of contact). FB and FA are forces acting on B and A respectively when they are in contact. A B FB FA A B
After collision

28. Momentum Back to Impulse 1 Click Back to FB t = Change in momentum
Consider the average force FB and average acceleration of B during the time of contact t :
FB t = Change in momentum
We define FB t as the impulse.

29. Momentum Impulse 3 Next Slide Before Collision +ve v After Collision
A car (mass 2000 kg) is moving with a speed 20 m s-1 has an head-on collision with a lorry (mass 5000 kg) which is initially at rest. After collision the lorry moves forward with 10 m s-1. Find the velocity of the car after collision and hence find the average force acting on the car if the time of contact is 0.2 s.
Before Collision
+ve
After Collision v

30. Momentum Back to Impulse 3 Click Back to By conservation of momentum,
Consider the impulse
The minus sign of the answer indicates that the direction of the force is backwards.

31. Momentum Impulse 3 Next Slide fixed wall Before collision fixed wall
A ball (mass 2 kg) is moving towards a wall with a speed 30 m s-1 . After collision, the ball moves backwards with a speed 20 m s-1 . Assume that the ball is in contact with the wall for 0.1 s. Find the average force acting on the ball and the wall respectively.
fixed wall
Before collision
fixed wall
After collision

32. Momentum Back to Impulse 3 Click Back to
Consider the impulse acting on the ball
The force acting on the ball is 1000 N. The minus sign of the answer indicates the direction of the force is acting backwards.
The force acting on the wall by the ball is also 1000 N, which is exactly the same as the force acting on the ball by the wall (Why?).
In this case, the conservation of momentum fails since the wall is fixed. However, we can still find the force acting on the ball.

33. Momentum Back to Impulse 3 Click Back to
Daily Examples : (Bumper of a car)

34. Momentum Newton’s Third Law 1 Next slide
A person is pressing the wall.
force on
wall
roller-skater
before
after
Two persons are pulling each other.
tension

35. Momentum Newton’s Third Law 1 Next Slide A person is starting to run.
Force on
blocks
the runner
before
after
Force acting
on gas
on rocket
A rocket is moving upwards..

36. Momentum Back to Newton’s Third Law 1 Click Back to
A person is standing on the earth.
reaction
force pressing
the ground
weight
force pulling
the earth