Question

A $0.5kg$ block slides from $A$ on horizontal track with an initial speed of $3m{s}^{-1}$ towards a weightless horizontal spring of length 1m and force constant $2N{m}^{-1}$. The part AB of the track is frictionless and the part $BC$ has the coefficient of static and kinetic friction as $0.22$ and $0.20$ respectively. If the distance $AB$ and $BD$ are $2m$ and $2.14m$ respectively, the total distance through which the block moves before it comes to rest completely is

• A. $2.5m$
• B. $4.42m$
• C. $4.24m$
• D. $2.44m$

Answer 1

The correct option is C $4.24m$

At $D,K.E.=\frac{1}{2}m{v}^2-{\mu }_{k}mg\left(BD\right)$

$=\frac{1}{2}\times 0.5\times 3^2-0.2\times 0.5\times 10\times 2.14$

$=2.25-2.14=0.11J$
Let the spring be pressed by distance $x,$ then

$0.11=\frac{1}{2}k{x}^2+{\mu }_{R}mgx$

$-\frac{1}{2}\times 2\times x^{2}0.2\times 0.5\times 10\times x$

or $x^2+x-0.11=0$ i.e. $x=0.1m$
Total distance covered
$=2+2.14+0.1=4.24m.$