Work, energy and power

In an inclined plane, the work done by the force pulling an object up the plane contributes to the gain in potnetial energy of the object.
Let a be the angle of the inclinded plane
m be the mass of the object
L be the length travelled by the object along the plane.
Assume the object is moving up the plane at constant speed by a force F, we have
F = m.g.sin(a) + Ff,
wherr Ff is the frictional force and g is the acceleration due to gravity
The work done by the force W = F.L
i.e. W = [mg.sin(a) + Ff].L = (mg.sin(a)).L + Ff.L ------------------ (1)
The second term on the right is the work done against friction
The first term on the right, which is the work done by the force on moving a distance L along the plane, can be written as,
(mg.sin(a)).L = mg.(L.sin(a)) = mg.h
where h = L.sin(a) and from geometry, it is the (vertical) height attained by the object when it travells a distance L along the plane.
thus, we have,
work done by force = increase in PE + work done against friction
that is to say, the term [increase in PE] just represents the[work done by the force along the plane].
On a horizontal surface, angle a=0, thus equation (1) becomes
work done by force W = Ff.L
the result is obvious for an object travelling at constant speed. The applied force F is used to overcome friction.
If the plane is smooth, Ff=0, then no force is needed to keep the object moving at constant speed. Hence, no work is done.

1.
It is not true.It is because W=Fs is already equal to W=mgh.Look at the following working you will understand it clearly.
W=Fs,W=mgsinxs,W=mg(h/s)s,W=mgh<<=PE
sinx=h/s,subsitude it to the above equation.
2.
Since W=mgh=Fs.Thus,the second statement is also wrong.The answer should contains Fs and work done against friction.In the simple case,F will be a net force.As a result,F major contain the applied force and the friction force.In this case,the friction against friction should be omissed.