G484: Module 1: Newton's Laws and Momentum

Newton's first law: a force is necessary to change the state of rest or of uniform motion in a straight line of a body.

• If you are stationary, you will remain stationary unless a resultant (net) force acts on you.
• If you want to change your direction of travel, a resultant force must act on you
• If you want to speed up or slow down, a resultant force must act on you.
• If you are moving with constant velocity, there is zero reultant force acting on you.

Force causes acceleration: zero resultant force, zero acceleration

Linear momentum: the mass of an object multiplied by its velocity. It is a vector. The symbol used for momentum is p.

p=mv

KE     =>    force x distance = change in KE    => Fd=0.5mv^2 - 0.5mu^2  => Nm=J

                                                      Scalar Quantity

Momentum   =>   force x time = change in mom   =>  mv - mu    =>  Ns

                                                       Vector Quantity

Newton's second law: The rate of change of the momentum of an object is directly proportional to the resultant (net) force acting upon it.

                                     F(proportional to) mv - mu/t

F(proportional to) m(v-u)/t,           which gives     F(proportional to) ma

One newton is the force that causes a mass of one kilogram to have an acceleration of one metre per second each second. 

1kg x 1ms^-2 = k x 1N

Newton's second law becomes F=ma if the mass is constant. 

Newton's third law states that when body A exerts a force on body B, then body B exerts a force on body A that is equal and of the same type but opposite in direction. 

Conditions of the two forces:

They must be equal in magnitude, they must be in opposite directions and they must be the same type of force. E.g. if one was an electrical force, then the other must also be electrical. 

The principle of conservation of momentum states that, in any direction, in the absence of external forces, the total momentum of a system remains constant. 

Impulse is defined by the expression FΔt. It equals the change in momentum of a body. It is equal to the area beneath a force-tim graph. 

A perfectly elastic collision is one in which no momentum or kinetic energy is lost. An inelastic collision is one in which momentum is conserved but kinetic energy is lost. 

Conservation of momentum can be applied to nuclear particles. CERN particle accelerator: a large number of particles were produced, and each left a track showing its path. The paths are curved because the collision took place in a strong magnetic field. The particle that spirals inwards as it loses energy is an electron.