To determine the distance, x, that a person can walk on the overhanging part of the plank before it begins to tip, we need to find the point of equilibrium.
First, let's find the total weight of the plank. The weight of the plank is given as 231N.
Next, let's find the total weight acting on the overhanging part of the plank. The weight of the person is given as 477N.
Since the person is walking on the overhanging part, the weight of the person acts at a distance of x from the right support.
From the point of equilibrium, the clockwise and counterclockwise moments must balance each other.
The counterclockwise moment is given by the weight of the person multiplied by the distance x:
Counterclockwise moment = Weight of the person ร distance x = 477N ร x
The clockwise moment is given by the weight of the plank multiplied by the distance d:
Clockwise moment = Weight of the plank ร distance d = 231N ร 1.34m
For the plank to be in equilibrium, the clockwise and counterclockwise moments must be equal:
477N ร x = 231N ร 1.34m
To find x, rearrange the equation:
x = (231N ร 1.34m) / 477N
Calculating the value of x:
x = (309.54 Nยทm) / 477N
x โ 0.648 m
Therefore, a person can walk on the overhanging part of the plank for a distance of approximately 0.648 meters before it begins to tip.