Question

One end of a slack wire (Youngs modulus $Y$, length $L$ and cross -sectional area A) is clamped to a rigid wall and the other end to a block (mass m) which rests on a smooth horizontal plane. The block is set in motion with a speed v. What is the maximum distance the block will travel after the wire becomes taut?

• A. $v\sqrt{\frac{mL}{AY}}$
• B. $v\sqrt{\frac{2mL}{AY}}$
• C. $v\sqrt{\frac{mL}{2AY}}$
• D. $L\sqrt{\frac{mv}{AY}}$

Answer 1

The correct option is A $v\sqrt{\frac{mL}{AY}}$

The strain energy of a elastic wire is given by $\frac{1}{2}VY{\epsilon }^2$

where V is the volume of wire and $\epsilon$ is the strain.

Let the maximum elongation be x. At this point block will come to rest and all the kE energy will be converted to strain energy .

$\epsilon =\frac{x}{L}$

$V=AL$

Now we know

$\frac{1}{2}ALY{\left(\frac{x}{L}\right)}^2=\frac{1}{2}m{v}^2$

$x=v\sqrt{\frac{mL}{AY}}$