**
6.2
The Law of Conservation of Momentum**

Here we will consider **collisions between
two objects** in a closed system.

Here **a closed system here means no other
external forces affect the situation** e.g. a collision between two objects -
the event.

If an external force like friction is
involved, total momentum cannot be conserved.

The **total momentum of an event **in a
closed system is the same before and after the event (e.g. a collision between
two objects).

This is called the '**Law of
Conservation of Momentum**' and you can use it do lots of calculations!

e.g. total momentum of two colliding
objects = total moment of objects after collision

e.g. for two colliding objects, where
**p = momentum:** **
p**_{1} + p_{2} = p_{3} + p_{4}

substituting m and v for the mass
and velocity gives ...

**
m**_{1}v_{1} + m_{2}v_{2}
= m_{1}v_{3} + m_{2}v_{4}

where v_{1} and v_{2}
are the initial velocities and v_{3} and v_{4} the
velocities after the collision,

(you are assuming there is no
change in mass, i.e. no bits have flown off!)

and if two objects stick together'
after the collision then: **
p**_{1} + p_{2} = p_{3}

substituting m and v for the mass
and velocity gives ...

**
m**_{1}v_{1} + m_{2}v_{2}
= m_{3}v_{3} (where m_{3} = m_{1} + m_{2})

where v_{1} and v_{2} are the initial
velocities and v_{3} and m_{3} (m_{3} = m_{1}
+ m_{2}) are the final velocity and mass after the collision.

In other words the large object
formed by collision has the momentum equal to the two momentums of
the colliding objects added together.

**
Momentum is conserved for both elastic and
inelastic collisions**

**For a perfect elastic collision,
no kinetic energy is lost - kinetic energy conserved.**

In an elastic collision, the
total energy in the kinetic energy stores of the colliding objects
is the same as before and after the collision.

You will not have to solve
problems for elastic collisions - the maths is too difficult for
GCSE level physics, with two sets of equations, for momentum (mv) and
kinetic energy (E = ½mv^{2}), to solve e.g. for the
resultant velocities!

For an** inelastic collision**,
kinetic energy is not conserved - kinetic energy is lost in some form
e.g. heat or sound.

In an inelastic collision, some
of the moving objects kinetic energy stores are lost and transferred
to other energy stores of the objects themselves or the environment.

This is because the atoms are
bashed together increasing their potential energy store (compressed
for a fraction of a second). They 'relax'
to their normal state by losing the energy as heat (thermal
energy) or sound.

For inelastic collisions you can
solve a variety of problems using the principle of 'conservation of
momentum'.

**See 6.4 for more complex momentum
calculations**

** **Problem
solving questions of more complex momentum calculations

INDEX physics notes:
Conservation of momentum, elastic and non-elastic collisions, Newton's 2nd
law calculations - problem solving

**
Keywords, phrases and learning objectives for elastic/inelastic collisions and
momentum**

Be able to explain and use the Law of Conservation of Momentum.

Know that momentum is conserved in both elastic collisions and inelastic
collisions.

Be able to describe and explain the difference between
elastic collisions, where kinetic energy is conserved and inelastic collisions
in which kinetic energy is not conserved.

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INDEX physics notes:
Conservation of momentum, elastic and non-elastic collisions, Newton's 2nd
law calculations - problem solving