Impulse & Momentum Physics 11

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

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)

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  1 st Law of Motion

Impulse-Momentum Impulse and momentum can be related in order to solve dynamics problems Substitute the definition for momentum into the impulse equation

Conservation Laws

Vectors Momentum Bar Charts

Collisions Physics 11

Collisions

Atomic Model of a Collision Slide 9-25 Atomic Model of a Collision

Review… 1 st Law of Motion: 2 nd Law of Motion:

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

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)

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

Momentum Bar Charts  Impulse J x 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.  p fx = p ix + J x  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

 A rubber ball is initially moving to the right with p ix = +2 kg m/s.  It collides with a wall which delivers an impulse of J x =  4 N s.  The figure shows the momentum bar chart to help analyze this collision.  The final momentum is p fx =  2 kg m/s. Momentum Bar Charts

Momentum Vector Diagrams Using the last example… p ix = +2 kg m/s p fx = -2 kg m/s J x = -4 N·s

Types of Momentum Problems Elastic collisions Inelastic collisions Explosions Initial Final

Types of Collisions Elastic  conserve both E k 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… 1 st Law of Motion: 2 nd Law of Motion: 3 rd of Motion: Law of Conservation of Momentum