# Momentum, Impulse, and Collisions. Momentum (P) A quantity that expresses the motion of a body and its resistance to slowing down. P = mv m = mass (kg)

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Momentum, Impulse, and Collisions

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)

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

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)

Impulse

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

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.

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

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.

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

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.

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

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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