The right angle uniform slender bar AOB has mass m. Assuming a frely hinged pivot O, determine the magnitude of the normal force at A and the magnitude of the pin reaction at O.
To determine the magnitude of the normal force at point A and the pin reaction at pivot O, we need to analyze the forces acting on the bar AOB.
Let's break down the problem and consider the various forces acting on the bar:
1. Weight (mg): The bar has a mass m, so it experiences a downward force due to gravity, which is given by the product of mass (m) and gravitational acceleration (g).
2. Normal force at A: This force is perpendicular to the surface of the bar at point A. It acts in such a way that it counterbalances the weight of the bar in the vertical direction.
3. Pin reaction at O: This force acts at the pivot O and keeps the bar in equilibrium. It maintains the rotational and translational stability of the bar.
To find the magnitudes of the normal force at A and the pin reaction at O, we need to consider the rotational equilibrium of the bar.
Since the bar is in equilibrium, the sum of the moments about any point, in this case, O, must be zero.
For the horizontal equilibrium:
1. The clockwise moment due to the normal force at A is zero since the lever arm distance is zero.
For the vertical equilibrium:
1. The anti-clockwise moment due to the weight (mg) is zero since the lever arm distance is zero.
Therefore, we can write the equation for vertical equilibrium as:
mg = Normal force at A
Hence, the magnitude of the normal force at A is equal to the weight of the bar, which is given by mg.
Now, let's analyze the forces acting at the pivot O.
The forces acting at O are the pin reaction R and the normal force NA. Since the bar is in equilibrium, the horizontal and vertical forces acting at O must sum up to zero.
For horizontal equilibrium:
1. The pin reaction R will create an anti-clockwise moment with a lever arm equal to the length of the bar (OB).
For vertical equilibrium:
1. The normal force at A will create a clockwise moment with a lever arm equal to the perpendicular distance from O to the line of action of the normal force.
Since the lever arms are not given, we cannot determine the exact magnitudes of the forces without additional information or calculations, such as knowing the length and dimensions of the bar.
To find the magnitudes of the pin reaction R and the normal force at A, we need specific details about the dimensions and angles of the bar.