Question

A picture of mass 2.5 kg hangs from a wire that rests on a nail in...

A picture of mass 2.5 kg hangs from a wire that rests on a nail in a wall. If the picture is lopsided so that the angle that the wire makes on one side is 10◦ and the angle that the wire makes on the other side is 20◦ , find the tension in each part of the wire.

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Answer #1

After dividing wire into two parts, Suppose

Suppose tension in left rope = T1

Tension in right rope = T2

Weight of picture, W = m*g

W = 2.5 * 9.8

= 24.5 N

Now Using force balance in wires

In horizontal direction:

T1 * cos 10 = T2 * cos 20

T1 = T2 * cos 20 / cos 10 deg

T1 = 0.9728 * T2

Force balance in vertical direction

W = T1*sin 10 + T2*sin 20  

24.5 = 0.9728 * T2 * sin 10 + T2* sin 20

24.5 = 0.1689 * T2 + 0.3420 * T2

24.5 =( 0.1689 + 0.3420) T2

T2 = 47.95 N

The magnitude of tension in right wire is 47.95 N

T1 = 0.9728 * T2

T1 = 0.9728 * 47.95

  T1 = 46.645 N

The magnitude of tension in left wire is 46.645 N

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