Question

A metal wire of length L is suspended vertically from a rigid support . When a Bob of mass M is attached to the lower end of the wire the elongation of the wire is l: Find
a) the elastic constant of the wire b) heat produced during extension

Answer 1

Elastic constant will be mg/l

Answer 2

Given:

Length of the wire: L

Mass of bob: M

Elongation of wire: l

To Find:

a) elastic constant of the wire Y=?

b) heat produced during extension W=?

Calculation:

a) Elastic constant is given by:

$Y=\frac{\frac{F}{A}}{\frac{\Delta L}{L}}$

Where, F is the force on the wire which is the weight of the bob.

F = Mg

A = is the area of the cross section of the wire.

ΔL= l (extension in the wire).

L is the length of the wire.

$Y=\frac{Mg/A}{l/L}=MgL/lA$

b)  Work done the wire will be the heat produced during extension.

$dW= F.dx\\W =\int\limits^l_0 {\frac {AY}{L}} \, xdx \\W= \frac{AYl^2}{2L}$

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