Question

In the arrangement shown block is released from rest from x = 0
(when the spring was in its natural length), on an incline having $\mu =0.5x$. The maximum elongation in the spring will be

• A. 1 m
• B. 1.5 m
• C. 2 m
• D. 2.5 m

Answer 1

The correct option is C 2 m

$W_g+W_f+W_N+W_{spring}=\Delta K$
$\left(50sin37\right)x_m-{\int }_0^{x_m}\left(0.5x.50cos37\right)dx+0-\frac{1}{2}k{x}_m^2=\frac{1}{2}m(v_f^2-v_i^2)$
(At the point of max. elongation v = 0)
$30x_m-10x_m^2-5x_m^2=030=10x_m+5x_{m}15x_m=30x_m=2m$