Tension on Cables: Finding the Equilibrium Point
How can we determine the tensions on both cables when a 900 kg mass is hung with identical angles of 60° from the horizontal?
What are the steps to calculate the tensions on the cables?
Is there a specific formula we can use to find the tensions in this situation?
Calculating Tensions on Cables
When dealing with a mass hanging from cables at identical angles, we can determine the tensions on the cables using trigonometry and the concept of equilibrium. Each cable exerts an upward force at an angle of 60° from the horizontal, creating a balanced system.
To find the tensions on both cables, we can use trigonometry. Each cable is exerting a force upward at an angle of 60° from the horizontal. Let's denote the tension in one cable as T1 and the tension in the other cable as T2. Since the mass is in equilibrium, the vertical component of the tension in each cable must counteract the weight of the mass:
T1sin(60°) + T2sin(60°) = mg
where m represents the mass and g is the acceleration due to gravity. Given that the angles are the same, we have:
2Tsin(60°) = 900 kg * 9.8 m/s²
Solving the equation further:
T = \frac{900 kg * 9.8 m/s²}{2sin(60°)} = 4417 N
Therefore, the tension in each cable is 4417 N. By following these steps, we can accurately determine the tensions on both cables when a 900 kg mass is suspended at identical angles of 60° from the horizontal.