Did you know?
Did you know that the tension in each vertical string can be found by using the principles of torque? Torque is a force that causes an object to rotate, and in this case, it is being applied to the uniform rod. By considering the torques acting on the rod, we can determine the tension in the strings.
First, let's label the distances of the weights from the same end: 1m, 5m, and 7m. The weight of the rod, 5kg, can be considered as acting at its midpoint, which is 4m from the same end.
To find the tension at point P, we need to consider the clockwise torque caused by the 5kg weight and the counterclockwise torque caused by the tension at P. The clockwise torque is calculated by multiplying the weight (mass x gravitational acceleration) by its distance from point P. In this case, it is (5kg x 9.8m/s^2 x 4m) = 196 Nm.
The counterclockwise torque is the product of the tension at P and its distance from the weight at 4m. Since it is at a distance of 2m, the counterclockwise torque is 2P Nm (where P represents the tension at point P).
To achieve balance and no rotational motion, the clockwise torque and counterclockwise torque must be equal. Therefore, we have the equation 2P = 196 Nm.
Similarly, for point Q, the clockwise torque caused by the 5kg weight is (5kg x 9.8m/s^2 x 2m) = 98 Nm, and the counterclockwise torque caused by the tension at Q is 6Q Nm (where Q represents the tension at point Q). Setting these torques equal, we have the equation 6Q = 98 Nm.
By solving these equations, we can find that the tension at point P is 98 N, and the tension at point Q is 32.67 N.