Topic 7  Momentum

Momentum is the product between mass and velocity.  Being a vector quantity, it has a direction, and the direction is very important when doing momentum calculations.  Momentum is not a thing that we can see, but it does explain many things that go on in physics.

  Momentum (kg m/s) = mass (kg) x velocity (m/s)

Units are kilogram metres per second (kg m/s) or newton seconds (Ns).  We can show that the units are the same.

In the example above, we only looked at the value of the momentum.  This is why we used the word speed.   It is very important to make sure that you pay attention to the signs when doing momentum calculations.

Think of a ball bouncing off a wall.  It leaves the wall at the same speed as before.  Let’s call going from right to left negative, and going from left to right positive.

Conservation of Momentum

An important principle:

  The total momentum of a system remains constant provided that no external forces act on the system. 

  This has important implications in the study of collisions.  In simple terms, we can say that the total momentum before =  total momentum after.  The key thing is that share of the momentum may change.

Collisions

Momentum is always conserved in collisions.

If objects bounce off each other, the collision is elastic.  If the total kinetic energy is the same (conserved) at the end as it is at the start, then the collision is perfectly elastic.  The rebound of particles against each other tends to be perfectly elastic.  A tennis ball bouncing off the floor is not perfectly elastic as it can lose up to 25 % of its kinetic energy in doing so.

If some kinetic energy is lost, converted into heat or light, then the collision is inelastic.

Think about two objects travelling in the same direction.  The table below shows the properties of the objects:

  We can show this as a diagram:

There are two important principles here:

1.      Conservation of momentum:

Total momentum before = total momentum after

Mu₁ + mu₂ = Mv₁ + mv₂

2. Energy is conserved:

Total energy before = total energy after

½Mu₁² + ½mu₂² = ½Mv₁² + ½mv₂² + E

The term E is the energy that is lost in the collision.  In a perfectly elastic collision E = 0.

When doing momentum calculations, always be careful about the directions you are using.

This question is a typical question you will find in the exam.  It is often called synoptic, because it tests several different concepts at the same time.  At A2 you will do a synoptic paper that has questions that can combine parts from several different modules.  At AS you will only be asked on things that appear in that module.

Impulse

The change in momentum is called the impulse and is given the physics code Dp.  We can define Newton’s Second Law in terms of change of momentum:

                                    Force = change in momentum

                                                      time interval                                                

                                    Þ Impulse (Ns) = Force (N) x time interval (s)

In code:

Dp = FDt

If we plot a force time graph, we can see that impulse is the area under the graph.

In this graph, both impulses are the same.  The forces and time intervals are different.

Impulse is the physics phenomenon that explains how a ball behaves when kicked or hit with a bat.  It also has important implications in road safety.  When a car is involved in a collision, we want the impulse to occur over a longer time interval to reduce the forces involved.