M = 1.8 kg
μ = 0.25
F acts at 45⁰ with horizontal.
s = displacement horizontally = 2 meters.
Frictional force along the horizontal in the direction opposite to the displacement
= Ff = μ * N = μ m g = 0.25 * 1.8 kg * 10 m/s² = 4.5 Newtons
Work done by the Frictional force = Wf = Ff . s = 4.5 * (-2 meters) = - 9 Joules
(it is negative as displacement is in the opposite direction to friction).
The component of force F, along the horizontal in the direction of s :
F Sin 45⁰ = F/√2
Since, the block moves with a uniform speed, there is no net force on the block. Hence
F/√2 = Ff = 4.5 Newtons
F = 4.5 √2 Newtons
Work done by F on the block = F . s = F/√2 * 2 = 9 Joules.
This is positive as the force does positive work on the block.
Gravitational force, ie., the weight and the normal force N are perpendicular to the displacement vector. Hence, the dot product is 0, for the work done.