I have read some questions regarding just Work and K.E in these Q&As: Relation and difference between work and kinetic energy AND Understanding relationship between work and energy.
My question includes the involvement of Friction as well.
Assume there is an object being pulled at an angle with the horizontal, with a force, for a certain distance along surface that has friction as well.
By drawing the free body diagram, I get sum of forces in the x-axis to be $$F(net) = (Fcosθ - μmg)$$ because Fcosθ is in the +ve x direction and friction (μmg) is acting in -ve x direction.
We know that: $$W = Fdcosθ$$ Which means, $$W = (Fcosθ - μmg) . d$$
Would this work done, be equal to the K.E of the box after being pulled for the distance d?
Since Energy is conserved when there is no friction or anything that disrupts the system, if accounting for Work done includes the repelling force of friction, this Work done should equal the K.E of the body.
Am I right in understanding the concept?