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

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

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

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

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

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) :

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

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

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

END of Momentum

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

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.

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

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

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

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.

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.

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.

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)

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)

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

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)

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

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

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.)

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.

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

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.

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

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.

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

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.

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

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

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..

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