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Momentum and Impulse Chapter 6 Section 1

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Linear Momentum Momentum can describe the motion of an object before and after a collision takes place. Momentum can describe the motion of an object before and after a collision takes place. –Examples: Bowling ball and the Pins Bowling ball and the Pins Automobile Accident Automobile Accident Sports Sports Rockets Rockets Etc… (Basically anything that has movement) Etc… (Basically anything that has movement)

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Inertia and Momentum Inertia is the tendency for an object to resist change Inertia is the tendency for an object to resist change –Object at rest, stays at rest –Object in motion, stays in motion Momentum is the tendency for an object to stay in motion Momentum is the tendency for an object to stay in motion Momentum = Inertia in motion Momentum = Inertia in motion

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Momentum Momentum – A vector quantity that is the product of an objects mass and its velocity. Momentum – A vector quantity that is the product of an objects mass and its velocity.

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Momentum Equation p = mv p = Momentum (lower case letter p) p = Momentum (lower case letter p) m = Mass m = Mass v = Velocity v = Velocity The symbol p comes from the word progress, which is defined as The quantity of motion with which a body proceed in a certain direction. The symbol p comes from the word progress, which is defined as The quantity of motion with which a body proceed in a certain direction.

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SI Units For Momentum p = mv Momentum = mass x velocity Momentum = mass x velocity = (kg)(m/s) = (kg)(m/s) =kgm/s =kgm/s SI units for Momentum – kgm/s SI units for Momentum – kgm/s There is no short way around the units for momentum. There is no short way around the units for momentum.

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Momentum as a Vector The direction of momentum is in the same direction as the velocity of the object. The direction of momentum is in the same direction as the velocity of the object.

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Momentum & Velocity An object that has no velocity (v=0 m/s) has no momentum. An object that has no velocity (v=0 m/s) has no momentum. An object that picks up speed, picks up momentum. An object that picks up speed, picks up momentum. –The more momentum an object has, the harder it is to make the object stop. An object that slows down, loses momentum. An object that slows down, loses momentum. –The less momentum an object has, the easier it is to make the object stop. Momentum is directly proportional to the velocity. Momentum is directly proportional to the velocity.

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Momentum of Different Objects Can two different objects have the same momentum, such as a Mack truck and a roller skate? Can two different objects have the same momentum, such as a Mack truck and a roller skate?

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Momentum of Different Objects Sure they can! Sure they can! In order for both to have the same momentum, the Mack truck would have to be moving really slow and the roller skate would have to be moving really fast in order for both objects to achieve the same momentum. In order for both to have the same momentum, the Mack truck would have to be moving really slow and the roller skate would have to be moving really fast in order for both objects to achieve the same momentum. Mack Truck = Roller Skate Mack Truck = Roller Skate m v = m v

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Momentum and Mass Even objects with small masses can have a lot of momentum, as long as the velocity is very large. Even objects with small masses can have a lot of momentum, as long as the velocity is very large. –Bullets –Hailstones –Hammer –Etc…

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Example Problem An astronaut with a mass of 45 kg wears a 32 kg suit and moves at 5.7 m/s on the moon. What is the total momentum of the astronaut and the suit? An astronaut with a mass of 45 kg wears a 32 kg suit and moves at 5.7 m/s on the moon. What is the total momentum of the astronaut and the suit?

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Example Problem Answer p = mv p = mv = (77kg)(5.7m/s) = (77kg)(5.7m/s) = 440 kgm/s = 440 kgm/s p = 440 kgm/s p = 440 kgm/s

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Changing Momentum Takes a Force Catching a baseball thrown very fast might sting the hand. Catching a baseball thrown very fast might sting the hand. Catching a slow-moving baseball causes no discomfort when it is caught. Catching a slow-moving baseball causes no discomfort when it is caught. When catching a ball, the velocity changes to zero once it is caught. When catching a ball, the velocity changes to zero once it is caught. –Change in velocity is an acceleration and if there is acceleration, then there must be a force present.

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Force and Momentum Momentum is closely related to force. Momentum is closely related to force. In fact, Newton wrote his Second Law of Motion mathematically, he wrote it not as F=ma, but in the following form: In fact, Newton wrote his Second Law of Motion mathematically, he wrote it not as F=ma, but in the following form: F = Δp/Δt Force = Change in momentum ÷ time interval

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Impulse-Momentum Theorem FΔt = Δp F = Force F = Force Δt = Time interval Δt = Time interval Δp = Change in momentum Δp = Change in momentum

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Impulse-Momentum Theorem Explained The derived version of the equation. Ft = Δp Ft = mΔv Ft = m( v f – v i )

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Impulse Impulse – For a constant external force, the product of the force and the time over which it acts on an object. Impulse – For a constant external force, the product of the force and the time over which it acts on an object. A large force will cause a change in an objects momentum in a short time, but a small force will take a much longer time to cause the same change in momentum. A large force will cause a change in an objects momentum in a short time, but a small force will take a much longer time to cause the same change in momentum.

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Everyday Use of The Theorem With out thinking, you use this theorem in everyday activities. What are some of these activities? With out thinking, you use this theorem in everyday activities. What are some of these activities?

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Example Problem A 1400 kg car moving with a velocity of 15m/s due east collides with a utility pole and is brought to rest in 0.30 seconds. Find the magnitude of the force exerted on the car during the collision. A 1400 kg car moving with a velocity of 15m/s due east collides with a utility pole and is brought to rest in 0.30 seconds. Find the magnitude of the force exerted on the car during the collision.

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Example Problem Answer 70,000 N to the west 70,000 N to the west Page 211 – Sample Problem 6B Page 211 – Sample Problem 6B

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Impulse For Stopping Times and Distances The impulse momentum theorem is the formula used by engineers and accident investigators. The impulse momentum theorem is the formula used by engineers and accident investigators. Larger mass objects have larger momentums, therefore it takes longer for a larger mass object to stop then a small mass. Larger mass objects have larger momentums, therefore it takes longer for a larger mass object to stop then a small mass. This directly affects the distance. This directly affects the distance. –Must use the kinematic equations

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Example Problem If the maximum coefficient of kinetic friction between a 2300kg car and a road is 0.50, what is the minimum stopping distance for a car moving at 29m/s? If the maximum coefficient of kinetic friction between a 2300kg car and a road is 0.50, what is the minimum stopping distance for a car moving at 29m/s?

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Example Problem Answer 86 meters 86 meters

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More Time = Less Force A change in momentum over a longer time will require less force. A change in momentum over a longer time will require less force. This idea is used in all kinds of safety equipment. This idea is used in all kinds of safety equipment.

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Falling Egg Whether your playing a game of egg toss or accidently dropped an egg. In order to keep the egg from breaking, the time of impact must be increased. Whether your playing a game of egg toss or accidently dropped an egg. In order to keep the egg from breaking, the time of impact must be increased. Why? Why?

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