Answer:
a) is demonstrated below, b) T=1.462N, c) T=14.6N
Step-by-step explanation:
a) Refer to the attached diagram.
Since the bird is standing in the middle of the line and each half is a straight line, Ta=Tb, so we will call the tension T=Ta=Tb and Tay=Tby
By trigonometry Tay=Ta·Sinθ
Since the system is in equilibrium W=Tay+Tby then:
W=2·Tay=2·Ta·Sinθ=2·T·Sinθ
Since W=mg, being m the mass of the bird and g, gravity:
[tex]mg=2TSin\theta[/tex]
Isolating T, we demonstrate that
[tex]T=\frac{mg}{2Sin\theta}[/tex]
b) Replacing θ=5º, m=0.026kg and g=9.8m/s² in the last equation, we can get the tension in Newtons:
[tex]T=\frac{0.026*9.8}{2Sin5}=1.462N[/tex]
c) With θ=0.5º
[tex]T=\frac{0.026*9.8}{2Sin0.5}=14.6N[/tex]
