A worker pulls a crate with a mass of 30kg from rest along a horizontal floor, by applying a constant force of magnitude 50 N at an angle of 30° to the horizontal. A frictional force of magnitude 20 N acts on the crate whilst it is moving along the floor.

The applied force is $F_{app} = 50 \text{ N}$ at an angle $\theta = 30^\circ$ to the horizontal.

The magnitude of the horizontal component of the applied force is $\boxed{43.30 \text{ N}}$.

6.3.2 work done by the horizontal component of the applied force.

The horizontal component of the applied force is $F_x = 43.301 \text{ N}$ (from 6.3.1).
The displacement is $d = 6 \text{ m}$.

Work done ($W$) is given by $W = F \cdot d \cos \phi$. Since the force is horizontal and the displacement is horizontal, $\phi = 0^\circ$ and $\cos(0^\circ) = 1$.

The work done by the horizontal component of the applied force is $\boxed{259.81 \text{ J}}$.

6.3.3 work done due to the frictional force acting on the box.

The frictional force is $F_f = 20 \text{ N}$.
The displacement is $d = 6 \text{ m}$.

The frictional force acts opposite to the direction of motion, so the angle between the force and displacement is $\phi = 180^\circ$.

The work done due to the frictional force is $\boxed{-120 \text{ J}}$.