3.5.2 Collisions

The principle of conservation of momentum states that for a closed system the total momentum in a specified direction remains constant as long as no external forces act on the system.

It is important to recognise that both momentum and total energy are conserved when objects collide. There are two types of collision:

• perfectly elastic:
• momentum is conserved, total kinetic energy is conserved.
• inelastic:
• momentum is conserved, total kinetic energy is not conserved.

As we know, linear momentum must always be conserved. We can resolve the different directions of momenta into 'x' 9horizontal) and 'y' (vertical) directions and ensure that each is constant.

3.5.1 Newton’s laws of motion

okay so Newton (v clever chap) has 3 laws of motion:

• First law: An object will remain at rest or continue to move with constant velocity unless acted upon by a resultant force.
• Second law: The net force acting on an object is directly proportional to the rate of change of momentum.
• Third law: When two objects interact they exert an equal and opposite force on each other.

The linear momentum of an object depends on its mass and velocity. We can calculate it using the equation:

p = m v

It has the unit kg m s^-1. It is a vector as it is a product of mass (scalar) and velocity (vector).

Newton's second law we can formulate the equation:

F = Δp/Δt

NOTE: The constant (k) in this equation can be made equal to 1 by defining the unit of force (the Newton) as the force required to give a 1kg mass an acceleration of 1m s^-2. It is also important to recognise that F = ma is a special case of this equation.

If we rearrange this equation we can get F Δt = Δp. The impulse of a force is defined as the product of force and the time for which this force acts on an object. It follows that the area under a force-time graph is equal to impulse.