A uniform plank AB of length 4.6 m and weight 508 N is suspended by a vertical rope at each end.A girl of weight 305 N stands in the position 1.6 m from one end.Calculate the tension in the rope at one end using the other end as axis of rotation.
Hint: the moment about the axis of roation is zero.
To calculate the tension in the rope at one end of the plank, we can use the principle of moments.
The principle of moments states that the sum of the clockwise moments about any point is equal to the sum of the anticlockwise moments about the same point.
Let's choose the other end of the plank as the axis of rotation. This means that the distance between the axis of rotation and the girl is 4.6 m - 1.6 m = 3 m.
First, we need to calculate the moment due to the weight of the plank. The weight of the plank acts in a downward direction and is located at the midpoint of the plank, which is 2.3 m from each end. So the moment due to the weight of the plank is:
Moment of plank = weight of plank x distance of plank's center of gravity from the axis of rotation
= 508 N x 2.3 m
Next, we need to calculate the moment due to the weight of the girl. The weight of the girl acts in a downward direction and is located at a distance of 1.6 m from the chosen axis of rotation. So the moment due to the weight of the girl is:
Moment of girl = weight of girl x distance of girl from the axis of rotation
= 305 N x 1.6 m
According to the principle of moments, the sum of the clockwise moments (negative moments) should be equal to the sum of the anticlockwise moments (positive moments). Therefore, the tension in the rope at one end can be calculated as:
Tension in rope = Moment of plank / distance of the other end from the axis of rotation
= (508 N x 2.3 m) / (4.6 m - 1.6 m)
Simplifying this expression will give you the numerical value of the tension in the rope at one end.