P2aL10 Momentum

Key Words

Conservation of momentum - momentum before is the same as the momentum after.

Direction  - a line along which something moves.

Elastic collision - a collision between objects in which they bounce off each other.

Inelastic collision - a collision between objects in which they stick together.

Kinetic energy - energy in a moving object.

Mass - the amount of material in an object.

Momentum - the product between mass and velocity.

Scalar - a quantity that has value but no direction.

Size - the value of a quantity

Transferred - energy has been moved.

Vector - a quantity that has both value and direction.

Velocity - speed in a certain direction

Grade E

All moving objects have momentum.  You cannot get hold of a momentum in shop.  You cannot see it in a moving object, but if you are hit by a moving object, you can definitely feel it.  However momentum is a very useful concept to explain collisions, rockets, and bullets coming out of guns.

The equation is:

momentum (kg m/s) = mass (kg) × velocity (m/s)

In Physics code:

p = mv

In triangle form:

The units are kilogram metres per second (kg m/s).

Momentum is a vector quantity and the direction of the velocity is very important in momentum calculations.  If two identical objects are moving in opposite directions, one will have a positive velocity and a positive momentum.  The other will have a negative velocity and negative momentum.  We usually say that from left to right is positive.

Grade C

An important rule:

Momentum is always conserved provided no outside force is acting on the system.

This is called the Law of Conservation of Momentum.  It means:

Momentum before = Momentum after

There are two kinds of collision:

• Elastic, where two vehicles  bounce apart after the collision.  Kinetic energy is conserved only in a perfectly elastic collision.
• Inelastic, where the two vehicles stick together.  Kinetic energy is lost.

Here is an inelastic collision.  Wagon 1 has a mass m1 and wagon 2 has a mass m2.  Wagon 1 has a velocity u1 where u is the velocity before the collision.  Wagon 2 has 0 velocity.

Before:

Wagon 1 has momentum = m1u1

During:

The two vehicles collide and stick together.

After:

The wagons have stuck together, and both travel off at a common velocity v.  The total mass is m1 + m2, as they have stuck together.

Momentum is conserved, which means that momentum before = momentum after.

Therefore:

m1u1 = (m1 + m2) v

Therefore the common velocity can be found:

v = (m1u1) ÷ (m1 + m2)

In an elastic collision, the vehicles bounce apart, so we get:

Again, momentum before = momentum after:

m1u1 = m1v1 + m2v2

If we add up all the kinetic energy before and after, and find it's the same, we can say that the collision was perfectly elastic.  Inelastic collisions result in the loss of kinetic energy

Grade A

Momentum is not just confined to objects moving in a straight line.  Spinning objects have angular momentum, which is the product between the moment of inertia and the angular velocity.

The moment of inertia is equivalent to the mass, and the angular velocity is the number of degrees per second.

You can experience this for yourself by spinning yourself around in a swivel chair.  Put your feet out and your rate of turning will reduce; put them back in and you will spin faster.