A uniform rod 8m long weighing 5kg is supported horizontally by 2 vertical parallel strings at P and Q and at distances of 2m and 6m from one end. Weights of 1kg, 1.5 kg, and 2kg are attatched at distances of 1m, 5m, and 7m respectively from the same end. Find the tension in each vertical string
To find the tension in each vertical string, we need to use the principle of moments, which 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 consider the point where the rod is supported by the vertical string at P. The clockwise moments about P can be calculated by multiplying the weight by the distance from P, while the anticlockwise moments can be calculated by multiplying the tension at P by the distance from P:
Clockwise moments about P:
1kg * 1m = 1kgm
1.5kg * 5m = 7.5kgm
2kg * 7m = 14kgm
Anticlockwise moments about P:
Tension at P * 2m = 2T
The sum of clockwise moments is equal to the sum of anticlockwise moments, so:
1kgm + 7.5kgm + 14kgm = 2T
22.5kgm = 2T
T = 22.5kgm / 2
T = 11.25kgm
Therefore, the tension in the vertical string at P is 11.25kgm.
Now, let's consider the point where the rod is supported by the vertical string at Q. We can use the same process as above, but this time we will only consider the weights and distances to the right of Q:
Clockwise moments about Q:
1.5kg * 5m = 7.5kgm
2kg * 7m = 14kgm
Anticlockwise moments about Q:
Tension at Q * 6m = 6T
The sum of clockwise moments is equal to the sum of anticlockwise moments, so:
7.5kgm + 14kgm = 6T
21.5kgm = 6T
T = 21.5kgm / 6
T = 3.58kgm
Therefore, the tension in the vertical string at Q is 3.58kgm.