A uniform ladder AB leans against a smooth vertical wall at an angle 60degree to the horizontal.the weight of the ladder is 200N. By taking moments about a suitable point,calculate the reaction at the wall
Take moments about foot of ladder of length L
200 (L/2) sin 30 = F L sin 60
50 = F sin 60
F = 57.7 N
To calculate the reaction at the wall, we need to determine the moment due to the weight of the ladder.
First, let's consider the forces acting on the ladder. There are two forces: the weight acting downwards, and the reaction force at the wall acting perpendicular to the wall.
To balance the forces and keep the ladder in equilibrium, the moment due to the weight of the ladder must be equal and opposite to the moment due to the reaction force at the wall.
To calculate the moment due to the weight of the ladder, we need to determine the perpendicular distance between the line of action of the weight and the point where we are calculating the moment.
Let's assume the distance between the point where the ladder contacts the wall (point A) and the center of gravity of the ladder is "d."
The moment due to the weight of the ladder (M_weight) can be calculated using the equation:
M_weight = Weight × Perpendicular distance
The weight of the ladder is given as 200N, so M_weight = 200N × d.
Next, let's consider the moment due to the reaction force at the wall. Since the ladder is in equilibrium, the moment due to the reaction force (M_reaction) should be equal and opposite to the moment due to the weight of the ladder.
Thus, we have:
M_reaction = -M_weight
M_reaction = -(200N × d)
Now, let's set up an equation for the sum of the moments:
M_reaction + M_weight = 0
-(200N × d) + (200N × d) = 0
The moments cancel each other out, resulting in 0.
Therefore, the reaction at the wall is 0 Newtons.