The Force Transformation
In classical Newtonian mechanics force is defined as rate of change of momentum:
Special relativity changes the definition of both momentum and time, so the definition of force must change.
If we have inertial frames O and O', with O' moving along the positive x axis of O with speed u,
In the coordinate frame O'
and
Substituting
into the first of these gives
But
Hence
From the definition of force
so 
If all the work done by a force manifests as an increase in the kinetic energy, KE, of the particle then
Dividing both sides by
gives 
Hence
Also
and