A 0.5 k g block slides from A on horizontal track with an initial speed of 3 m s – 1 towards a weightless horizontal spring of length 1 m and force constant 2 N m – 1 . The part A B of the track is frictionless and the part B C has the coefficient of static and kinetic friction as 0.22 and 0.20 respectively. If the distance A B and B D are 2 m and 2.14 m respectively, the total distance through which the block moves

Step-by-step solution

At D ,   K E = 1 2   m v 2   –   μ k m g   B D =   1 2   ×   0.5   ×   3 2   –   0.2   ×   0.5   ×   10   ×   2.14 =   2.25   –   2.14 = 0.11   J 0.11 = 1 2   k x 2   +   μ R m g x ⇒ x 2 + x – 0.11 = 0 ⇒ x = 0.1   m T o t a l   d i s t a n c e   c o v e r e d = 2   +   2.14   +   0.1 &#16