Momentum is conserved for all collisions as long as external forces don’t interfere.

LAW OF CONSERVATION OF MOMENTUM In the absence of outside influences, the total amount of momentum in a system is conserved. The momentum of the cue ball is transferred to other pool balls. The momentum of the pool ball (or balls) after the collision must be equal to the momentum of the cue ball before the collision p before = p after

Whenever objects collide in the absence of external forces, the net momentum of the objects before the collision equals the net momentum of the objects after the collision. 8.5 Law of Conservation and Collisions Motion of the cue ball Motion of the other balls

Figure 8.10 Momentum of cannon and cannonball

The momentum before firing is zero. After firing, the net momentum is still zero because the momentum of the cannon is equal and opposite to the momentum of the cannonball. 8.4 Conservation of Momentum Velocity cannon to left is negative Velocity of cannonball to right is positive (momentums cancel each other out!)

8.5 Two Types of Collisions Elastic Collision: When objects collide without sticking together --Kinetic energy is conserved --No heat generated Inelastic Collision: When objects collide and deform or stick together. --Heat is generated --Kinetic energy is not conserved

Changes in Velocity Conserve Momentum A.Elastic collisions with equal massed objects show no change in speed to conserve momentum B. Elastic collisions with inequally massed objects show changes in speed to conserve momentum –Larger mass collides with smaller mass—smaller mass object’s speed is greater than the larger mass object –Smaller mass object collides with larger mass object—larger mass object’s speed is much less than the smaller mass object – C. Addition of mass in inelastic collisions causes the speed of the combined masses to decrease in order for momentum to be conserved

a.A moving ball strikes a ball at rest. 8.5 Examples of Elastic Collisions when the objects have identical masses Note: purple vector arrow represents velocity: speed and direction

a.A moving ball strikes a ball at rest. 8.5 Examples of Elastic Collisions when the objects have identical masses Momentum of the first ball was transferred to the second; velocity is identical

b.Two moving balls collide head-on. 8.5 Examples of Elastic Collisions when the objects have identical masses

b.Two moving balls collide head-on. 8.5 Examples of Elastic Collisions when the objects have identical masses The momentum of each ball was transferred to the other; each kept same speed in opposite direction

c.Two balls moving in the same direction at different speeds collide. 8.5 Examples of Elastic Collisions when the objects have identical masses

The momentum of the first was transferred to the second and the momentum of the second was transferred to the first. Speeds to conserve momentum. c.Two balls moving in the same direction at different speeds collide.

Example of an elastic collision with objects same speed but different masses What happens to the speed of the smaller car after the elastic collision with the more massive truck? Notice that the car has a positive velocity and the truck a negative velocity. What is the total momentum in this system?

Example of an elastic collision with objects same speed but different masses What happens to the speed of the smaller car after the elastic collision with the more massive truck? (the car’s speed increases to conserve momentum) Notice that the car has a positive velocity and the truck a negative velocity. What is the total momentum in this system? (40,000 kg x m/s)

8.5 Inelastic Collisions Start with less mass, end up with more mass Notice how speed changes to conserve momentum (more mass, less speed—inverse relationship!)

Calculating conservation of momentum Equation for elastic collisions m 1 v 1 + m 2 v 2 = m 1 v 1 + m 2 v 2 Equation for inelastic collision m 1 v 1 + m 2 v 2 = (m 1 + m 2 )v 2 Before collision After collision Before collision After collision

Conservation of Momentum in an elastic collision Before elastic collisionAfter elastic collision Cart A mass = 1 kg Cart B mass = 1 kg Cart A speed = 5 m/s Cart B speed = 0 m/s Cart A mass = 1 kg Cart B mass = 1 kg Cart A speed = 0 m/s Cart B speed = 5 m/s AB

Conservation of Momentum in an elastic collision Before elastic collisionAfter elastic collision Cart A mass = 1 kg Cart B mass = 1 kg Cart A speed = 5 m/s Cart B speed = -5 m/s Cart A mass = 1 kg Cart B mass = 1 kg Cart A speed = -5 m/s Cart B speed = 5 m/s 5 m/s AB

Conservation of Momentum in an elastic collision Before elastic collisionAfter elastic collision Cart A mass = 1 kg Cart B mass = 5 kg Cart A speed = 5 m/s Cart B speed = 0 m/s Cart A mass = 1 kg Cart B mass = 5 kg Cart A speed = 0 m/s Cart B speed = 1 m/s AB

Conservation of Momentum in an elastic collision Before elastic collisionAfter elastic collision Cart A mass = 6 kg Cart B mass = 1 kg Cart A speed = 10 m/s Cart B speed = 0 m/s Cart A mass = 6 kg Cart B mass = 1 kg Cart A speed = 2 m/s Cart B speed = 48 m/s AB

Conservation of Momentum in an inelastic collision Big fish mass = 4 kg Small fish mass = 1 kg Small fish speed = 5 m/s Large fish speed = 0 m/s Before inelastic collision Big fish mass + Small fish mass = Small fish + Large fish speed = After inelastic collision 5 kg 1 m/s m1v1 = v2 m1 + m2

think! One glider is loaded so it has three times the mass of another glider. The loaded glider is initially at rest. The unloaded glider collides with the loaded glider and the two gliders stick together. Describe the motion of the gliders after the collision. 8.5 Collisions

think! One glider is loaded so it has three times the mass of another glider. The loaded glider is initially at rest. The unloaded glider collides with the loaded glider and the two gliders stick together. Describe the motion of the gliders after the collision. Answer: The mass of the stuck-together gliders is four times that of the unloaded glider. The velocity of the stuck-together gliders is one fourth of the unloaded glider’s velocity before collision. This velocity is in the same direction as before, since the direction as well as the amount of momentum is conserved. 8.5 Collisions

1.Conservation of Momentum in an elastic collision m1v1 = v2 m2 Before elastic collision After elastic collision Cart A mass = 1 kg Cart B mass = 5 kg Cart A speed = 5 m/s Cart B speed = 0 m/s Cart A mass = 1 kg Cart B mass = 5 kg Cart A speed = 0 m/s Find Cart B speed AB

2.Conservation of Momentum in an elastic collision m1v1 = v2 m2 Before elastic collision After elastic collision Cart A mass = 5 kg Cart B mass = 2 kg Cart A speed = 10 m/s Cart B speed = 0 m/s Cart A mass = 5 kg Cart B mass = 2 kg Cart A speed = 0 m/s Find Cart B speed AB

Consider a 6-kg fish that swims toward and swallows a 2-kg fish that is at rest. If the larger fish swims at 1 m/s, what is its velocity immediately after lunch? 8.5 Conservation of momentum for inelastice collisions m1v1 = v2 m1 + m2 Find the speed of the two fish after the inelastic collision