Conservation of

Momentum

Newton’s Laws combined predict that momentum is conserved when no outside forces act on a system.

Conservation of Momentum: !   Without outside forces, the momentum of a

system is unchanged.

!   The momentum of individual components may change, but the total momentum is unchanged.

Momentum is the mass times the velocity of an object. !   Equation p = mv

!   p is momentum (kgm/s)

!   m is mass (kg)

!   v is velocity (m/s)

You try. Find the momentum for each object. 1.  A 500kg car traveling at 20 m/s.

(500kg)(20m/s) = 10000 kgm/s

2.  A 0.10 kg fish swimming at a velocity of 8 m/s. (0.10kg)(8m/s) = 0.80 kgm/s

3.  A 75kg man running at a speed of 7 m/s. (75kg)(7m/s) = 525 kgm/s

The momentum of a system is the

sum of the momentums of each

part of the system. !   Equation: ptotal = p1 + p2 +p3 + p4 + ……

You try. Find the total momentum of

each system. 1.  2 steel spheres. Each 0.5 kg. Traveling at 2 m/s in the

same direction. (0.5 kg)(2m/s) + (0.5 kg)(2m/s) = 1kgm/s + 1 kgm/s = 2 kgm/s

2.  2 steel spheres. Each 0.5 kg. Traveling at 2 m/s in the opposite directions.

(0.5 kg)(2m/s) + (0.5 kg)(-2m/s) = 1kgm/s - 1 kgm/s = 0 kgm/s

3.  2 steel spheres. Each 0.5 kg. One traveling at 2 m/s. The other is at rest.

(0.5 kg)(2m/s) + (0.5 kg)( 0 m/s) = 1kgm/s + 0 kgm/s = 1 kgm/s

Since momentum includes direction, the conservation of it creates a symmetry.

An example:

!   Fireworks!

! https://youtu.be/qn_tkJDFG3s

!   Cam you identify the pairs that cancel each other out?

There is also symmetry in Action Reaction Forces

!   We will be studying collisons between objects. If we consider both objects as part of the system, their collision is not considered an outside force.

!   Definition of Collision: the meeting of particles or of bodies in which each exerts a force upon the other, causing the exchange of energy or momentum.

Billards is a great example of the symmetry

of conservation of momentum

!   What is the best shot to sink any numbered ball? (draw collision into your notes)

!   Momentum before?

!   Momentum after?

Elastic Collision !   A collision between bodies in which the total kinetic

energy of the bodies is conserved.

!   Elastic collisions, such as the collision of a rubber ball on a hard surface, result in the reflection or "bouncing" of bodies away from each other.

!   In a perfectly elastic collision, no energy is turned into thermal energy internal to the bodies, and none is spent on permanently deforming the bodies or radiated away in some other fashion.

Example of an elastic collision

Inelastic collision

!   A collision between bodies in which the total kinetic energy of the bodies is not conserved.

!   Inelastic collisions, such as the collision of two balls of clay, tend to result in the slowing and sometimes the sticking together of the colliding bodies.

!   In an inelastic collision, the total momentum of the two bodies remains the same, but some of the initial kinetic energy is transformed into thermal energy of the bodies, used up in deforming the bodies, or radiated away in some other fashion.

Epic Inelastic Collision

!   Birth of the moon:

! https://www.youtube.com/watch?v=hahpE8b6fDI

!   Momentum is still conserved. The individual atoms have gained momentum (directions are random).

Momentum is always conserved. !   If you consider both objects part of a system,

then –

!   Equation: p total before = p total after

You try. Find the momentum.

1.  2 steel spheres. Each 0.5 kg. One traveling at 2 m/s. The other is at rest. What is the momentum before?

(0.5 kg)(2m/s) + (0.5 kg)( 0 m/s) = 1kgm/s + 0 kgm/s = 1 kgm/s

What is the total momentum after they collide?

Must be 1 kgm/s

You try. Find the momentum.

2.  2 steel spheres. Each 0.5 kg. Traveling at 2 m/s in the opposite directions. What was the total momentum before?

(0.5 kg)(2m/s) + (0.5 kg)(-2m/s) = 1kgm/s - 1 kgm/s = 0 kgm/s

!   What is the total momentum after?

Must be 0 kgm/s – If they don’t come to a stop or stick together, how is 0 total momentum possible?

Testing Conservation of Momentum aboard the ISS .

! https://youtu.be/4IYDb6K5UF8

We will use a simulation. This is the same sim from your homework.

http://polytechpanthers.com/apps/pages/index.jsp?uREC_ID=556228&type=u&termREC_ID=&pREC_ID=540344