movement of wire at the signal boxthe wire

Question

Movement of wire at the signal box:

The wire working on railway signal is 5mm in diameter and 300m long. If movement at the signal end is to be 25cm, make calculations for movement which should be given to the end of wire at the signal box. Assume that the pull of 2500N on wire and take modulus of elasticity for wire material as 2 × 10⁵  N/mm².

Sol.: Given data:

P = 2500N

D = 5 mm

L = 300m = 300 × 1000 mm

D_m  = 25cm

E = 2 × 105 N/mm2.

We know that, σ = P/A

σ = P/ ( Π /4 × D²)

σ = 2500/ ( Π /4 × 5²)

σ = 127.32 N/mm².

e =   σ/E = 127.32/2 × 10⁵

e = 0.0006366

As  e =   δL/L

δL = e.L = 0.0006366 × 300 × 1000 = 190.98mm = 19.098 cm

Total movement which is required to be given at the signal box end = 25 + 19.098 = 44.098 cm .......ANS