Momentum and Impulse Problems (AS)

Definition: Momentum is a vector quantity, calculated by multiplying the mass of an object by its velocity. Its units are kg m/s.
The law of conservation of momentum states that the total momentum before an event (such as a collision or explosion) is equal to the total momentum after the event, providing no external forces act on the system.
Impulse is the change in momentum of an object when a force is applied for a given time. It is calculated as force multiplied by time (Ft) and its units are Ns (Newtons-seconds).
Consider Newton’s second law in terms of momentum: The rate of change of momentum of an object is directly proportional to the force applied to it, and happens in the direction where the force is applied.
Differentiating momentum with respect to time gives us Force: F = dp/dt
Impulse can also be determined using the area under a force-time graph.
Types of collisions: In an elastic collision, both momentum and kinetic energy are conserved. In an inelastic collision, only momentum is conserved - total kinetic energy decreases due to aspects such as heat or sound.
Coefficient of restitution (e): This dimensionless quantity characterises the collision between two objects. It is the ratio of relative speed of separation to relative speed of approach after and before the collision, respectively.
The value of e lies between 0 and 1. For a perfectly elastic collision e = 1, for a perfectly inelastic collision e = 0.
Oblique collisions: These imply that not only should the total linear momentum be conserved in the direction of motion, but also in a direction perpendicular to it.
To solve complex problems, break down the motion into perpendicular components, then apply the principles of momentum and impulse separately in these dimensions.
Practise solving problems involving conservation of momentum, including one-dimensional problems (direct collision) and two-dimensional problems (angled collisions). Use vectors to represent quantities and resolve them into components when necessary.
Be familiar with mathematical proofs of the principles of conservation of momentum and impulse, such as by using Newton’s second and third laws.