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Momentum, Impulse, and Collisions

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Momentum (P) A quantity that expresses the motion of a body and its resistance to slowing down. P = mv P = momentum (kg. m/s or N. s) m = mass (kg) v = velocity (m/s)

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Try it… A toy car has a mass of 5kg. If it is moving at a velocity of 5m/s, what is its momentum? 25kg·m/s What is the momentum of a 25kg boy moving at a speed of 1m/s? 25kg·m/s

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Worksheet Answers

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Project Time

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Impulse measures a change in momentum; arrived at by multiplying the average force acting on a body by the length of time it acts. Impulse = F(t) F = force (N or Newtons) t = time (s)

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Another one… An 8N force acts upon an object for 5 seconds. What impulse is given this object? 40N·s

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Impulse-momentum Theorem Force is reduced when the time interval of an impact is increased. Examples Nets or giant air mattresses used to catch people

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Putting it all together… F=ma (Newton’s 2 nd Law) a=Δv/t Insert “Δv/t” for “a” in “F=ma” This gives us “F=mΔv/t” Multiply by “t” to get- F(t) = m(v f -v i ) change in momentum Notice impulse, on the left side, is equal to the change in momentum of an object.

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Try it… A ball changes velocity from 20m/s to 30m/s. If it has a mass of 5kg, what impulse was necessary to cause this change? 50N·s How long would it take a 5N force to change the velocity of the ball? (Hint: use Impulse=F(t)) 10s

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Law of Conservation of Momentum The Law of Conservation of Momentum: The total momentum of all objects interacting with one another remains constant regardless of the nature of the forces between the objects. m 1 v 1,i + m 2 v 2,i = m 1 v 1,f + m 2 v 2,f total initial momentum = total final momentum

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Conservation of Momentum So far we only have considered the momentum of only one object at a time. Now we will look at two or more objects interacting with each other. PICTURE THIS… no momentum You are playing pool. You strike the cue ball it hits the 8 ball. The 8 ball had no momentum before they collided. loses momentum gains momentum During the collision the cue ball loses momentum and the 8 ball gains momentum. loses is the same amount that the 8 ball gained. The momentum the cue ball loses is the same amount that the 8 ball gained.

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Momentum is Conserved Newton’s third law leads to conservation of momentum During the collision, the force exerted on each bumper car causes a change in momentum for each car. The total momentum is the same before and after the collision.

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Elastic Collisions A collision in which the total momentum and the total kinetic energy are conserved is called an elastic collision. Elastic means that after a collision the objects remain separated. Two objects collide and return to their original shapes with no loss of total kinetic energy. After the collision the two objects move separately. Both the total momentum and total kinetic energy are conserved.

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Inelastic Collisions Perfectly inelastic collision A collision in which two objects stick together after colliding and move together as one mass is called a perfectly inelastic collision. Example: The collision between two football players during a tackle.

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Video time http://youtu.be/Dz5q0 KKSlf4 http://youtu.be/Dz5q0 KKSlf4 http://www.youtube.co m/watch?v=FSAR86 MMJ2w&safety_mode =true&persist_safety_ mode=1&safe=active http://www.youtube.co m/watch?v=FSAR86 MMJ2w&safety_mode =true&persist_safety_ mode=1&safe=active

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Kinetic Energy in Inelastic Collisions In an inelastic collision the total kinetic energy does not remain constant when the objects collide and stick together. Some energy is converted into sound energy and internal energy as the objects deform during the collision. Elastic in physics refers to a material that when work is done to deform the material during a collision the same amount of work is done to return the material to its original shape. Inelastic material does not return to its original shape and therefore some energy is converted to sound or heat.

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Real Collisions Most collisions are not perfectly inelastic (they don’t stick together and move as one) Most collisions are not elastic. Even nearly elastic collisions result in some decrease of kinetic energy. A football deforms when kicked A sound is produced (sound signifies a decrease in kinetic energy)

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For all intensive purposes… We will consider all collisions in which objects do not stick together to be elastic collisions. Therefore, total momentum and total kinetic energy will stay the same before and after the collision.

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There are 2 types of collisions Elastic m 1i v 1i + m 2i v 2i = m 1f v 1f + m 2f v 2f Where 1 implies object 1, 2 implies object 2 Where i implies initial & f implies final Inelastic m 1i v 1i + m 2i v 2i = m T v T Where T implies total Use + and – velocities to show direction.

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Try these… A 2kg ball strikes another ball head on at an initial velocity of +2m/s. If the second ball had a mass of 3kg and was initially moving at -1m/s, what is the final velocity of the 2kg ball if the v f of the 3kg ball is now +1.33m/s? Set it up- m 1i v 1i + m 2i v 2i = m 1f v 1f + m 2f v 2f 2kg(2m/s)+3kg(-1m/s) = 2kg(v 1f )+3kg(1.33m/s) v 1f = -1.5m/s

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Last one… A 500kg car is driving at a velocity of 10m/s. Another car (700kg) hits it from behind at a velocity of 25m/s and the two cars interlock bumpers. What is the resulting velocity of the two cars? Set it up- m 1i v 1i + m 2i v 2i = m T v T 500kg(10m/s)+700kg(25m/s) = 1,200kg(v T ) v T = 18.75 m/s

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