A uniform ladder has a weight of 100N. One end presses against the beam of the house and the other against the floor as shown in the diagram. The normal reaction from the wall is Fw and the reaction from the floor is Fg at an angle of 60° to the horizontal.
(a) Draw vector diagrams to show (i) the forces on the staircase and (ii) the horizontal and vertical components of Fg.
(b) Calculate the magnitude of the vertical (Fv) and horizontal (Fh) components of Fg.
(c) Calculate the magnitude of Fg.
(d) Calculate Fw

Fig 1

Answer

(a)

((b) The force Fg can be resolved into two forces at right angles to each other
Fh and Fv.

Recall Sin θ = ^{opposite}/_{hypotenuse} and Cos θ = ^{adjacent}/_{hypotenuse}

so Sin 60° = ^{Fv}/_{Fg} -----Eq 1

and Cos 60° = ^{Fh}/_{Fg} --- Eq2

From Eq1 Fg = = ^{Fh}/_{Cos 60°} --- Eq3

From Eq2 Fg = ^{Fv}/_{Sin 60°}--- Eq4

Fig 2

Figure 2 can be redone to show the components of Fg (Fv and Fh)

The ladder is in equilibrium:
Recall from Newton's First and Second Laws the conditions for static equilibrium: