Question

A picture of mass 5 kg is hung from a wire on a wall. If the wire is divided into two parts by a nail protruding from the wall, one part making an angle of 15◦ and the other making an angle of 10◦ , both with respect to the horizontal, what is the force in each part of the wire?

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 = 5*9.8 = 49 N

Now Using force balance in wires

In horizontal direction:

T1*cos 15 deg = T2*cos 10 deg

T1 = T2*cos 10 deg/cos 15 deg = 1.019*T2

Force balance in vertical direction

T1*sin 15 deg + T2*sin 10 deg = W

1.019*T2*sin 15 deg + T2*sin 10 deg = 49

T2 = 49/(1.019*sin 15 deg + sin 10 deg)

T2 = 112.03 N (Magnitude of tension in right wire)

T1 = 1.019*112.03

T1 = 114.15 N (Magnitude of tension in left wire)

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