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Warm-up U7-#1 1/13/14 1) What is the force felt on a 3200kg truck moving at 16 m/s which runs into a haystack bringing the truck to a stop in 25.6 seconds. Ft = m v F (25.6 s ) = 3200 kg (0-16 m/s ) F(25.6 s ) = - 51200 kgm/s F = - 2,000 N B m=3200kg v i =16m/s v f = 0m/s t=25.6s F=?

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Law of Conservation of Momentum- Momentum is neither gained nor lost in the absence of an external force momentum before = momentum after p before = p after

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BEFORE – object at rest momentum zero. AFTER – cannon and ball go in opposite directions. Momentums cancel total momentum = zero. p cannon before + p ball before = 0 p cannon after + p cball after = 0 beforeafter Collision #1 – Object at rest or Explosions

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ex 1) A 2 kg rifle shots a 0.001kg bullet at 200 m/s. What will be the recoil velocity of the rifle? G: m rifle = 2 kg m bullet = 0.001 kg v bullet = 200 m/s p before = p after p before = 0 U: v rifle = ? Eq: p after = 0 p after = (mv) bullet + (mv) rifle Sub: 0=(0.001 kg *200 m/s )+(2 kg *v rifle ) -2 kg *v rifle = 0.2 kgm/s Solve: v rifle = -0.1 m/s -

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Collision #2 - Elastic Collisions Elastic collision- When objects collide without being permanently deformed and without generating heat. Objects do not stick together! Kinetic Energy is conserved in elastic collisions. (m 1 v 1 + m 2 v 2 ) Before = (m 1 v 1 + m 2 v 2 ) after

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Ex. G: A 1000 kg car traveling at 20.0 m/s hits a 3000 kg truck at rest. If the truck is traveling 10 m/s forward after the elastic collision, what is the cars final velocity? Before: m car =1000 kg m truck =3000 kg v car =20 m/s v truck =0 After: v car = ? v truck = 10 m/s (m c v c + m t v t ) Before = (m c v c + m t v t ) after 1000 kg *20 m/s +0=1000 kg *v car +3000 kg *10 m/s 20,000 kgm/s - 30,000 kgm/s = 1000kg * v car -10,000 kgm/s = 1000kg * v car v car = -10 m/s -

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Collision #3 - Inelastic Collisions Inelastic collision- collision where the objects become distorted or generate heat. Objects stick together so the after the collision there is only one object. (m 1 v 1 + m 2 v 2 ) before = (m 1 +m 2 )(v f ) after

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Example 3: Sam, who is 85kg, jumps into a 300 kg rowboat initially at rest. His initial velocity was 5 m/s forward. What is the velocity of Sam in the boat after he lands? Before: m sam =85kg m row =300kg v sam =5m/s v row = 0 After: v f = ? (m s v s + m rb v rb ) before = (m s +m rb )(v f ) (85kg*5m/s + 0) = (300kg+85kg)v f 425kgm/s = 385kg * v f v f = 1.1 m/s

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Warm-up 1/14/14 Mike is traveling forward at 20.0 m/s in his 1000 kg car and hits Justices 1,500 kg car going slower at 8 m/s in the same direction. Justices car is traveling 15 m/s forward after the elastic collision, what is the final velocity of Mikes car? v 1i = 20 m/s GIVEN: m 1 = 1000 kg UNKNOWN: EQUATION: m 1 v 1i + m 2 v 2i = m 1 v 1f + m 2 v 2f SUBSTITUTE: SOLVE: v 2i = 8 m/s m 2 = 1500 kg v 1f = ? m/s (1000)(20) + (1500)(8) = (1000)(v 1f ) + (1500)(15) v 2f = 15 m/s v 1f = 9.5 m/s 20,000 + 12,000 = (1000)(v 1f ) + 22,500 9500 = (1000)(v 1f ) 20,000 + 12,000 – 22,500 = (1000)(v 1f ) 9500/1000 = v 1f

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Problem 1 A 40 kg child runs across a store at 4.0 m/s and jumps onto a 15 kg shopping cart initially at rest. At what speed will the shopping cart and the child move together across the store assuming negligible friction? v 1i = 4.0 m/s GIVEN: m 1 = 40 kg UNKNOWN: EQUATION: m 1 v 1i + m 2 v 2i = (m 1 + m 2 )v f SUBSTITUTE: SOLVE: V f = 2.9 m/s v 2i = 0 m/s m 2 = 15 kg v f = ? m/s What type of collision is this? (40)(4.0) + (15)(0) = (40 + 15)v f 160 + 0 = (55)v f 160 = (55)v f 160/55 = v f Inelastic

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Problem 2 Tanner throws a 0.20 kg football and knocks over a 0.90 kg vase at rest. (bad Tanner!) After the collision the football bounces straight back with a speed of 3.9 m/s while the vase is moving at 2.6 m/s in the opposite direction. How fast did Tanner throw the football? GIVEN: m 1 = 0.20 kg UNKNOWN: EQUATION: m 1 v 1i + m 2 v 2i = m 1 v 1f + m 2 v 2f SUBSTITUTE: SOLVE: v 2i = 0 m/s m 2 = 0.90 kg v 1i = ? m/s (0.20)(v 1i ) + (0.90)(0) = (0.20)(-3.9) + (0.90)(2.6) v 1f = -3.9 m/s v 2f = 2.6 m/s (0.20)(v 1i ) + 0 = (-0.78) + (2.34) (0.20)(v 1i ) = 1.56 v 1i = 1.56/0.20 v 1i = 7.8 m/s

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Problem 3 After missing an easy lay up, Whitney tosses a 0.75 kg basketball at a 1.2 kg water jug initially at rest on the sidelines. The ball is thrown to the right at 8.5 m/s and continues to move to the right at 3.0 m/s after the collision. What is the velocity of the jug after the collision? v 1i = 8.5 m/s GIVEN: m 1 = 0.75 kg UNKNOWN: EQUATION: m 1 v 1i + m 2 v 2i = m 1 v 1f + m 2 v 2f SUBSTITUTE: SOLVE: v 2i = 0 m/s m 2 = 1.2 kg v 2f = ? m/s (0.75)(8.5) + (1.2)(0) = (0.75)(3.0) + (1.2)(v 2f ) v 1f = 3.0 m/s v 2f = 3.4 m/s 6.375 + 0 = 2.25 + (1.2)(v 2f ) 6.375 – 2.25 = (1.2)(v 2f ) 4.125 = (1.2)(v 2f ) 4.125/1.2 = v 2f

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Problem 4 What is the final velocity of a 85 kg halfback rushing to the right at 10 m/s that hits a 130 kg linebacker running to the left at 8 m/s. After the elastic collision, the linebacker has slowed to 2 m/s. v 1i = 4.0 m/s GIVEN: m 1 = 85 kg UNKNOWN: EQUATION: m 1 v 1i + m 2 v 2i = (m 1 + m 2 )v f SUBSTITUTE: SOLVE: V f = 2.9 m/s v 2i = 0 m/s m 2 = 15 kg v f = ? m/s (40)(4.0) + (15)(0) = (40 + 15)v f

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1)In an experiment, a toy wooden car with a mass of 300g, initially at rest, is struck in the rear by a 30g dart traveling at 15 m/s as shown. With what speed does the car with the dart stuck in it move after the collision?

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1)A 50 kg astronaut traveling at 8 m/s to the left catches a 10 kg meteor traveling at 20 m/s to the left. What is the final velocity of the astronaut holding the meteor?

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2) In an experiment, a toy wooden car with a mass of 300g, initially at rest, is struck in the rear by a 30g dart traveling at 15 m/s as shown. With what speed does the car with the dart stuck in it move after the collision? 30g 300g 30g 300g V= 0 m/s V= 15 m/s V= ?

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3) A 50 kg astronaut traveling at 8 m/s to the left catches a 10 kg meteor traveling at 20 m/s to the left. What is the final velocity of the astronaut holding the meteor?

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Warm-up 1/14/14 Megan is traveling forward at 20.0 m/s in her 1000 kg car and hits Samanthas 1,500 kg car going slower at 8 m/s in the same direction. Sams car is traveling 15 m/s forward after the elastic collision, what is the final velocity of Megans car? v 1i = 20 m/s GIVEN: m 1 = 1000 kg UNKNOWN: EQUATION: m 1 v 1i + m 2 v 2i = m 1 v 1f + m 2 v 2f SUBSTITUTE: SOLVE: v 2i = 8 m/s m 2 = 1500 kg v 1f = ? m/s (1000)(20) + (1500)(8) = (1000)(v 1f ) + (1500)(15) v 2f = 15 m/s v 1f = 9.5 m/s 20,000 + 12,000 = (1000)(v 1f ) + 22,500 9500 = (1000)(v 1f ) 20,000 + 12,000 – 22,500 = (1000)(v 1f ) 9500/1000 = v 1f

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Warm-up 1/14/14 Mike is traveling forward at 20.0 m/s in his 1000 kg car and hits Josephs 1,500 kg car going slower at 8 m/s in the same direction. Josephs car is traveling 15 m/s forward after the elastic collision, what is the final velocity of Mikes car? v 1i = 20 m/s GIVEN: m 1 = 1000 kg UNKNOWN: EQUATION: m 1 v 1i + m 2 v 2i = m 1 v 1f + m 2 v 2f SUBSTITUTE: SOLVE: v 2i = 8 m/s m 2 = 1500 kg v 1f = ? m/s (1000)(20) + (1500)(8) = (1000)(v 1f ) + (1500)(15) v 2f = 15 m/s v 1f = 9.5 m/s 20,000 + 12,000 = (1000)(v 1f ) + 22,500 9500 = (1000)(v 1f ) 20,000 + 12,000 – 22,500 = (1000)(v 1f ) 9500/1000 = v 1f

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MOMENTUM AND COLLISIONS

MOMENTUM AND COLLISIONS

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