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A monkey weighs 6.00 x 102 N and swings from vine to vine. As the monkey grabs a new vine, both vines make an angle of 35.0° with the vertical. In such a condition of static equilibrium, what is the net force on the new vine? ANS: 366 N

Respuesta :

Answer:

[tex]T=366.23\ N[/tex]

Explanation:

Given:

  • mass of monkey, [tex]w=600\ N[/tex]
  • angle of vine from the vertical, [tex]\theta=35^{\circ}[/tex]

Now follow the schematic to understand the symmetry and solution via Lami's theorem.

The weight of the monkey will be balanced equally by the tension in both the vines:

Using Lami's Theorem:

[tex]\frac{w}{sin\ 70^{\circ}} =\frac{T}{sin\ 145^{\circ}}[/tex]

[tex]\frac{600}{sin\ 70^{\circ}} =\frac{T}{sin\ 145^{\circ} }[/tex]

[tex]T=366.23\ N[/tex]

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