Chapter 9 – Momentum & Collisions

Impulse

Elastic & Inelastic Collisions

HW Assignment Due on 12/16/12

Linear Momentum

Momentum is a vector; its direction is the same as the

direction of the velocity.

Linear Momentum

Change in momentum:

(a) mv

(b) 2mv

Forces and Motion - Questions

• A constant force acts on an object.

• How does the speed of the object change with

time?

• Now have a force opposing the first force. How

does the time needed to change the direction of

motion relate to the magnitude of a force

opposing that motion?

Momentum and Newton’s Second Law

Newton’s second law, as we wrote it before:

is only valid for objects that have constant mass. Here is a

more general form, also useful when the mass is changing:

Impulse

Shows effect of time interval that a force acts over. Impulse is a

vector, in the same direction as the average force.

Impulse

We can rewrite

as

So we see that

The impulse is equal to the change in momentum.

Impulse

Therefore, the same change in

momentum may be produced

by a large force acting for a

short time, or by a smaller

force acting for a longer time.

Example 9-2 : Jumping for Joy

• Pg. 261

• 72 kg person jumps

• Impulse?

Conservation of Linear Momentum

The net force acting on an object is the rate of change of its

momentum:

If the net force is zero, the momentum does not change:

Conservation of Linear Momentum

Internal Versus External Forces:

Internal forces act between objects within the system.

As with all forces, they occur in action-reaction pairs. As all pairs act

between objects in the system, the internal forces always sum to zero:

Therefore, the net force acting on a system is the sum of the external forces acting on it.

Conservation of Linear Momentum

Furthermore, internal forces cannot change the momentum of a

system.

However, the momenta of components of the system may change.

Conservation of Linear Momentum

An example ( EXAMPLE 9-3 ) of internal forces moving components of a system:

• Pg. 264

• Mass 1 = 130 kg

• Mass 2 = 250 kg

• Momentum after 1.2 sec

of pushing

• Find a, v, then p

• Other ways to answer?

Different Methods

• Honors-side � use IMPULSE concept

– Answer?

• AP-side � use acceleration, velocity

– Answer?

Inelastic Collisions

Collision: two objects striking one another

Time of collision is short enough that external forces may

be ignored

Inelastic collision: momentum is conserved but kinetic

energy is not

Completely inelastic collision: objects stick together

afterwards

Inelastic Collisions

Solving for the final momentum in terms of the initial momenta

and masses:

Inelastic Collisions

Ballistic pendulum: the height h can be found using conservation

of mechanical energy after the object is embedded in the block.

Elastic Collisions

In elastic collisions, both kinetic energy and momentum are

conserved.

One-dimensional elastic collision:

Elastic Collisions

We have two equations (conservation of momentum and

conservation of kinetic energy) and two unknowns (the final

speeds). Solving for the final speeds:

Elastic Collisions

Two-dimensional collisions can only be solved if some of the final

information is known, such as the final velocity of one object:

3rd Six-Weeks Test• Tuesday, December 11

• Covers Chapters 5-9

• Study Quizzes!!

• Simple momentum/impulse question but with conceptual questions on collisions

– Definitions

– Setting a problem up ( given enough info? ) / True-False