Impulse & Momentum

Physics 11

Momentum

Momentum

The product of a particle’s mass and velocity is called the momentum of the particle:

Momentum is a vector, with units of kg m/s.

A particle’s momentum vector can be decomposed into x- and y-components.

Momentum

Impulse

When an object is accelerated, typically the force will only be applied for a given time

So instead of considering Newton’s Second Law as we have previously discussed it, we will rearrange the equation

Impulse

Impulse

Use Newton’s Second Law and substitute the definition for acceleration

Rearrange the equation so there are no terms in the denominator

This expression is known as impulse (J)

vmtFJ

t

vmF

amF

Momentum

Momentum can also be defined starting from Newton’s Second Law

The rate of change of momentum can also be used to determine the force

Momentum is defined as the product of an object’s mass and velocity 1st Law of Motion

vmpt

vmvmF

t

vmF

amF

if

Impulse-Momentum

Impulse and momentum can be related in order to solve dynamics problems

Substitute the definition for momentum into the impulse equation

ptF

pptF

vmvmtF

vmtF

if

if

Conservation Laws

Conservation Laws

Conservation Laws

Vectors

Momentum Bar Charts

Collisions

Physics 11

Collisions

Atomic Model of a Collision

Slide 9-25

Atomic Model of a Collision

Review…

1st Law of Motion:

2nd Law of Motion:

vmp

ptF

Conservation of Momentum

The vector quantity momentum will be conserved in any collision That is, the sum of all momenta prior to

the collision will be equal to the sum of all momenta following a collision

Every object that has mass and velocity will have momentum and must be included in the total momentum of the system

Collisions

With any collision, it is imperative that you diagram the system prior to and following the collision and identify all objects involved in the collision

This allows you to ensure that you calculate the total momentum for the system to properly analyze the situation

While this may seem onerous, generally we will be looking at a maximum of two particles

Recall Momentum

Momentum

Impulse

vmp

pvmtFJ

Momentum Conservation Momentum is conserved

This is an expression of Newton’s first law: “An object at rest or in uniform motion will remain at

rest or in uniform motion unless acted on by an external force.”

External forces can change the momentum of a system (Impulse)

FI pp

pvmtFJ

'pp

Momentum Conservation

In interactions between two bodies, momentum of one object can change, but the total momentum of the system remains constant.

'' 2121 pppp

'' 22112211 vmvmvmvm

Momentum Bar Charts

Impulse Jx transfers momentum to an object.

If an object has an initial momentum of 2 kg m/s, a +1 kg m/s impulse exerted on the object increases its momentum to 3 kg m/s. pfx = pix + Jx

We can represent this “momentum accounting” with a momentum bar chart.

The figure shows how one 1 unit of impulse adds to 2 units of initial momentum to give 3 units of final momentum.

Momentum Bar Charts

Types of Momentum Problems Elastic collisions

Inelastic collisions

Explosions

Initial

Initial

Initial Final

Final

Final

Types of Collisions

Elastic conserve both Ek and momentum

Inelastic conserve only momentum

Collision

A billiard ball, mass 155g, is travelling at 3.5m/s across the table. It strikes another ball at rest, mass 150g and comes to rest. What is the velocity of the second ball after the collision? Is the collision elastic or inelastic?

Summary…

1st Law of Motion:

2nd Law of Motion:

3rd of Motion: Law of Conservation of

Momentum

vmp

ptF