An object is accelerating on a rough surface with frictional force of 10N. Is the friction doing any work on the object? This question might look stupid to some but I am in great confusion. An object, say a box, is moving on a surface with some velocity v and is accelerating. It means that the force applied by the box is more than the frictional force. So, is friction doing any work on the box? 
 A: This is the scenario you describe:

You are applying a force $F_t$ on the box, so when the box moves a distance $d$ you have done an amount of work $F_t\,d$.
The box is applying a force $F_f$ to the ground (10N in this example) so when the box moves a distance $d$ it will have done work $F_f\,d$ on the ground.
So the work is being supplied by you (or whoever is doing the pushing) and part of that work is done on the box and the rest ends up being done on the ground. The work done on the box is the total work minus the work done on the ground:
$$ W_\text{box} = F_t\,d - F_f\,d = (F_t - F_f)d = F_\text{net}\,d $$
where $F_\text{net}$ is just the net force on the box.
A: The way to analyse this example is to first evaluate the net force on the box (the system) which in this case will be the applied force minus the frictional force and then multiply this net force by the displacement of the box along the line of action of the net force.
The work done will give you the change in kinetic energy of the box.
This is the work-energy theorem.
You can think of the frictional force doing negative work on the box because the frictional force is in the opposite direction the motion of the box.
What this means is that energy is "flowing" out of the box and in this case becoming heat.
A: According to the definition of the work ($\delta W=F\mathrm dx$), it is better that we say friction doesn't do work. Because, at each point of contact area, friction force is fixed and doesn't move.
Friction converts some portion of energy used to move the box, to heat.
