Collisions. Direct collisions, elastic (0 < e ≤ 1) and inelastic (e = o).

Oblique collisions of smooth elastic spheres in two dimensions.

Imagine that we have done quite a bit on this section and yet we only get to collisions now. A collision truly is the interaction between two bodies that are free to move.

Newton experimented quite a bit with this mechanics problem and determined the coefficient of Resititution was defined by

It is a good strategy to do as we do in relative velocity and find the velocity of one body while keeping the other one as the observer stationary, use the following formulae, but don't forget to apply it to all the components of the velocity.

Momentum is a conserved quantity, meaning that the

TOTAL momentum cannot change in a closed system

(one not affected by external (outside) forces)

This law is also true in special relativity.

Ok what does that mean ?

What do you require for a system ?

All you need is a mininum of 2 objects.

Both will have a ..............

And at some stage both will also have a ................

Therefore we can calculate their ........................ when they interact with each other.

The Total Momentum is the sum of the individual bodies momenta

object 1 momentum m1v1 + object 2 momentum m2v2

TOTAL momentum cannot change in a closed system

If we have 2 bodies then their combined momentum is conserved after any collision between the 2 bodies.

Change in Momentum

Momentum problems

A runaway Engine of 16000kg travelling at 25m/s, collides with 5 carriages each of mass 2000kg that are at rest. If the whole train couples together and continues to roll along the track at what speed will this be at? Sticking together problem

A loaded gun fires a bullet, the 2g bullet leaves the gun at 400ms-1 if the gun is 2.5kg at what velocity does the rifle re-coil ?

Zero momentum before the interaction, explosions, firing a bullet or a canonball.

for more problems of a cooler nature try these

The problems on pg 181 are different, because we know about collision so e is involved

We shall follow this algorithm to solve these problems

  1. State the Initial velocities, Masses and Final Velocities in a table for both bodies
  2. Calculate the momentum before the collision and allow it to equal the momentum after, usually we will find ourselves with an equation with 2 unknowns
  3. Now use Newtons experimental law of restitution, to determine another equation featuring the 2 knowns from the table.
  4. Using simultaneous equations solve for the unknowns

Now go and do Exercise 7c

Wally does collisions elastic & non elastic here at

Start with the original set up on walters page, run it and reset it, click on the tabs for the momentum & kinetic energy,

Now lets change a mass, the blue car or the red ? examine

r 0.7 0.5 b 0.5 -0.1

Imagine them moving in the same direction and one hits the other

Now what if they are heading towards each other, now what outcomes can you expect?

Predict the outcomes of a self made scenario and declare to the class what you think will happen,

just remember the 2 rules

Energy can neither be created nor destroyed


Momentum is conserved in a closed system

Its really enjoyable to solve these problems give them a shot