There are some mechanics problems which can’t be solved with s.u.v.a.t.

Problems where the force applied (and therefore the acceleration of the object) is not constant.

This is the case in collisions

**Momentum**

Linear Momentum is the product of the mass and velocity of an object.

Symbol: p

**p=mv**

Units: **kgms ^{-1}**

- Momentum is a vector.
- The momentum vector is co-linear to the velocity vector and in the same direction (it's magnitude will obviously be different)

**What collisions do?**

In A2/A-level physics, collisions are events which simply redistribute the available momentum between the two colliding objects. As usual we have to consider idealised conditions; in this case, something called a** 'closed system'**.

**Closed Systems**

Conservation laws in mechanics only apply to Closed System, ie. **external forces do not affect the motion of the object involved. **

(This means minimising frictional forces and arranging motion perpendicular to the direction of weight, i.e. gravitational acceleration)

**Newton's Law**

The foundation of the Conservation of Linear Momentum is Newton's Second Law of Motion:

**F ∝ ∆p/∆t**

F= ∆p/∆t only if/when we define a force of 1 Newton to equal 1 kgms^{-2}

**Impulse 1:**

rearrange F= ∆p/∆t to get:

**F∆p = ∆t**

- Where the product F ∆t is known as the Impulse.
- No symbol other than FΔt
- units: Ns
- Impulse is a vector.

**Impulse 2:**

During a collision, the objects involved exert equal but opposite Impulses on each other.

(this is the part where Newton’s Third Law applies)

**Impulse 3:**

- But an Impulse is equal to the CHANGE in momentum. So each object experiences an equal but opposite change in its momentum. However, the total momentum hasn’t changed. One object gains some, the other loses an equal amount.
- Also, if an Impulse is equal to the CHANGE in momentum then their units must be equivalent, i.e. Ns = kgms-1 (take care, this does NOT mean that Impulse = momentum. Neither can you use Ns as the units of momentum – only use it for a momentum CHANGE)

**Conservation 1:**

This is the Principle of the Conservation of Linear Momentum:

**In a close system, the total linear momentum before an interaction is equal to the total linear momentum after it. **

**Conservation 2:**

Linear momentum is ALWAYS conserved in interaction within closed systems, The same is true of the TOTAL energy (Kinetic + elastic strain + internal + sound)

**Kinetic Energy**

However, kinetic energy may or may not be conserved. It depends on the type of collision:

- Elastic Collision
- Inelastic Collison
- Super elastic "collision"

**Elastic Collision**

- The term "elastic" in dynamics means that
**Kinetic Energy is conserved**(again, still assuming a closed system) - i.e. the total KE before the interaction is equal to the total KE after it.
- A key additional feature of Elastic collisions is the: Relative velocity of approach is equal to the relative velocity of separation.
- e.g. in an elastic collision, if one object approaches a stationary object at 30ms
^{-1}, then after they have collided the difference between their velocities will still be 30ms^{-1}

**Inelastic Collision**

- In inelastic Collision some of the KE is transferred to other forms of energy during the collision
- eg. strain energy in deforming one or both of the colliding objects.
- Almost all real-world interactions are inelastic.
- Inelastic Collision do not require the 2 objects to stick together. They may or may not, but the collision can still be inelastic.
- In inelastic collisions the total kinetic energy after the event is not equal to the initial total kinetic energy.

**Super elastic Collision**

- This is where 2 objects are made to spring apart
- eg. the combustion and ejection of rocket fuel propels gas particles in one direction and the rocket in the other.

Make sure you know all the equations as you must need them in A2/A-level Physics exam! 👨🏫

**The Impulse Momentum equation:**

**F ∆t = mv - mu**

**The Work-Energy equation**

**Fs = ½mv ^{2} - ½mu^{2}**

Reference:

https://www.researchgate.net/figure/diagram-of-elastic-and-inelastic-collisions-Note-in-the-final-state-inelastic-case_fig2_48306542

This is the end of the topic!

Drafted by Cherry (Chemistry)