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Take out tables. On a separate sheet: Make a list of every equation we’ve already used in this class that has the velocity term in it.

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Here is your choice: a. I toss a bullet at you. b. I shoot a bullet at you from a gun. Which is more dangerous to you? Why?

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Linear Momentum & Impulse

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Linear Momentum = mass in motion A measure of how hard it is to stop an object. It is like a quantity of motion. How is it different from inertia?

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Momentum (p) depends on: mass & velocity of object. p = mv m in kg v in m/s Units are … kg mno name. s

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Momentum is a Vector Quantity Same direction as velocity All Energy KE too is a scalar

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Ex 1. A 2250 kg pickup truck has v = 25 m/s east. What is the truck’s momentum? p = mv= (2250 kg)(25 m/s) = 5.6 x 10 4 kg m s

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Change in momentum - accl occurs any time an object changes velocity (speed or direction).

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Momentum Change & Newton’s 2 nd Law F = ma F = m( v/ t) F t =m vm (v f - v i ) for const mass. F t = p Impulse. p = Change in momentum

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Equations of Momentum Change J =F t = p Impulse = change momentum. p f – p i. p = mv f – mv i for velocity change with constant mass can factor out mass you can write, m (v f - v i ) or m v.

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Force is required to change velocity or momentum of a body in motion. Force must be in contact for some time.

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Increased force & contact time on object give greatest impulse p = m v.

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Hit a homerun needs large impulse. The more contact time, the less force needed to give same impulse p.

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Impulse (J) is the momentum change. It has the same units. kg mor Ns s It is like force but includes a contact time component!

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Ex 2. How long does it take an upward 100N force acting on a 50 kg rocket to increase its speed from 100 to 150 m/s?

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F = 100 N v = 50 m/s m = 50 kg Ft = m v t = m v F 50 kg(50 m/s) 100 kg m/s 2 = 25 s.

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Concept: A pitcher throws a fastball to a catcher. Who exerts a larger force on the ball? Explain.

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Concept: Explain, in terms of impulse and momentum, how airbags help avoid injury in a car crash.

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Examples of Impulse/ Change in Momentum Baseball batter swinging through ball. Applying brakes of car over time to stop.

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Ex 3. How long does it take a 250 N force to increase to speed of a 100 kg rocket from 10 m/s to 200 m/s?

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Ft = m vt = m v F F = 250 N m= 100 kg v =190 m/s t = 100kg(190m/s) 250 kg m/s 2. = 76 s.

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Ex 4. The speed of a 1200 kg car increases from 5 to 29 m/s in 12 s. What force accelerated the car?

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Ex 5: A 0.4 kg ball is thrown against a wall with a velocity of 15 m/s. If it rebounds with a velocity of 12 m/s: a) what was its v? b) What was its p?

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v = v f – v i. -12 m/s – (15 m/s) = - 27 m/s. p = m v = 0.4kg(27m/s) =10.8 kg m/s

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Running with momentum. 15 min. https://www.youtube.com/watch?v=jLIyDf kQcskhttps://www.youtube.com/watch?v=jLIyDf kQcsk Relaxing with impulse.13 minutes. https://www.youtube.com/watch?v=0nOHL Thv2mwhttps://www.youtube.com/watch?v=0nOHL Thv2mw

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Understanding Car Crashes 22 min start 8:53 Hewitt Momentum 4:20 https://www.youtube.com/watch?v=2Fwhj UuzUDghttps://www.youtube.com/watch?v=2Fwhj UuzUDg http://www.youtube.com/watch?v=yUpiV2I_IRI

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Hwk read text 208 – 211 do pg 214 #1- 4 concepts do p 211 #1 - 4. Impulse prbs. Also worksheet “Impulse Momentum”

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Which are units of Impulse? Nm N/s Ns N/m A ball mass 0.10 kg is dropped from 12-m. Its momentum just as it strikes the ground is: 1.5 kgm/s 1.8 kgm/s 2.4 kgm/s 4.8 kgm/s

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A 0.060-kg tennis ball, initially moving at 12 m/s, is struck by a racquet causing it to move in the opposite direction at a speed of 18 m/s. What is the impulse exerted by the racquet on the ball? 0.36 kgm/s 0.72 kgm/s 1.1 kgm/s 1.8 kgm/s

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Graphs

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Constant force f - t graph: p /Impulse is area under curve F t. Force N

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Non-Constant Force Force vs. time graph. The area under the curve = impulse or p change in momentum. What is the impulse during the 9 seconds of contact? 225 Ns

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Consv Momentum Demos.

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Conservation of Momentum If no external force acts on a closed system, the total momentum remains unchanged even if objects interact.

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What is a system? Two or more objects that interact in motion. One may transfer part or all of its momentum to the other(s). Common examples: collisions, explosions.

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One Ball transfers all its momentum.

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The astronaut transfers part of his momentum to the second astronaut.

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Conservation of Momentum Calc’s Total momentum before = total after interactions. Collisions. Explosions Pushing apart.

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P before = p after m 1 v 1 + m 2 v 2 = m 1f v 1f + m 2f v 2f v 1 and v 2 velocities for objects one and two. m 1 and m 2 masses of objects To Calculate:

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Recoil From Explosions

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Recoil illustrates conservation of momentum where initial and final momentum = 0. 0 = p 1 + p 2.

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1. The cannon is 100kg and the cannonball is 5 kg. If the ball leaves the cannon with a speed of 100 m/s, find the recoil velocity of the cannon.

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Before FiringAfter Firing m 1 v 1 + m 2 v 2 = m 1f v 1f + m 2f v 2f 0 = (100kg)v cf + (5kg)(100m/s) -500 kgm/s = (100 kg) v cf - 5 m/s = v cf recoil velocity of cannon

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Extra Example – not on sheet A 63-kg astronaut is in spacewalk when the tether breaks. The astronaut throws a 10-kg oxygen tank directly away from the spaceship at 12 m/s. Assuming the astronaut was initially at rest, what is his final speed after throwing the tank? 1.9 m/s

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Hwk. Read text p 215-218. Do pg 221 #2, and pg 233 #17, 19, 20, 24, 25.

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Recoil Hewitt 6:25 https://www.youtube.com/watch?v=1-s8NZ8xKW0

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Let’s say a 4 kg fish swimming at 5 m/s, eats a 1 kg fish. What is their final velocity? Stick em together problems

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Bg fishsm.fish Bg fish sm.fish m 1 v 1 + m 2 v 2 = m 1f v 1f + m 2f v 2f (4kg)(5m/s)+(1 kg)0 =(4kg)v 1 +(1kg)v 2 But the final velocities are equal so factor out the v f : 20 kg m/s = v f (4+1kg) v f = (20 kg m/s) / (5kg) = 4m/s

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Fish lunch Hewitt 4:00 https://www.youtube.com/watch?v= MK0B5hEU7OI

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Find the final velocity of the cart and brick together 2. A 2 kg brick is dropped on a 3 kg cart moving at 5.0 m/s.

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cartbrickcartbrick m 1 v 1 + m 2 v 2 = m 1f v 1f + m 2f v 2f (3kg)(5.0m/s) + 0 = (3kg)v 1 + (2kg)v 2 150 kg m/s = v (3kg + 2 kg) (150 kg m/s )/5 kg = 3.0 m/s

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Elastic & Inelastic Collisions Totally Elastic: no KE lost at all (to heat, light, sound etc.) Usu. Involves objects that don’t make contact or bounce off. Totally Inelastic: involves greatest loss of KE. Usu damage done. Most extreme case – objects stick together.

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Which is totally elastic? Inelastic?

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Inelastic Collision m c = 1000 kg m t = 3000 kg v c = 20 m/s v t =0 p c = p t =

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m 1 v 1 + m 2 v 2 = m 1f v 1f + m 2f v 2f ( 1000kg)(20m/s) + 0 = (1000)v + (3000)v ( 20000 kg m/s) = (1000kg + 3000kg)v ( 20000 kg m/s) = (4000 kg)v ( 20000 kg m/s) = v 4000 kg v = 5 m/s

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Elastic Collision m c = 1000 kg m t = 3000 kg v c = 20 m/s v t =0 Find final velocity of the car if truck has final velocity of 10 m/s.

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m 1 v 1 + m 2 v 2 = m 1f v 1f + m 2f v 2f (1000kg)(20m/s) + 0 = (1000kg)v c +(3000kg)(10m/s) 20,000 kg m/s = (1000kg)v c +30000 kg m/s 20,000 kg m/s – 30,000 kg m/s = v c (1000kg) - 10 m/s = v c

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Do Now: On July 4 th my family likes to shoot off fireworks. One rocket was shot straight up, climbed to a height 18-m and exploded into hundreds of pieces in all directions at its highest point. Thinking about conservation laws, think about the rocket at its highest point just before & just after it explodes: How does the rocket’s momentum compare before & after the explosion? How does its KE compare compare before & after the explosion?

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Inelastic Collisions Stick em together KE “lost” converted Elastic Collisions – no KE lost. Bounce off each other. Pg 233 #17, 19, 20, recoil prbs24, 25. Sentences, equations, show work w/units.

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In class pg 221 #1 write out and hand in to be graded. and do pg 219 #1 – 4 calcs

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Film Car Crashes or Running with momentum. http://www.youtube.com/watch?v=yUpiV2I_IRI

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