A loudspeaker of mass 23.0kg is suspended a distance of h = 1.80m below the ceiling by two cables that make equal angles with the ceiling. Each cable has a length of l = 3.90m. What is the tension T in each of the cables?
Use 9.80 m/s^2 for the magnitude of the acceleration due to gravity.

T = 243.80 N

Explanation:

In order to calculate the tension T in each of the cables, you take into account the Newton second law for the vertical component of the forces involved.

    (1)

where you have used the fact that both cables have the same tension T, and they make the same angle with the horizontal.

W is the weigh of the loudspeaker and has the folowing values:

Next, you can calculate the angle θ by using the information about the length of the cables and the distance from the ceiling to the loudspeaker:

Finally, you solve the equation (1) for T, and then you replace the values of the other parameters:

The tension in each cable is 243.80N

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