System: Total Momentum

System: Total Momentum

...mm)(m 2211 vvv

tot

v

v

v

v

vSystem

+4 m/s

-1 m/s

m2 = 2 kg

m1 = 0.5 kg

Find total momentum of the system:

A)2 kg m/s C) 4 kg m/s

B)3 kg m/s D) 0 kg m/s

1. Impulse = Change in Momentum

2. Ft = Change in momentum

3. If F = 0, momentum does not change.

“Conservation” of momentum.

How does momentum of the system change after they collide? No external forces.

+4 m/s

-1 m/s

A)Positive change in momentum

B)Negative change in momentum

C)Zero change in momentum

Conservation of Momentum

mB

collide!

mA

VA

VB

mA VA’

mB

VB’

Total mv Before = Total mv After

(if no external force on the system)

Be careful with positive and negative signs!

Positive Negative

'm'mmm BBAABBAA vvvv

Example: Using momentum conservation

-3 m/s

'm'mmm BBAABBAA vvvv

+4 m/s

0 m/s ?

m2 = 2 kg

m1 = 0.5 kg

Momentum conserved even if many particles are

involved.

http://www.tutorialwiz.com/explosion/images/f.jpg

Total momentum before explosion

=

Total momentum after

explosion

Squid Propulsion (Explosion)

http://www.biology.ualberta.ca/courses.hp/zool250/animations/Squid.swf

mvtot = 0

Before

After

(mv)water = (mv)squid

Total momentum = 0

Recoil: Total Momentum = 0

Before

After

vbulletvrecoil

(mv)bullet + gun = 0

-mgunvrecoil + (mv)b = 0

Elastic collision: Bounces

Momentum is Conserved & No Energy "lost" Momentum is

always conserved if no external

forces are applied to the system!

Inelastic collision: Stick

Momentum is Conserved but Energy is not

V2 = V

V2 = 0

V1 = -V

Bouncy ball (elastic)

Dead ball (inelastic)

Calculate change in momentum for each.

V1 = -V

Low Friction Carts on Track

m

v

m (at rest)

Before After

v/2

v = 0v

m

v

m

Inelastic

Inelastic

v

m

v

m

Elastic v

m

v

m

Low Friction Carts on Track

m

v1

m

Before AfterElastic

v2 v2 v1

Before AfterElastic

m

v1

m

v2 v2 v1

Purpose:

Experimentally (and mathematically) prove conservation of momentum in a collision or an explosion.

Lab: Conservation of Momentum

Procedure: Develop and perform an experiment to prove conservation of momentum.

Results should show:

momentum before an event = momentum after an event.

within 10%.

Lab: Conservation of Momentum

Things to consider:

Explosion, elastic collision or inelastic collision?

Will masses stay constant throughout the event?

What materials will give good data?

What measurement tools will you use?

How to measure velocities and masses before and after the event?

Before beginning the experiment:

Write down anticipated procedure and a materials list, then get materials.

Do preliminary experiments to make sure your technique will work.

Think through equations to make sure to measure and record correct data.

Make a data table to use during experiment.

Get teacher initials on prep sheet, before starting the experiment.

Momentum Conservation/Transfer

• Impulse on basketball and tennis ball

vM

m

M v≈0

v’

(m+M)vbefore mvafter

Actually, the floor provides an external force and this illustrates energy

conservation.