Question

Two blocks $A$ and $B$ are connected to each other by a string and a spring; the string passes over a frictionless pulley as shown in the figure. Block $B$ slides over the horizontal top surface of a stationary block $C$ and the block $A$ slides along the vertical side of $C$, both with the same uniform speed. The coefficient of friction between the surfaces of blocks is $0.4$. Force constant of the spring is $1240\, N / m$. If mass of block $A$ is $4\, kg$. Calculate the energy (in joule) stored in the spring. (Take $g =10\, m / s ^{2}$ )

Answer 1

Normal reaction between blocks $A$ and $C$ will be zero. Therefore, there will be no friction between them. Both $A$ and $B$ are moving with uniform speed. Therefore, net force on them should be zero.

For equilibrium of $A$
$m _{ A } g = kx$
$\therefore x =\frac{ m _{ A } g }{ k }=\frac{4 \times 10}{1240}$
$=\frac{40}{1240}=\frac{1}{31}$
Energy stored in spring
$U =\frac{1}{2} kx ^{2}=\frac{1}{2}(1240)\left(\frac{1}{31}\right)^{2}$
$=0.6452 \approx 0.65\, J$