Question

A large bird cage for an eagle is being hung in an aviary at the Oklahoma City Zoo. The mass of the cage is 25.0 kg and it is hung a distance h = 1.60 m below the top of the aviary by two cables. The cables are of equal length so that they make equal angles with the aviary roof. Each cable has a length of l = 3.10 m .

Determine the tension force, T, in each cable. (This is also the force the cables applies to the bird cage.)

Answer 1

as, height = 1.6 m, length of cable = 3.1 m.let, cable makes the angle with horizontal be ß. so,

sin ß = 1.6/3.1

ß = 30.8°

and,
the force of gravity (downwards) is mg, ie 25 * 9.8 = 245 N

Now let the tension in both the strings be T, therefore, the total upward force will be 2Tsin(30.8°)

Therefore 245 = 2Tsin(30.8°)
122.5 = Tsin(30.8°)
T = 122.5 / 0.51
T = 240.2 N

so, the tenion force on each cable is 240.2 N.