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Physics Teacher Notes - Grothaus Chapter 8 – Momentum Title: Momentum *** Momentum is conserved for all collisions as long as external forces don’t interfere *** 8.1 Momentum Which is more difficult to stop: small car or big truck Truck has more momentum than the car. WHY? Momentum is merely inertia in motion or “mass in motion” Momentum = mass x speed (p = mv) When direction doesn’t matter we can use speed: mass x speed = mv A moving object can have a large momentum if it has a large mass, a high speed, or both. Large truck vs. roller skate? Does a stationary object have momentum? No, it has inertia, but no momentum (zero velocity) What happens when you double the speed? Double the mass? 8.2 Impulse Changes Momentum If momentum changes, either mass or velocity changes If the mass stays the same, then it is the velocity that changes. What happens when velocity changes??? What causes acceleration? Force! The greater the force, the greater its change in velocity and the greater its change in momentum Remember Newton’s second law: Conceptual Physics Page 1 of 7 Chapter 8 – Momentum Physics Teacher Notes - Grothaus F = ma or Newton wrote it as F m If we multiply both sides by t, we get v t Ft mv Impulse: The change in momentum depends on the force that acts and the length of time it acts. Figure 8.2: pushing a car – brief push vs. push for long time Both time and force are important in changing an object’s momentum force x time interval is called impulse impulse = Ft The greater the impulse exerted on something, the greater will be the change in momentum Impulse = change in momentum Or 𝐹𝐹 = ∆(𝐹𝐹) Increasing Momentum What’s the best way to increase momentum of an object? Baseball player, golfer, As much force as possible, for as long as possible “follow through” Examples: pulling a bow all the way back, long cannon barrel, long range rifle Other examples? Decreasing Momentum Conceptual Physics Page 2 of 7 Physics Teacher Notes - Grothaus Chapter 8 – Momentum In a car that’s out of control, hit haystack or brick wall? Carpet vs. hard floor; pillow or brick Throw a glass or an egg? Wall vs. haystack: momentum is decreased by same impulse Product of force and time Contact time – the time during which your momentum is brought to zero Haystack – small force, but long contact time Wall – big force, but short contact time Figures on p. 127 A longer contact time reduces the amount of force and decreases the resulting deceleration If time is extended 100 times, the force of impact is reduced 100 times When we want the force small, extend the time Ex. Airbags, padded floors for gymnasts, pulling back when catching a ball Other examples? Bungee Jumping – p. 128 Jump down from a chair – bending knees can extend the time by 10 to 20 times Boxer p. 128 Dish on carpet or floor? Why? Egg in a sheet activity Parkour fall tutorial http://www.youtube.com/watch?v=RgPd29MlHpg 8.3 Bouncing If a flower pot falls onto your head and breaks – ouch If a flower pot falls and then bounces – bigger ouch Conceptual Physics Page 3 of 7 Physics Teacher Notes - Grothaus Chapter 8 – Momentum The impulse required to bring an object to a stop and then to “throw it back again” is greater than the impulse required merely to bring the object to a stop Think about if you catch it – impulse to bring momentum to zero Then throw it – have to provide more impulse This is provided by your hand Above example, it’s provided by your head! Gold rush – paddle wheels (Lester A. Pelton) Breaking bricks – science project https://www.youtube.com/watch?v=aPNCNFeDJIw Science of breaking bricks https://www.youtube.com/watch?v=A4Qpu3M4aO8 Slo mo https://www.youtube.com/watch?v=OwKO2PSphls 35 bricks https://www.youtube.com/watch?v=5sFYgt-rkNk 8.4 Conservation of Momentum Newton’s second law – a net force must be applied to an object for it to accelerate (change in velocity) Same thing – but different language: an impulse must be applied to an object for there to be a change in momentum Conceptual Physics Page 4 of 7 Physics Teacher Notes - Grothaus Chapter 8 – Momentum (remember that a change in velocity results in a change in momentum and vice versa) The force or the impulse has to be external, not internal Dash board, molecular forces within baseball, etc Cannon: 3rd law – force of cannonball is equal and opposite to the forced causing the recoil of the cannon This is internal to the system so the net force is still zero Net momentum is also still zero Figure 8.10, p. 131 Momentum is a vector quantity– magnitude and direction p = mv velocity has direction and the momentum is in the same direction as the velocity If in opposite directions, will be different signs and can cancel each other out Cannon/cannonball – the net momentum of the system is still zero The Law of Conservation of Momentum – momentum of a system The law of conservation of momentum states that, in the absence of an external force, the momentum of a system remains unchanged. (always conserved if make the system big enough – cannon/cannonball, etc.) Newton’s Third Law Fundamental! 8.5 Collisions Conservation of Momentum Whenever objects collide in the absence of external forces, the net momentum of both objects before the collision equals the net momentum of both objects after the collision. net momentum before = net momentum after Conceptual Physics Page 5 of 7 Physics Teacher Notes - Grothaus Chapter 8 – Momentum Elastic collisions (bouncy): Billiard balls / golf balls When objects collide without being permanently deformed and without generating heat, the collision is said to be an elastic collision. Figure 8.11 p. 132 Inelastic Collisions (sticky): A collision in which the colliding objects become distorted and generate heat during the collision is an inelastic collision. Head on car crash is one example When two things collide and get tangled or coupled together, it’s a totally inelastic collision. (even though there’s no damage, they are now considered one unit and their original form has changed) Figure 8.12 p. 133 Still conservation of momentum -- just momentum is shared between both objects Problems: Remember the following: Change in momentum = Impulse 𝐹𝐹 = ∆(𝐹𝐹) also: Conceptual Physics Page 6 of 7 Physics Teacher Notes - Grothaus Chapter 8 – Momentum (netmv)before = (netmv)after If there are two objects before that combine to one object after, the following happens: m1v1 m2 v2 (m1 m2 )vafter There is usually some external force like friction or gravity so you want to look at the momentum right before and right after the collision occurs 2 colliding trucks, momentum is same before and right after – friction provides an impulse that will reduce momentum afterward Billiard balls, etc. Later, we’ll discuss kinetic energy (energy of moving things). Momentum is conserved, but in an inelastic collision, kinetic energy is lost to sound, heat, damage, etc. In an elastic collision, almost all kinetic energy is conserved. Perfectly elastic collisions are rare, some loss of energy usually occurs. This is different at the microscopic level. Conceptual Physics Page 7 of 7