A uniform bar of length 1.0m is pivoted 20cm from one end. The bar is kept in equilibrium by a spring balance 10cm from the other end. Given that the reading of the spring balance is 0.8N,determine the reaction force at the pivot
To determine the reaction force at the pivot, we need to consider the principle of rotational equilibrium. The principle states that for an object to be in rotational equilibrium, the sum of the clockwise moments around any point must be equal to the sum of the anticlockwise moments around the same point.
In this scenario, let's consider moments around the pivot point. The distance between the pivot point and the spring balance is 20cm, and the distance between the pivot point and the opposite end is 80cm (1.0m - 20cm).
We know that the reading of the spring balance is 0.8N, which represents the force acting at a distance of 10cm from the pivot point. To find the moment caused by this force, we multiply the force by its perpendicular distance from the pivot point:
Moment = Force × Distance
Moment = 0.8N × 0.10m
Moment = 0.08 Nm
Now, we assume that the pivot exerts a reaction force F at the pivot point. The reaction force has no moment arm because it acts directly at the pivot point. Therefore, its moment contribution is zero.
Since the net moments around the pivot point must be zero for rotational equilibrium, we can write the equation:
Sum of clockwise moments = Sum of anticlockwise moments
0.08 Nm = F × 0
Solving this equation, we find that the reaction force at the pivot is 0.08 N.