Question

A spring of spring constant $k$ placed horizontally on a rough horizontal surface. It is compressed against a block of mass m which is placed on rough surface, so as to store maximum energy in the spring. If the coefficient of friction between the block and the surface is $\mu$, the potential energy stored to the spring is : (block does not slide due to force of spring.)

• A. $\frac{{\mu }^2{m}^2{g}^2}{4k}$
• B. $\frac{{2\mu m}^2{g}^2}{k}$
• C. $\frac{{\mu }^2{m}^2{g}^2}{2k}$
• D. $\frac{{3\mu }^2{mg}^2}{k}$

Answer 1

The correct option is C $\frac{{\mu }^2{m}^2{g}^2}{2k}$

Equating force we get $\mu mg=kx$

$x=\frac{\mu mg}{k}$

Potential energy $PE=\frac{1}{2}k{x}^2=\frac{1}{2}\frac{{\mu }^2{m}^2{g}^2}{k}$