Momentum & Collisions Colonial Forge High School Advanced Placement Physics Fall 2015

Objectives To introduce the concepts of Momentum Impulse Inelastic collisions Elastic collisions Glancing collisions

Linear Momentum Defined as mass of object times the velocity of the object p = mv The unit is This is a vector quantity which means...

Momentum Components We can break momentum into its x and y components p x = mv x and p y = mv y

Momentum and KE We are told p = mv, so But Therefore

Newton Alternative ?! If F = ma, then

Impulse To change an object’s momentum, a continuous force must be applied over a period of time. The force can slow, stop or reverse the motion of the object. If we can increase the amount of time over which the momentum is changed, the force is lessened.  this is why we have seatbelts and air bags

Why do I care?

Are seatbelts worth it? How many of you wear your seatbelt 100% of the time? What’s the purpose of an air bag? Seat belt?  to increase the time over which you slow down Air Bags Explained

Impulse Equation Since impulse (J) is defined as the change in momentum, our equation is J = FΔt = Δp Proof the units work

Impulse From a Graph** (Mathematically, we can use the average force over the time interval.) The area under the curve of a force- time graph equals the impulse.

Take a Look… AUDI RS6

It is a single car....

This is the driver!

Did you notice the driver’s seat?

Conservation of Momentum In an isolated system, momentum of a collision is conserved. No external forces A collision may be the result of physical contact between two objects “Contact” may also be from interaction of electrons

The formula This means the total momentum before the collision equals the total momentum after the collision m 1 v 1i + m 2 v 2i = m 1 v 1f + m 2 v 2f Momentum is conserved in ALL collisions

Types of Collisions 1. Perfectly Inelastic Collision Momentum is conserved Kinetic energy is not conserved as some of it is converted to other types of energy (heat, sound, work, etc) resulting in permanent deformation of the object  remember the audi? Perfectly inelastic collisions occur when the objects stick together

The math? Momentum conserved looks like m 1 v 1i + m 2 v 2i = (m 1 +m 2 )v f

The Reality… You rarely get a perfectly inelastic collision.

2 nd Type of Collision 2. Elastic Collision Momentum is conserved Kinetic energy is conserved Bounce off each other (You may get two equations and two unknowns.) m 1 v 1o + m 2 v 2o = m 1 v 1f + m 2 v 2f ½m 1 v 1o 2 +½m 2 v 2o 2 = ½m 1 v 1f 2 + ½m 2 v 2f 2

Glancing Collisions These are collisions that occur at an angle. Not head-on! Solve using vector analysis! The math is straight-forward albeit a little more complicated.

Car Design? What’s the purpose of a crumple zone? What would happen if the car was made of rubber and everything bounced off readily? What would happen if it was completely rigid? Think about a hamster in it’s little ball…

What does it look like? Crash Testing Video--start at 17 secs One More For Fun

In Summary… Impulse The goal may be to increase the time over which the momentum of an object is changed—this lessens the force applied Momentum Inelastic—stick together Only momentum conserved Elastic—bounce off Momentum & Kinetic energy conserved

The Equations J = FΔt = Δp p = mv K = ½ mv 2