Momentum, Impulse, and Collisions https://www.youtube.com/watch?v=2UHS883_P60&index=1&list=PLZHDrmpjw4My5KJXCT2inbz7pOv1lqsRk

Momentum (p) expresses the resistance of a body to slowing down. related to inertia p = mv m = mass (kg) v = velocity (m/s) Unit is kg m/s

Example A toy car has a mass of 5 kg. If it is moving at a velocity of 4 m/s, what is its momentum? 20 kg•m/s Given Unknown Equation Substitute Solve  

Your Turn What is the momentum of a 25 kg boy moving at a speed of 1.2 m/s? 30 kg•m/s

Impulse (I) measures a change in momentum Impulse = ∆p = m∆v Impulse = ∆p = m(vf – vi)

Impulse (I) To calculate multiply the average force acting on a body by the length of time the force acts. Impulse = F(∆t) F = force (N or Newtons) ∆t = time (s) Unit is N s See equation sheet.

Putting it all together… F(t) = m(vf-vi) Notice impulse, on the left side, is equal to the change in momentum of an object.

Impulse

Example An 8 N force acts upon an object for 5 seconds. What impulse is given this object? 40 N•s Given Unknown Equation Substitute Solve  

(Hint: use Impulse=F(t)) Your Turn 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.

There are 2 types of collisions Elastic – Bounce off m1v1i + m2v2i = m1v1f + m2v2f Where m1 means mass of object 1, m2 means mass of object 2 Where i means initial & f means final Inelastic – stick together m1v1i + m2v2i = mTvT Where T means total Use + and – velocities to show direction.

2kg(2m/s)+3kg(-1m/s) = 2kg(v1f)+3kg(1.33m/s) Example A 2 kg ball strikes another ball head on at an initial velocity of +2 m/s. If the second ball had a mass of 3 kg and was initially moving at -1 m/s, what is the final velocity of the 2 kg ball if the vf of the 3 kg ball is now +1.33m/s? Define variables. Then: m1v1i + m2v2i = m1v1f + m2v2f 2kg(2m/s)+3kg(-1m/s) = 2kg(v1f)+3kg(1.33m/s) v1f = -1.5m/s

500kg(10m/s)+700kg(25m/s) = 1,200kg(vT) Last one… A 500 kg car is driving at a velocity of 10 m/s. Another car (700 kg) hits it from behind at a velocity of 25 m/s and the two cars interlock bumpers. What is the resulting velocity of the two cars? Define variables. Then: m1v1i + m2v2i = mTvT 500kg(10m/s)+700kg(25m/s) = 1,200kg(vT) vT = 18.75 m/s