All moving objects have what Newton called a quantity of motion.

MOMEMTUM MOMENTUM

MOMEMTUM MOMENTUM All moving objects have what Newton called a quantity of motion. What is this quantity of motion? Today we call it momentum. Momentum is a characteristic of a moving object that is related to the mass and the velocity of the object.

Momentum MOMEMTUM MOMENTUM Momentum is a property of moving matter. Momentum describes the tendency of objects to keep going in the same direction with the same speed. Changes in momentum result from forces or create forces.

Momentum MOMEMTUM MOMENTUM The momentum of a ball depends on its mass and velocity. Ball B has more momentum than ball A.

MOMEMTUM MOMENTUM Momentum vs. Inertia Inertia is another property of mass that resists changes in velocity; however, inertia depends only on mass. Inertia is a scalar quantity. ( 10 kg) Momentum is a property of moving mass that resists changes in a moving object s velocity. Momentum is a vector quantity. (10 kg x m/s east)

MOMEMTUM MOMENTUM Kinetic Energy and Momentum Kinetic energy and momentum are different quantities, even though both depend on mass and speed. Kinetic energy is a scalar quantity. Momentum is a vector, so it always depends on direction. Two balls with the same mass and speed have the same kinetic energy but opposite momentum.

MOMEMTUM MOMENTUM Momentum Ball A is 1 kg moving 1m/sec, ball B is 1kg at 3 m/sec. A 1 N force is applied to deflect the motion of each ball. What happens? Does the force deflect both balls equally? Ball B deflects much less than ball A when the same force is applied because ball B had a greater initial momentum.

MOMEMTUM Calculating Momentum The momentum of a moving object is its mass multiplied by its velocity. That means momentum increases with both mass and velocity. Momentum (kg m/sec) Mass (kg) p = m v Velocity (m/sec)

1. You are asked for momentum. 2. You are given masses and velocities. 3. Use: p = m v 4. Solve for car: p = (1,300 kg) (13.5 m/s) = 17,550 kg m/s 5. Solve for cycle: p = (350 kg) (30 m/s) = 10,500 kg m/s MOMEMTUM MOMENTUM Comparing momentum A car is traveling at a velocity of 13.5 m/sec (30 mph) north on a straight road. The mass of the car is 1,300 kg. A motorcycle passes the car at a speed of 30 m/sec (67 mph). The motorcycle (with rider) has a mass of 350 kg. Calculate and compare the momentum of the car and motorcycle. The car has more momentum even though it is going much slower.

MOMEMTUM MOMENTUM Conservation of Momentum The law of conservation of momentum states when a system of interacting objects is not influenced by outside forces (like friction), the total momentum of the system cannot change. If you throw a rock forward from a skateboard, you will move backward in response.

MOMEMTUM MOMENTUM Conservation of Momentum

MOMEMTUM MOMENTUM Collisions in One Dimension A collision occurs when two or more objects hit each other. During a collision, momentum is transferred from one object to another. Collisions can be elastic or inelastic.

MOMENTUM Calculating Conserved Momentum Remember P=mv So if it is conserved, then P i = P f Before and after all collisions the momentum remains the same if external forces do not interfere.

MOMENTUM Law of Conservation of Momentum and Collisions

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. Law of Conservation of Momentum and Collisions Motion of the cue ball Motion of the other balls

Momentum of cannon and cannonball

Conservation of Momentum 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. Velocity cannon to left is negative Velocity of cannonball to right is positive (momentums cancel each other out!)

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 http://www.walter-fendt.de/ph14e/ncradle.htm http://www.walter-fendt.de/ph14e/collision.htm B. Elastic collisions with unequal 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 http://www.walter-fendt.de/ph14e/collision.htm C. Addition of mass in inelastic collisions causes the speed of the combined masses to decrease in order for momentum to be conserved

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

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

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 b. Two moving balls collide head-on. The momentum of each ball was transferred to the other; each kept same speed in opposite direction

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

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

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 1i + m 2 v 2i = m 1 v 1f + m 2 v 2f Before collision After collision Equation for inelastic collision m 1 v 1i + m 2 v 2i = (m 1 + m 2 )v f Before collision After collision

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

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

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

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

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

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.

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.

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

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

8.5 Conservation of momentum for inelastice collisions 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? m1v1 = v2 m1 + m2 Find the speed of the two fish after the inelastic collision