Question

Suppose a ladder of length L = 8 m and mass m = 20 kg is leaning up against a wall such that it makes an angle of θ = 70 degree angle with the floor and is not moving. For this problem, we'll say there is no one standing on the ladder. Just like the very last problem on the discussion worksheet, we'll also imagine that the ladder is up against a very smooth wall so that there is no frictional force exerted on the ladder by the wall, but there is a frictional force between the bottom of the ladder and the floor. What is the magnitude of the fictional force between the ladder and the floor?

Answer 1

Answer:

fr = 269.3 N

Explanation:

Let's use Newton's second law, for this it is good to see the attached diagram,

X axis

    fr -F2 = 0

    fr = F2

Y Axis

   N-W = 0

We must include the rotation balance, place the rotation point at the bottom of the ladder and take the positive counterclockwise turns.

    Σ τ  = 0

    F2 x -W y / 2 = 0

We look for x and y with trigonometry

    sin 70 = y / L

   cos 70 = x / L

   y = L sin70

   x = L cos 70

We substitute and calculate F2

   F2 L cos 70 = W  L sin 70 / 2

   F2 = mg/2  tan 70

   F2 = 20 9.8/2  tan 70

   F2 = 269.3 N

From the first equation (x axis)

   fr = F2

   fr = 269.3 N