Question

a ladder of length l is placed between wall and the ground as shown in the diagram if velocity of a and b is 4 metre per second find the velocity of a and b with angle made by a ladder with the ground is 37 degrees​

Answer 1

Step-by-step explanation:

The free-body diagram of the ladder is shown in figure. Note that all the three forces acting on the ladder have to pass through a common point O, otherwise it cannot be in equilibrium.

The total reaction force F from the horizontal surface is inclined at an angle α(>θ) to the horizontal. The horizontal component of this force is friction force and its vertical component is the normal reaction applied by the ground on the ladder.

(b) Applying the conditions of equilibrium, we get

∑F

x

=0⇒f−N=0⇒f=N...(i)

∑F

y

=0⇒N

1

−Mg=0⇒N

1

=Mg...(ii)

Taking torque about centre of the rod

′

C

′

,∑τ

C

=0

(N

1

)

2

L

cosθ−(f)

2

L

sinθ−N

2

L

sinθ=0...(iii)

Substituting the value of N

1

and f from Eqs. (i) and (ii) in Eq. (iii), we get

Mg

2

L

cosθ−NLsinθ=0

⇒N=

2tanθ

Mg

=

2

1

Mgcotθ...(iv)

Thus, the net force applied by ground on the ladder is

F=

N

1

2

+f

2

F=

2

1

Mg

4+cot

2

θ