The tension in the wire attached at 150 cm (T₁) is approximately 110.25 N, and the tension in the wire attached at 50 cm (T₂) is 88.2 N.
How to determine tension in each wire
Given:
Length of the tube, L = 5 meters
Mass of the tube, m = 9 kg
Acceleration due to gravity, g ≈ 9.8 m/s²
The total weight of the tube (W) can be calculated as:
Weight (W) = mass × acceleration due to gravity
Weight (W) = 9 kg × 9.8 m/s² = 88.2 N
Now, the tube's weight acts at its center of mass, which is at L/2 = 2.5 meters from either end.
Let T₁ and T₂ be the tensions in the wires attached at 150 cm (1.5 meters) and 50 cm (0.5 meters) from the end of the tube, respectively.
Using the principle of torque balance:
The clockwise torque is due to the tension in the wire at 50 cm, and the counterclockwise torque is due to the tension in the wire at 150 cm.
T₂ × 2.5 meters = W × 2.5 meters
T₂ = (W × 2.5 meters) / 2.5 meters = 88.2 N
Now, find the tension in the wire at 150 cm:
T₁ × 2 meters = W × 2.5 meters
T₁ = (W × 2.5 meters) / 2 meters = (88.2 N × 2.5 meters) / 2 meters = 110.25 N
Therefore, the tension in the wire attached at 150 cm (T₁) is approximately 110.25 N, and the tension in the wire attached at 50 cm (T₂) is 88.2 N.