Question

You want to lean your dad's ladder on a smooth wall. If the mass of ladder is 4.42 kg and coefficient

of friction of the floor is 0.53, what is the minimum angle, theta-min at which the ladder does nofip? What
do you think the maximum angle theta-max could be? Sketch and label your free body diagram.
(5 marks)​

Answer 1

angle minimum θ = 41.3º

Step-by-step explanation:

For this exercise let's use Newton's second law in the condition of static equilibrium

N - W = 0

N = W

The rotational equilibrium condition, where we place the axis of rotation on the wall

We assume that counterclockwise rotations are positive

fr (l sin θ) - N (l cos θ) + W (l/2 cos θ) = 0

the friction force formula is

fr = μ N

fr = μ W

we substitute

μ m g l sin θ - m g l cos θ + mg l /2 cos θ = 0

μ sin θ - cos θ + ½ cos θ= 0

μ sin θ - ½ cos θ = 0

sin θ / cos θ = 1/2 μ

tan θ = 1/2 μ

θ = tan⁻¹ (1 / 2μ)

θ = tan⁻¹ (1 (2 0.57))

θ = 41.3º