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Momentum and Impulse

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What is Momentum? Momentum – The product of the mass and velocity of an object. Has magnitude and direction. Momentum = p = mv P = momentum M = mass V = velocity Units: kg∙m/s

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Inertia? Remember Newton’s 1 st Law? An object at rest will stay at rest and An object in motion will stay in motion in the same speed and direction unless acted on by an outside force.

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What’s Inertia Got to Do with It? Momentum is directly related to the second part of Newton’s 1 st Law –An object in motion stays in motion (same speed and direction) unless acted on by a force

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Let’s practice A 1200 kg car drives west at 25 m/s for 3 hours. What is the car’s momentum? Identify the variables: –1200 kg = mass –25m/s, west = velocity –3 hours = time P = mv = 1200 x 25 = 30000 kg m/s, west

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How hard is it to stop a moving object? Impulse: Product of force and time interval during which the force acts. Impulse equals momentum change. Impulse = FΔt F = force (N) Δt = time elapsed (s) Units: N∙s

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How hard is it to stop a moving object? Using Newton’s 2 nd Law we get Impulse = change in momentum FΔt= mΔv

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Why does an egg break or not break? An egg dropped on a tile floor breaks, but an egg dropped on a pillow does not. Why? FΔt= mΔv In both cases, m and Δv are the same. If Δt goes up, what happens to F, the force? Right! Force goes down. When dropped on a pillow, the egg starts to slow down as soon as it touches it. A pillow increases the time the egg takes to stops.

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Practice Problem A 57 gram tennis ball falls on a tile floor. The ball changes velocity from -1.2 m/s to +1.2 m/s in 0.02 s. What is the average force on the ball? Identify the variables: Mass = 57 g = 0.057 kg Δvelocity = +1.2 – (-1.2) = 2.4 m/s Time = 0.02 s using FΔt= mΔv F x (0.02 s) = (0.057 kg)(2.4 m/s) F= 6.8 N

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Car Crash Would you rather be in a head on collision with an identical car, traveling at the same speed as you, or a brick wall? Assume in both situations you come to a complete stop. Take a guess http://techdigestuk.typepad.com/photos/uncategorized/car_crash.JPG

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Car Crash (cont.) The answer is… It Does Not Matter! Look at FΔt= mΔv In both situations, Δt, m, and Δv are the same! The time it takes you to stop depends on your car, m is the mass of your car, and Δv depends on how fast you were initially traveling.

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Conservation of Momentum

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Just like energy, momentum is conserved. The total momentum at the start will equal the total momentum at the end

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Vectors! Remember that momentum is a vector value, so if two momentums are in opposite directions, they are opposite signs and end up cancelling (at least in part)

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Two Flavors!! Collisions may be –Elastic – the objects completely bounce off each other Billiards (pool) ball have elastic collisions –Inelastic – the objects stick together at the collision and travel together thereafter Car Crashes have become inelastic with better engineering

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Momentum Formulas The standard formula for momentum is P=mv What happens if we have two objects that collide and bounce off each other…..elastic?? We can make a formula for this due to the conservation of momentum! M 1 V 1i + M 2 V 2i = M 1 V 1f + M 2 V 2f

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Practice Elastic A 50 kg skater traveling at 10 m/s hits a 40 kg skater sitting still, imparting all his momentum into the 2 nd skater. What is the velocity of the 2 nd skater? M 1 V 1i + M 2 V 2i = M 1 V 1f + M 2 V 2f (50 kg)(10 m/s) + (40 kg)(0 m/s) = (50 kg)(0 m/s) + (40 kg)V 2f (500 kg*m/s) + (0 kg*m/s) = (0 kg*m/s) + (40 kg)V 2f 12.5 m/s = V 2f

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Practice Problem A 50 kg skater traveling at 10 m/s hits a 40 kg skater sitting still. The 1 st skater ends up at 2 m/s. What is the velocity of the 2 nd skater? M 1 V 1i + M 2 V 2i = M 1 V 1f + M 2 V 2f ( 50 kg)(10 m/s) + (40 kg)(0 m/s) = (50 kg)(2 m/s) + (40 kg)V 2f (500 kg*m/s) + (0 kg*m/s) = (100 kg*m/s) + (40 kg)V 2f 10 m/s = V 2f

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Practice Problem A 50 kg skater traveling at 20 m/s hits a 40 kg skater moving in the same direction at 3 m/s. The 1 st skater ends up at 5 m/s. What is the velocity of the 2 nd skater? M 1 V 1i + M 2 V 2i = M 1 V 1f + M 2 V 2f (50 kg)(20 m/s) + (40 kg)(3 m/s) = (50 kg)(5 m/s) + (40 kg)V 2f (1000 kg*m/s) + (120 kg*m/s) = (125 kg*m/s) + (40 kg)V 2f 24.875 m/s = V 2f

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Inelastic Collision Formula Since the objects travel together after the collision, we have a slightly different formula for inelastic collisions M 1 V 1i + M 2 V 2i = (M 1 + M 2 )V f This shows the final momentum is created by the total mass of the two objects together

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Practice Inelastic A 50 kg skater traveling at 20 m/s picks up a 40 kg passenger skating sitting still, what is the velocity of the two skaters? M 1 V 1i + M 2 V 2i = (M 1 + M 2 )V f (50 kg)(20 m/s) + (40 kg)(0 m/s) = (90 kg)V f (1000 kg*m/s) + (0 kg*m/s) = (90 kg)V f 11.1 m/s = V f

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Practice Problem A 50 kg skater traveling at 20 m/s picks up a 40 kg passenger skating in the same direction at 5 m/s, what is the velocity of the two skaters? M 1 V 1i + M 2 V 2i = (M 1 + M 2 )V f (50 kg)(20 m/s) + (40 kg)(5 m/s) = (90 kg)V f (1000 kg*m/s) + (200 kg*m/s) = (90 kg)V f 13.3 m/s = V f

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Practice Problem A 50 kg skater traveling at 20 m/s picks up a 40 kg passenger skating in the opposite direction at 5 m/s, what is the velocity of the two skaters? M 1 V 1i + M 2 V 2i = (M 1 + M 2 )V f (50 kg)(20 m/s) + (40 kg)(-5 m/s) = (90 kg)V f (1000 kg*m/s) - (200 kg*m/s) = (90 kg)V f 8.89 m/s = V f

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