Question

A stainless steel cable (density J = 7.8 x 103 kg / m ’) of section 1.5 mm2 is subjected to a pulse that moves at a speed of 200 m / s. Its breakdown voltage is 500 N / mml.
> Detach if the cable breaks or holds up when the impulse passes.
The data.
Wire section: S = 1.5 mm ^ 2
Steel density: d:. 7.8 * 10 ^ 3 kg / m "
Pulse speed 200 m / s
Breaking tension of stainless steel: F = 500 N / mm2
Voltage due to impulsn: F =?

Answer 1

The relation between wave velocity and tension on a stretched string is given by

Where is the mass per unit length of the wire.

Here, v = 200 m/s

Density of wire = 7800 kg/m³

Cross section of wire = 1.5 mm² = 1.5*10^-6 m²

Thus linear density = D*A = 7800*1.5*10^-6 = 0.0117 kg/m

Thus,

The breaking tension is F = 500N.

So, the cable will hold up.