Final answer:
The tension of each wire in the metal tube is Tension_1 = 33.075 N and Tension_2 = 11.025 N.
Step-by-step explanation:
To find the tension of each wire, we can use the principle of static equilibrium. The sum of the forces in the vertical direction must be zero, since the tube is not moving vertically. The downward force is the weight of the tube, which is given by the mass multiplied by the acceleration due to gravity. The upward forces are the tensions in the wires. Let's call the tension in the first wire T1 and the tension in the second wire T2.
Using the principle of static equilibrium, we can write the following equation:
2T1 + 2T2 = mg
where m is the mass of the tube and g is the acceleration due to gravity.
We also know that the distance between the first wire and the center of mass of the tube is 50 cm, and the distance between the second wire and the center of mass of the tube is 150 cm. We can use these distances to find the torques exerted by the tensions on the tube. The torques must balance each other out to maintain static equilibrium.
Using the torque formula, we can write the following equations:
T1 * 0.5 m = T2 * 1.5 m
T1 = 3T2
By substituting T1 = 3T2 in the first equation, we can solve for T2:
2(3T2) + 2T2 = mg
8T2 = mg
T2 = mg/8
Finally, by substituting T2 in the equation T1 = 3T2, we can solve for T1:
T1 = 3 * (mg/8)
Now we can plug in the given values: m = 9 kg and g = 9.8 m/s² to calculate the tensions:
T2 = (9 kg * 9.8 m/s²)/8 = 11.025 N
T1 = 3 * 11.025 N = 33.075 N
Therefore, the tension of each wire is Tension_1 = 33.075 N and Tension_2 = 11.025 N.