Taken from the Internet, momentum can be defined as:



As the relationship suggests, a body will have more momentum if its mass and / or velocity increases. Remembering that all measurable quantities in science have "base" units, the quantity of momentum is measured as a product of the mass in Kilograms and velocity in Metres per Second.


Example:


Q. A golf ball is driven from the tee, it has a mass of 60g and leaves the face of the golf club at 40.2 m/s (90mph). What is its momentum?


A. 60g =0.06Kg therefore:



Note that the representation 'p' is used for momentum, as 'm' is already in use. Momentum is a 'vector' , it has magnitude and direction. 


There is one fundamental rule to remember with regards to momentum. Momentum, in a closed system, will be conserved. In other words in a system isolated from other influences, the total momentum before an event will be the same as the total of the momentum after the event. 



In the desktop toy "Newton's Cradle", one or more steel spheres is raised and released, the momentum of the ball is conserved as the energy transfers to the other end of the cradle. If one ball is released, only one ball will respond, there is a conservation of momentum at work. The Newton's Cradle will slow down and stop eventually as it is operating in an open system, with external influences such as friction / air resistance and gravity causing some energy to be wasted.


Another favourite example is that of the game of snooker, where the white cue ball is used to strike the other balls. Snooker is a game full of physics! Consider a regulation ball with an average mass 156g and a diameter of 57mm:



If we have the situation where the white cue ball is struck with the snooker cue, it will be travelling at a velocity v1 and so will have a momentum of mass x velocity.


When the white ball strikes the red ball, a certain amount of momentum is transferred to the red ball , which then moves away from the white ball at a velocity v2. The velocity of the white ball is reduced, and can sometimes be reduced to zero but the total momentum of the two balls is the same as it was before the collision.


Q. A 156g regulation white cue ball is struck, causing it to move towards a regulation 156g red ball at approximately 4 m/s. After the collision, the red ball moves away from the white cue ball in a straight line at 3.2 m/s.


Calculate the momentum of each ball before and after the collision, and from this information calculate the resultant velocity of the cueball.


A. We assume that this is a closed system, as we have not been given any indication otherwise. We need to make sure first of all that our values given are in the correct units. 156 g is 0.156 kg, velocities are already given in metres per second and therefore do not need to be amended.


Before the collision between the two balls, the white cue ball possesses a momentum of: 



and the red ball possesses no momentum as it is not moving. 


After the collision, the red ball moves away at 3.2 m/s with a momentum of 


. 

The law of conservation of momentum tells us therefore that the white ball still possesses a certain amount of momentum, given by 




The mass of the white cueball has not altered, therefore its velocity can be calculated by simply rearranging the equation for momentum:



If, for some reason you ever need to convert ms-1 to kmh or mph you can do this (or see Appendix P3) :




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