Question

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.

Answer 1

Answer:

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.

$Tsin\theta+Tsin\theta-W=0$     (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:

$W=Mg=(23.0kg)(9.8m/s^2)=225.4N$

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:

$sin\theta=\frac{1.80m}{3.90m}=0.461\\\\\theta=sin^{-1}(0.461)=27.48\°$

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

$2Tsin\theta-W=0\\\\T=\frac{W}{2sin\theta}=\frac{225.4N}{2sin(27.48\°)}=243.80N$

The tension in each cable is 243.80N