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
To calculate the reaction at the wall, we can use the principle of moments. Moments are calculated by multiplying the force by the perpendicular distance from the point of rotation.
Here's a step-by-step explanation of how to calculate the reaction at the wall:
Step 1: Draw a diagram of the ladder leaning against the wall. Label the points A (where the ladder touches the ground), B (where the ladder touches the wall), and the center of gravity, G.
Step 2: Identify the forces acting on the ladder. In this case, there are two forces: the weight of the ladder (200N) acting downwards at the center of gravity, G, and the reaction force at the wall, R, acting perpendicular to the wall at point B.
Step 3: Choose a suitable point to take moments. In this case, let's choose point A, where the ladder touches the ground.
Step 4: Find the perpendicular distance between the point of rotation (A) and the line of action of each force. The perpendicular distance for the weight is the horizontal distance from A to G (denoted as d), and the perpendicular distance for the reaction force at the wall is the length of the ladder (denoted as L).
Step 5: Write down the equation for the principle of moments:
Sum of clockwise moments = Sum of anticlockwise moments
d * 200N = L * R
Step 6: Since we are interested in finding the reaction force at the wall (R), rearrange the equation to solve for R:
R = (d * 200N) / L
Plug in the values for d (the horizontal distance from A to G) and L (the length of the ladder), which should be provided in the problem statement. The unit of force should be in Newtons (N).
By substituting the values, you can calculate the reaction force at the wall.