Conservation of Momentum

• The sum of the momentums of two bodies before they collide is equal to the sum of their momentums after they collide if there are no external forces exerted on them.

Σpi = Σpf OR

p1i + p2i = p1f + p2f OR

m1v1i + m2v2i = m1v1f + m2v2f

Collision Types

• Inelastic Collisions :

• the bodies involved in the collision either begin as a single mass before the collision or become a single mass after the collision.

Σpi = Σpfis still true, but the masses act as asingle entity either before or after thecollision.

Inelastic Collisions

pi = p1f + p2f

OR p1i + p2i = pf

(m1 + m2) vi = m1v1f + m2v2f

OR m1v1i + m2v2i = (m1 + m2) vf

Inelastic collisions

• Include situations involving – Recoil– Explosions– coupling train cars and other real life situations

where the masses either combine or separate due to a collision.

Elastic Collisions

• The bodies involved in the collision remain as separate, unconnected bodies both before and after the collision.

Σpi = Σpf

p1i + p2i = p1f + p2f

m1v1i + m2v2i = m1v1f + m2v2f

Elastic Collisions

• It is difficult to analyze elastic collisions without having both at least three of the four variable in the equation

Inelastic Collision Example

Step 1. Identify all the given values and put them by each “car”

Step 2. Find the initial momentums of each car

Step 3. Find the initial momentum of the system

Step 4. Determine what happens (cars stick together) . They become a SINGLE mass (with one velocity)!

• A mineral wagon is moving at a speed of 4 meters per second. It’s mass is 2000 kg. It collides with a car that is not moving whose mass is 4000 kg. The cars stick together. What is the velocity of the two cars after they collide?

Identify Givens

Calculate initial momentum of each

Initial momentums of each

How do you find the initial momentum of the SYSTEM ?

Initial System Momentum

Final Momentum

• The two bodies collide and stick together (is this elastic or inelastic????

• The masses now act as a SINGLE mass (after the collision)

Inelastic collisions

• After the collision the two bodies become one.

• The system now has a final momentum that is the result of a single mass and a single final velocity.

Inelastic Collisions

• m1+m2 = mf = 2,000 kg + 4,000 kg = 6,000 kg

• From the Law of conservation of momentum, the sum of the initial momentums equals the sum of the final momentums.

CONSERVATION!

• AndThe sum of the initial momentums is equal to

8,000 kg*m/s.SOthe final momentum after the collision is equal

to 8,000 kg*m/s

INITIAL Momentum = FINAL Momentum

What is the final Velocity?

once coupled, the cars slow down but continue to move in the same direction.

Elastic Collision

• The mineral wagon above has a mass of 2,000 kg and is moving at 4.0 m/s toward the guard van on a level frictionless track. The guard van is moving at 1.0 m/s toward the mineral wagon and has a mass of 4,000 kg

• The train cars collide and do not lock together as a single mass. Find the velocity of the guard van if the mineral wagon is moving at 1.0 m/s to the left after the collision.

• What are the given values? Be sure to identify direction!!!

Find initial momentum of each

• Find initial momentum of the system (watch the signs!)

• The bodies then bounce off of each other and remain as separate bodies after the collision.

• Even if they are separate, the total initial momentum of the system must be equal to the total final momentum of the system.

• What is the given velocity of the mineral wagon? In what direction is it going?