The ladder will slip at the point where the reaction at the wall is just over
the force due to friction.
Response:
- The minimum height below which the ladder will slip, is approximately 5.48 meters above the ground.
The given parameter are;
The coefficient of friction, μ = 0.753
Length of the ladder = 9.9 m
Mass of the ladder = 39 kg
Required:
The minimum height below which the ladder will slip.
Solution:
Assumption: The friction of the wall on the ladder is 0.
The weight of the ladder, W = The normal reaction = N
The friction force, = The reaction force of the wall,
= W × μ
Which gives;
= 39 × 9.81 × 0.753 ≈ 288.09
The friction force, ≈ 288.09 N =
Taking moments about the contact between the ladder and the ground, we have;
× h = W × x
Where;
Which gives;
θ = The angle made by the ladder and the ground
Therefore;
288.09 × 9.9·sin(θ) = 39 × 9.81 × x = 382.59 × 4.95·cos(θ)
Which gives;
The minimum height below which the ladder will slip, h ≈ <u>5.48 m</u>
Learn more about friction here: