Question

A loudspeaker of mass 17.0kg is suspended a distance of h = 2.40m below the ceiling by two cables that make equal angles with the ceiling. Each cable has a length of l = 2.50m .

What is the tension T in each of the cables?

Use 9.80m/s2 for the magnitude of the acceleration due to gravity.

Answer 1

Acording to the previous free body diagram we know that both tensions should have the same magnituds as the cables make equal angles with the ceilling. Eitherway this can be seen and proved easily from the summation of all forces acting along the x direction as follows:

Since the system is in equilibrium along both y and x axes. Now moving one of the terms to the right hand side we get:

, from where

WHICH INMEDIATELY LEADS US TO THE CONCLUSION THAT T1 MUST BE EQUAL TO T2(T1=T2).

Now from the summation of all forces acting along the y-axis we get:

From where we can solve for T1 or T2 which we already proved that have the same magnituds, so we can wrte down T1=T2=T=Tension in each cable. So this way we finally get:

or

or

or

*** Equation

Now right from the graph we know using a little of trigonometry, that

This way plugging this value for into our *** Equation we get:

End