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Momentum and Impulse

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Momentum: A measure of how difficult it is to stop a moving object. Momentum = mass x velocity p = mv Unit for momentum:

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Comparing momentum and kinetic energy p = mv # 1 If the velocity triples, by what factor will the momentum change? K = ½ mv 2 # 2 If the velocity triples, by what factor will the kinetic energy change?

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Question # 3 Momentum = m∙v Can a bullet have the same momentum as an Army tank? Answer: Y- yes N- no

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Question # 4 If the boulder and the boy have the same momentum, will the boulder crush the boy? (Hint: Which would have the larger speed?) Answer Y-yesN- No

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Problem Examples What is the momentum of a 1500 kg race car moving at 24 m/s ? p car = m∙v p = 1500 kg x 24 m/s p = 36,000 kg∙m/s How fast would a 2 kg cat have to be moving to have the same momentum as the race car? p cat = m∙v = kg∙m/s v = kg∙m/s ÷ 2 kg v = 18,000 m/s!!!

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Now, your turn… # 5 What is the momentum of a 10,000 kg locomotive moving at 2 m/s? # 6 How fast would a 500 kg VW bug have to be moving to have the same momentum as the locomotive?

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Momentum of a system of objects Momentum is a vector and therefore has both magnitude and direction. If two objects are moving in opposite direction, then one direction must be chosen as negative and the other as positive before determining the momentum of the system. What is the momentum of this two-object system, taking “right” to be the positive direction?

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Question # 7 A 4 kg object moves to the right at 8 m/s. A 12 kg object approaches it, moving to the left at 4 m/s. Taking “right” to be the positive direction, what is the momentum of the two-object system?

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How do you change the momentum of an object? PUSH on it for a period of TIME. Impulse: the product of the force exerted on an object and the time interval during which it acts. Impulse = Force x time Impulse = F∙t

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# 8 A truck that crashes into a wall experiences a force of 20,000 N. If the truck comes to a stop in 3 seconds, how much impulse was imparted to the truck?

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The same change in momentum may be the result of a SMALL force exerted for a LONG time, or a LARGE force exerted for a SHORT time.

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Whether you drop an egg on the floor or on a pillow, it loses all of its momentum. The same impulse is applied in either case, but the stopping time is so much less for the floor, the force is proportionally greater. Impulse = Force x time

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The impulse given to an object is equal to the change in momentum of the object. Impulse = change in momentum Impulse = F∙t Change in momentum = mv = mv f – mv o Therefore: F∙t = mv = mv f – mv o Impulse Change in momentum

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Question # 9 A boy pushed on a 8 kg crate at rest with a net force of 20 N for 4 seconds. How fast was the crate moving afterwards? F∙t = mv = mv f – mv o F∙t = mv f

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Question #10 A boy pushed on a 8 kg crate initially moving at 2 m/s with a net force of 20 N for 4 seconds. How fast was the crate moving afterwards? Ft = mv = mv f – mv o Ft + mv o = mv f

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Conservation of Momentum

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System- a collection of objects that is being observed. Closed system- no objects enter or leave the system Isolated system- no external forces act on any object in the system. The objects can exert forces on one another. In a closed, isolated system, the total momentum will remain the same- it will be CONSERVED.

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= Recoil = Conservation of Momentum Momentum Before = Momentum After = After firing, the equal but opposite momenta cancel. Is this a closed, isolated system? Momentum before = momentum after

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Recoil m 1 v 1 = m 2 v 2 A 0.01 kg bullet is fired at a speed of 350 m/s. What is the recoil speed of the 3.0 kg rifle? m bullet v bullet = m rifle v rifle V rifle = 0.01kg x 350 m/s / 3.0 kg V rifle = 1.17 m/s

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Recoil is an application of Newton’s Third Law: For every force there is an equal, but opposite force

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Conservation of Momentum in Collisions Elastic collision- A collision in which objects collide and bounce off each other with no energy loss. (occurs very rarely) Inelastic collision- A collision in which objects collide and some of the kinetic energy is transformed into heat energy. (almost all collisions) Completely inelastic collision- the objects stick together after the collision- will result in the maximum kinetic energy loss- in fact, sometimes ALL kinetic energy is lost if the objects stop completely.

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Momentum before= momentum after m 1 v 1 =(m 1 + m 2 ) v Momentum after a completely inelastic collision

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m 1 v 1o = m 2 v 2f m 1 v 1o - m 2 v 2o = - m 1 v 1f + m 2 v 2f m 1 v 1o + m 2 v 2o = m 1 v 1f + m 2 v 2f Three Examples of conservation of momentum in collisions with equations:

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Conservation of momentum Recoil: m 1 v 1 = m 2 v 2 Completely (totally) Inelastic collisions: m 1 v o + m 2 v o = (m 1 + m 2 )v f Other collisions m 1 v o + m 2 v o = m 1 v f + m 2 v f

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