Momentum and Collisions

…What Would You Rather Be Hit With!!!! Today’s Choices Are… …Mr. Friel’s Dry Erase Marker!!! …Mr. Friel’s Whiffle Ball !!! …Mr. Friel’s kg shot put!!! Now Choose!!!!!

Why did you make your decision? Now…the Bonus Round!!! Who would you rather have throw the object? …Mr. Friel or …Aroldis Chapman, 105 mph flamethrower for the Cincinnati Reds

What factors were involved in your decision? - mass - velocity Remember, F net = ma = m (Δv/Δt) - it takes force to alter the motion of an object Ex. Randy Johnson Pitch

Momentum (p) – possessed by any object in motion (must have mass and velocity) p = mv - SI Units are kg m / s - Vector quantity, the direction of the momentum is the same as the velocity The amount of momentum is also directly proportional to the inertia when an object is moving. SI SI

As long as no external force (friction) acts on an object in motion, momentum is conserved (Δp = 0) Any change in momentum due to an outside force is known as impulse.

F = ma F = m (Δv/Δt), multiply both sides by Δt Impulse = FΔt = mΔv = Δp Vector quantity, the direction is the same as the direction of the force.

 The theorem states that the impulse acting on the object is equal to the change in momentum of the object. ◦ ◦ If the force is not constant, use the average force applied

Think about how an airbag works in a car - increases Δt - decreases ΔF What if you hit the steering wheel? - ouch… What are some other objects that take advantage of impulse?

Let’s do another quick example, everyone climb up onto your chair… …now jump off… …how did you land? …what happed to your knees?

 The momentum of each object will change  The total momentum of the system remains constant

When objects collide, total momentum change (impulse) = 0 Initial momentum (p B + p A ) is equal to final momentum (p B ’ + p A ’) Notice how Δp for object A and Δp for object B are exact opposites. Δp A = - Δp B

Law of conservation of momentum – the momentum of any closed, isolated system does not change - no net external forces

 Mathematically: ◦ Momentum is always conserved for the system of objects ◦ p 1init + p 2init = p 1final + p 2final

 Momentum is conserved in any type of collision  Collisions are one of the following: ◦ Perfectly elastic ◦ Perfectly inelastic ◦ Somewhat elastic

 Only happens in a closed system (no friction in collision, no thermal energy loss).  Both momentum and kinetic energy conserved in a perfectly elastic collision.

 Inelastic collisions ◦ Kinetic energy is not conserved ◦ Perfectly inelastic collisions occur when the objects stick together  Not all of the KE is necessarily lost  In a perfectly inelastic collision, the final velocity is the same for both objects  Example of Perfectly Inelastic Collision - Office Linebacker Example of Perfectly Inelastic Collision - Office Linebacker

 When two objects stick together after the collision, they have undergone a perfectly inelastic collision  Conservation of momentum becomes ◦ Because the masses have stuck together after colliding and are moving at the same velocity

 Perfectly elastic collision ◦ Both momentum and kinetic energy are conserved  Actual collisions ◦ Most collisions fall between perfectly elastic and perfectly inelastic collisions ◦ In this case, kinetic energy is not conserved either.

 Both momentum and kinetic energy are conserved  Typically solved using systems of equations – two equations, two unknowns

 For a collision of two objects in three-dimensional space, the conservation of momentum principle implies that the total momentum of the system in each direction is conserved

 The “after” velocities have x and y components  Momentum is conserved in the x direction and in the y direction  Apply conservation of momentum separately to each direction