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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 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? 25N·s What is the momentum of a 25kg boy moving at a speed of 1m/s? 25N·s

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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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Impulse

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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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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 ) 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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The Law of Conservation of Momentum In an isolated system, the total momentum does not change. The total momentum remains constant in any type of collision.

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Two Types of Collisions…. Elastic The two objects collide and then separate. Inelastic When two objects collide and move together as one mass.

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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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