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5. Ropes 3 m and 5 m in length are fastened to a holiday decoration that is suspended over a town square. The decoration has a mass of 5 kg. The ropes, fastened at different heights, make angles of 52 and 40 with the horizontal. Find the tension in each wire and the magnitude of each tension. Hint: The lengths of the wires have nothing to do with the tension in each wire. slader

Respuesta :

Answer:

Explanation:

Let T1 be the tension in rope of length 3 m and T2 be the tension in the rope of length 5 m.

Mass = 5 kg

Resolve the components of T1 and T2 and maintain the equilibrium in vertical and in horizontal direction.

First take equilibrium in horizontal direction:

[tex]T_{1}Sin52+T_{2}Sin40 = 5\times 9.8[/tex]

0.788 T1 + 0.642 T2 = 49 .... (1)

Take the equilibrium in horizontal direction

[tex]-T_{1}Cos52+T_{2}Cos40 =0[/tex]

-0.62 T1 + 0.766 T2 = 0    .... (2)

By solving equation (1) and (2) we get

T2 = 30.26 N

T1 = 37.53 N

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