COLLISIONS We use the Conservation of Momentum Law for Collisions: m 1 v 1i + m 2 v 2i = m 1 v 1f +...

COLLISIONS

We use the Conservation of Momentum Law for Collisions:

m1v1i + m2v2i = m1v1f + m2v2f

COLLISIONSLimitations of the Conservation of

Momentum

External forces - forces caused by agents external to the "system“. The “system” is only mass 1 and mass 2.

Examples1) ‘external’ friction (the felt of a pool

table)2) air resistance3) gravity

COLLISIONS

Internal forces - forces that only act BETWEEN the objects in the system; such as the 'push' given by one skater to the other, the explosive force between the cannon and a cannon ball.

These forces are actually necessary for the exchange of momentum.

COLLISIONS

Significance?

Internal forces occur between the masses; they act on both masses. They provide the impulse that changes the momentum.

External forces occur between the individual mass and its surroundings. So the object loses its momentum to the surroundings and not to the other object.

COLLISIONS

Two Types of Collisions:

1. Elastic (ideal case) 2. Inelastic

No Energy Is Lost Energy Is LostObjects rebound: a) objects pass

through one another b) objects stick

togetherc) objects may

rebound but too much Energy is lost

(see next page)

m1

m1

m2

m2

Nearly all ordinary collisions are inelastic

COLLISIONS1. Objects pass through 2. Objects that stick

“Perfect Inelastic”Friction on block of wood from bullet

Friction on bullet from block of wood

The friction that occurs between BOTH objects is an “internal” force. Internal forces are absolutely needed to exchange momentum, but energy is still lost.

The friction that occurs between BOTH objects is an “internal” force. Internal forces are absolutely needed to exchange momentum, but energy is still lost.

INELASTIC COLLISIONS

COLLISIONS

Inelastic Analysis CASE 1:

The objects STICK TOGETHER

PERFECT inelastic collision

Maximum loss of KE.

If the two objects are stuck together at the end, what can we say about their final velocities?

COLLISIONS

fii

ffii

ffii

vmmvmvm

vmvmvmvm

vmvmvmvm

)( 212211

212211

22112211

Conservation of Momentum

Note that the final velocities are now the same

The above equation is the PERFECT INELASTIC form of the Cons. Of Momen.

We can alter the Conservation of Momentum Equation to account for that:

COLLISIONS

Example:

A 0.053 kg piece of clay is thrown at 21 m/s at a 1.3 kg wood cube sitting motionless on ice (frictionless). It hits the cube and sticks to it and they both slide on the ice together. Find their final velocity.

COLLISIONS

COLLISIONS

Example:


COLLISIONS

fii vmmvmvm )( 212211

Example:


fv)3.1053.0()0)(3.1()21)(053.0(

COLLISIONS

fii vmmvmvm )( 212211

Example:


fv)3.1053.0()0)(3.1()21)(053.0(

m/s 82.0

353.1113.1

f

f

v

v

COLLISIONS

Inelastic Analysis CASE 2:

The objects DON’T stick together

Use the regular Conservation of Momentum Law.

COLLISIONSExample:

A 0.123 kg arrow is moving at 42 m/s. It passes through a 5.2 kg piece of balsa wood sitting motionless on a frictionless surface and the arrow emerges moving at 33 m/s. How fast is the piece of balsa wood moving?

COLLISIONS

COLLISIONS

ffffiiii vmvmvmvm 22112211

Example:


COLLISIONSExample:


m/s 214.0

2.5113.1

2.5059.4166.5

)2.5()33)(123.0()0)(2.5()42)(123.0(

2

2

2

2

22112211

f

f

f

f

ffffiiii

v

v

v

v

vmvmvmvm

COLLISIONS

Elastic Analysis:

For a “perfect” elastic collision

NO ENERGY IS LOST

COLLISIONS

afterbefore KEKE 2222

12112

12222

12112

1ffii vmvmvmvm

That means:

With the Conservation of Momentum:

ffii vmvmvmvm 22112211

We have two equations and can solve for two unknowns!

COLLISIONS We use the Conservation of Momentum Law for Collisions: m 1 v 1i + m 2 v 2i = m 1 v 1f +...

Documents

Transcript of COLLISIONS We use the Conservation of Momentum Law for Collisions: m 1 v 1i + m 2 v 2i = m 1 v 1f +...