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Mechanics III Momentum and Impulse Physics I Honors What is Momentum? It is a vector quantity that is the product of an object’s mass and velocity. mv What Are the Units? m kg s Physics I Honors What Is Momentum? Two identical cars at different speeds…have different amounts of momentum. Two different cars are the same speed…have different amounts of momentum. Momentum relates to the size of the car and how fast it is moving. That is to say, momentum is related to the car’s mass and its velocity… Physics I Honors Large Momentum Examples – Huge ship moving at a small velocity P = mv –High velocity bullet P = mv Physics I Honors Momentum Examples • A large truck has more momentum than a car moving at the same speed because it has a greater mass. • Which is more difficult to slow down? The car or the large truck? Physics I Honors Here Are Some Thoughts… • Hitting a baseball or a golf ball requires a short period of time. • Stopping a train, a ship, or a car takes a while. • Obviously, the train or the ship have more momentum than the baseball. Physics I Honors How does the object change momentum? • Because momentum is mass x velocity, – and the mass of the object does not change, – any change in momentum means the velocity changes. = mv Physics I Honors The force that causes a change in momentum in time t, is called an impulse. • The act of hitting a baseball or a golf ball over a period of time or stopping a train or ship or car is the impulse that changes the momentum of the ball. • Force x time is the impulse. • Impulse causes a change in momentum. • It is a vector quantity whose direction is that of the force. Physics I Honors i.e. • P = mv • Δp = mΔv = m(vf – vi) • Ft = mΔv Physics I Honors Concept check • What is the change in momentum of a 2 kg ball going from 3m/s to 6m/s in the same direction? • What Impulse will cause this change? • What force will cause this change if applies for 10 ms.? Physics I Honors Conservation of Momentum Physics I Honors Newton’s Second Law • Newton’s Second Law can now be restated as the change in momentum per unit time! • A force is required to change momentum… • …the speed relates to how long (time) the force must be applied! F = ma = mv/t • So: F t = mv Physics I Honors Impulse Physics I Honors When Force is Limited • Apply a force for a long time. – Examples: • Follow through on a golf swing. • Pushing a car. F Physics I Honors t Maximize Momentum Change Apply a large force for a short time. – Examples: • Boxing • Karate F t Physics I Honors Relation of Force and Impulse • If forces come in equal and opposite pairs, what about Impulse? • If Impulses are equal what is the difference caused by a bigger mass? • Hint a 600 lb sumo wrestler and 90 lb nerd collide with equal Impulse. What difference would you observe????? Physics I Honors Conservation of Momentum (and energy?) Physics I Honors The Law of Conservation of Momentum! • Momentum cannot be created or destroyed. • The amount of momentum in the universe is constant. • This means that the total momentum in the system doesn’t change. Physics I Honors Momentum Is Conserved! • In a closed system, the amount of momentum before an event, such as a collision or explosion, is equal to the amount of momentum after the event, unless the system is acted upon by an outside force. PA + PB = PA' + PB' Physics I Honors Newton’s Third Law and Momentum! • When two objects collide Newton’s Third Law applies. • Impulses are equal in magnitude but opposite in direction. • New momentums are equal to old momentums. • Internal forces cannot cause a change in momentum. • Momentum is conserved in all collisions that occur in a closed, isolated system. Physics I Honors Momentum and Collisions Elastic Collisions – objects rebound – Momentum is conserved – Kinetic energy is conserved Inelastic Collisions – object stick together an usually become distorted and generate heat – Momentum is conserved – Kinetic energy is not conserved Physics I Honors Collisions Before v2 v1 m1 m2 v1 ' After m1 v2 ' m2 m1v1 m2 v 2 m1v'1 m2 v'2 Physics I Honors Elastic Collisions Conserve Energy and Momentum Before Collision After Collision Case 1: Equal masses Case 2: M>M Case 3: M<M Physics I Honors Inelastic Collisions • Momentum is conserved • Kinetic energy is not conserved v = 10 v=0 M M Before Collision p = Mv M After Collision p = 2Mv’ v’ = 5 M Physics I Honors What about rebound? p = p2 - p1 = -p1 - p1 p1 = -2p1 p2 = -p1 Physics I Honors quiz • 1. What is the impulse momentum theorem? • 2. A baseball of mass 0.14 kg is moving at +35 m/s. • a. Find the momentum of the baseball • b. Find the velocity at which a bowling ball, mass 7.26 kg, would have the same momentum as the baseball. Physics I Honors More quizzical • Explain the difference between elastic and inelastic collisions. • Explain the law of conservation of momentum • Explain the law of conservation of energy • What is their significance in studying collision? Physics I Honors A problem? • A 80kg student going east at 5m/s, collides with a 60kg student going west at 10m/s. After the collision , the heavier student rebounds at 3m/s. What is the speed and direction of the lighter student after the crash? Physics I Honors