Question

A 0.5 kg block slides from Aon horizontal track with an initial speed of 3 ms^-1 towards a weightless horizontal spring of length 1m and force constant 2 Nm^-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 2.14 m respectively, the total distance through which the block moves before it comes to rest com­pletely is

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

Answer 1

Answer: (C)

4.24 m

Answer 2

At D.K.E. = $\frac { 1 } { 2 }$ mv² - μ_kmg(BD)

= $\frac { 1 } { 2 }$ × 0.5 × 3² – 0.2 × 0.5 × 10 × 2.14

= 2.25 – 2.14 = 0.11 J

Let the spring be pressed by distance x, then

0.11 = $\frac { 1 } { 2 }$ kx² + μ_R mgx

= $\frac { 1 } { 2 }$ × 2 × x² + 0.2 × 0.5 × 10 × x

or x² + x – 0.11 = 0

i.e., x = 0.1 m

Total distance covered

= 2 + 2.14 + 0.1 = 4.24m