Question 7.5: A uniform ladder is standing on rough ground and leaning aga...
A uniform ladder is standing on rough ground and leaning against a smooth wall at an angle of 60° to the ground. The ladder has length 4 m and mass 15 kg. Find the normal reaction forces at the wall and ground and the friction force at the ground.
The diagram shows the forces acting on the ladder.
The forces are in newtons.
The diagram shows that there are three unknown forces S, R and F so we need three equations from which to find them. If the ladder remains at rest (in equilibrium) then the resultant force is zero and the resultant moment is zero. These two conditions provide the three necessary equations.
Equilibrium of horizontal components: S – F = 0 ①
Equilibrium of vertical components: R – 15g = 0 ②
Moments about the foot of the ladder:
R × 0 + F × 0 + 15g × 2 cos 60° – S × 4 sin 60° = 0
⇒ 147 – 4S sin 60° = 0 ③
⇒ S =\frac{147}{4 sin 60°} = 42.4
From ① F = S = 42.4
From ② R = 147 .
The force at the wall is 42.4 N those at the ground are 42.4 N horizontally and 147 N vertically.
