Force And Momentum

> When two or more bodies collide the effect they have on each other depends on there initial velocities(Before the collision) and on there masses.

Momentum = Mass x Velocity

> The unit of momentum is kgmsֿ¹

Force = Mass x Acceleration

F = ma

> Newtons First Law - An object remains at rest or in uniform motion unless acted on by a force

> Newtons Second Law - The rate of change of momentum of an object is proportional to the resultant force on it. In other words, the resultant force is proportional to the change of momentum per second.

> Initial momentum = mu

u = Initial velocity

Final momentum = mv

v = Final velocity

Change in momentum = Final momentum - Initial momentum

Change in momentum = mv - mu

> Newtons second law stats that the force is proportional to the change in momentum per second.

F α change in momentum / time taken = mv - mu / t = m (v - u) / t = ma

a = v - u / t = The acceleration of the object

> When m is constant:

Δ(mv) = mΔv

> Where Δv is the change of velocity of the object

F = Δ(mv) / Δt

> When m is changing at a constant rate:

Δ(mv) = vΔm

F = vΔm / Δt

Where Δm / Δt = Change of mass per second

Impulse = FΔt = Δ(mv)

> Therefore, The impulse of a force acting on an object is equal to the change of momentum of the object

> In a Force-Time graph, the area under the line = change in momentum = Ft

Force of impact, F = Change of momentum / Contact time = mv / t

F = mv - mu / t

> When an object rebounds it's momentum reverses

The change in momentum = Final momentum - Initial momentum

Impact Force, F = Change in momentum / Contact time = (-mv) - (mu) / t

> Newtons third law - When two objects interact, they exert an equal and opposite force on each other.

mьvь + mаvа = mаuа + mьuь

> The principle of conservation of momentum states that in a system of interacting objects, as long as there are no external resultant forces acting on the system, then the total moment remains constant.

Total momentum after = Total momentum Before

> If in a collision the objects together then they will have the same final velocity.

(mь + mа)V = mаuа + mьuь

1.4 Elastic And Inelastic Collision

> An elastic collision is a collision in which there is no lose of kenetic energy.

> If the objects stick together when they collide then the collision is totally inelastic.

> If the collision is only partially inelastic then the objects will separate but have less kinetic energy than before.

1.5 Explosion

In an explosion the initial momentum = 0

The total momentum immediately after the explosion = Momentum A + Momentum B

= mаvа + mьvь