# Momentum and Impulse. What is Momentum? Momentum – The product of the mass and velocity of an object. Has magnitude and direction. Momentum = p = mv P.

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Momentum and Impulse

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

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.

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

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

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

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

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.

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

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

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.

Conservation of Momentum

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

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)

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

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

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

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

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

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

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

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

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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