Question

A uniform ladder having length 10 m mass 24 kg is resting against a vertical wall at an angle 53

Answer 1

Complete the question

Answer 2

There are four forces acting on the ladder of length L and making ?=53 degrees with the vertical smooth wall and on a horizontal rough floor.

1. the weight W=(10x9.8) =98N acting downwards through the middle of the ladder

2. vertical reaction on the floor acting upwards, equal to W.

These two forces form a couple of magnitude

W(L/2)sin?

3. Normal reaction N on the wall (horizontal) at the top end of the ladder, equal in magnitude to

4. Frictional force F acting horizontally at the bottom of the ladder.

These two forces form another couple equal to FLcos?.

Since the ladder is in equilibrium, the two couples must be equal, thus

W(L/2)sin? = FLcos?

From which we can solve for F

= (W/2)tan?

= (98/2) tan 53o

= 65 N